GeoAI: A Model-Agnostic Meta-Ensemble Zero-Shot Learning Method for Hyperspectral Image Analysis and Classiﬁcation

algorithms
Article
GeoAI: A Model-Agnostic Meta-Ensemble Zero-Shot
Learning Method for Hyperspectral Image Analysis
and Classification
Konstantinos Demertzis * and Lazaros Iliadis
Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Xanthi, Greece;
liliadis@civil.duth.gr
* Correspondence: kdemertz@fmenr.duth.gr; Tel.: +30-694-824-1881
Received: 13 February 2020; Accepted: 4 March 2020; Published: 7 March 2020
Abstract: Deep learning architectures are the most effective methods for analyzing and classifying
Ultra-Spectral Images (USI). However, effective training of a Deep Learning (DL) gradient classifier
aiming to achieve high classification accuracy, is extremely costly and time-consuming. It requires
huge datasets with hundreds or thousands of labeled specimens from expert scientists. This research
exploits the MAML++ algorithm in order to introduce the Model-Agnostic Meta-Ensemble Zero-shot
Learning (MAME-ZsL) approach. The MAME-ZsL overcomes the above difficulties, and it can be used
as a powerful model to perform Hyperspectral Image Analysis (HIA). It is a novel optimization-based
Meta-Ensemble Learning architecture, following a Zero-shot Learning (ZsL) prototype. To the best
of our knowledge it is introduced to the literature for the first time. It facilitates learning of
specialized techniques for the extraction of user-mediated representations, in complex Deep Learning
architectures. Moreover, it leverages the use of first and second-order derivatives as pre-training
methods. It enhances learning of features which do not cause issues of exploding or diminishing
gradients; thus, it avoids potential overfitting. Moreover, it significantly reduces computational cost
and training time, and it offers an improved training stability, high generalization performance and
remarkable classification accuracy.
Keywords: model-agnostic meta-learning; ensemble learning; GIS; hyperspectral images; deep
learning; remote sensing; scene classification; geospatial data; Zero-shot Learning
1. Introduction
Hyperspectral image analysis and classification is a timely special field of Geoinformatics which
has attracted much attention recently. This has led to the development of a wide variety of new
approaches, exploiting both spatial and spectral content of images, in order to optimally classify them
into discrete components related to specific standards. Typical information products obtained by the
above approaches are related to diverse areas; namely: ground cover maps for environmental Remote
Sensing; surface mineral maps used in geological applications; vegetation species maps, employed
in agricultural-geoscience studies and in urban mapping. Recent developments in optical sensor
technology and Geoinformatics (GINF), provide multispectral, Hyperspectral (HyS) and panchromatic
images at very high spatial resolution. Accurate and effective HyS image analysis and classification is
one of the key applications which can enable the development of new decision support systems. They
can provide significant opportunities for business, science and engineering in particular. Automatic
assignment of a specific semantic label to each object of a HyS image (according to its content) is one of
the most difficult problems of GINF Remote Sensing (RES).
With the available HyS resolution, subtle objects and materials can be extracted by HyS imaging
sensors with very narrow diagnostic spectral bands. This can be achieved for a variety of purposes, such
Algorithms 2020, 13, 61; doi:10.3390/a13030061 www.mdpi.com/journal/algorithms

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as detection, urban planning, agriculture, identification, surveillance and quantification. HyS image
analysis enables the characterization of objects of interest (e.g., land cover classes) with unprecedented
accuracy, and keeps inventories up to date. Improvements in spectral resolution have called for
advances in signal processing and exploitation algorithms.
A Hyperspectral image is a 3D data cube, which contains two-dimensional spatial information
(image feature) and one-dimensional spectral information (spectral bands). Especially, the spectral
bands occupy very fine wavelengths. Additionally, image features related to land cover and shape
disclose the disparity and association among adjacent pixels from different directions at a confident
wavelength. This is due to its vital applications in the design and management of soil resources,
precision farming, complex ecosystem/habitat monitoring, biodiversity conservation, disaster logging,
traffic control and urban mapping.
It is well known that increasing data dimensionality and high redundancy between features
might cause problems during data analysis. There are many significant challenges which need to
be addressed when performing HyS image classification. Primarily, supervised classification faces
a challenge related to the imbalance between high dimensionality and incomplete accessibility of
training samples, or to the presence of mixed pixels in the data. Further, it is desirable to integrate the
essential spatial and spectral information, so as to combine the complementary features which stem
from source images.
Deep Learning methodologies have significantly contributed towards the evolution and
development of HyS image analysis and classification [1]. Deep Learning (DL) is a branch of
computational intelligence which uses a series of algorithms that model high-level abstraction data
using a multi-level processing architecture.
It is difficult for all Deep Learning algorithms to achieve satisfactory classification results with
limited labeled samples, despite their undoubtedly well-established functions and their advantages.
The approaches with the highest classification accuracy and generalization ability fall under the
supervised learning umbrella. For this reason, especially in the case of Ultra-Spectral Images, huge
datasets with hundreds or thousands of specimens labeled by experts are required [2]. This process is
very expensive and time consuming.
In the case of supervised image classification, the input image is processed by a series of operations
performed at different neuronal levels. Eventually, the output generates a probability distribution for
all possible classes (usually using the Softmax function). Softmax is a function which takes an input
vector Z of k real numbers and normalizes it into a probability distribution consisting of k probabilities,
proportional to the exponentials of the input numbers [3].
σ(z)j =
ezj
K
k=1 ezk
j = 1, . . . , k where σ : Rk
→ Rk
Z = (z1, . . . . . . , zk) ∈ Rk
(1)
For example, if we try to classify an image as Lim−a, or Lim−b, or Lim−c, or Lim−d, then we generate
four probabilities for each input image, indicating the respective probabilities of the image belonging
to each of the four categories. There are two important points to be mentioned here. First, during
the training process, we require a large number of images for each class (Lim−a, Lim−b, Lim−c, Lim−d).
Secondly, if the network is only trained for the above four image classes, then we cannot expect to
test it for any other class; e.g., “Lim−x.” If we want our model to sort images as well, then we need to
get many “Lim−x” images and to rebuild and retrain the model [3]. There are cases where we do not
have enough data for each category, or the classes are huge but also dynamically changing. Thus, the
cost of data collection and periodic retraining is enormous. A reliable solution should be sought in
these cases. In contrast, k-shot learning is a framework within which the network is called upon to
learn quickly and with few examples. During training, a limited number of examples from diverse
classes with their labels are introduced. The network is required to learn general characteristics of
the problem, such as features which are either common to the samples of the same class, or unique
features which differentiate and eventually separate the classes.

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In contrast to the learning process of the traditional neural networks, it is not sufficient for the
network to learn good representations of the training classes, as the testing classes are distinct and
they are not presented in training. However, it is desirable to learn features which distinguish the
existing classes.
The evaluation process consists of two distinct stages of the following format [4]:
Step 1: Given k examples (value of k-shot), if k = 1, then the process is called one-shot; if k = 5,
five-shot, and so on. The parameter k represents the number of labeled samples given to the algorithm
by each class. By considering these samples, which comprise the support set, the network is required
to classify and eventually adapt to existing classes.
Step 2: Unknown examples of the labeled classes are presented randomly, unlike the ones
presented in the previous step, which the network is called to correctly classify. The set of examples in
this stage is known as the query set.
The above procedure (steps) is repeated many times using random classes and examples which
are sampled from the testing-evaluation set.
As it is immediately apparent from the description of the evaluation process, as the number of
classes increases, the task becomes more difficult, because the network has to decide between several
alternatives. This means that Zero-shot Learning [5] is clearly more difficult than the one-shot, which
is more difficult than the five-shot, and so on. Although humans have the ability to cope with this
process, traditional ANN require many more examples to generalize effectively, in order to achieve
the same degree of performance. The limitation of these learning approaches is that the model has
access to minimum samples from each class and the validation process is performed by calculating the
cross-entropy error of the test set. Specifically, in the cases of one-shot and Zero-shot Learning (ZsL),
only one example each of the candidate classes and only meta-data is shown at the evaluation stage.
Overall, k-shot learning is a perfect example of a problematic area, where specialized solutions are
needed to design and train systems capable to learn very quickly from a small support set, containing
only 1–5 samples per class. These systems can offer strong generalization to a corresponding target set.
A successful exploitation of the above k-shot learning cases is provided by meta-learning techniques
which can be used to deliver effective solutions [6].
In this work, we propose a new classification model, which is based on zero-shot philosophy, named
MAME-ZsL. The significant advantages of the proposed algorithm is that it reduces computational cost
and training time; it avoids potential overfitting by enhancing the learning of features which do not
cause issues of exploding or diminishing gradients; and it offers an improved training stability, high
generalization performance and remarkable classification accuracy. The superiority of the proposed
model refers to the fact that the instances in the testing set belong to classes which were not contained
in the training set. In contrast, the traditional supervised state-of-the-art Deep Learning models were
trained with labeled instances from all classes. The performance of the proposed model was evaluated
against state-of-the-art supervised Deep Learning models. The presented numerical experiments
provide convincing arguments regarding the classification efficiency of the proposed model.
2. Meta-Learning
It is a field of machine learning where advanced learning algorithms are applied to the data and
metadata of a given problem. The models “learn to learn” [7] from previous learning processes or
previous sorting tasks they have completed [8]. It is an advanced form of learning where computational
models, which usually consist of multiple levels of abstraction, can improve their learning ability. This
is achieved by learning some or all of their own building blocks, through the experience gained in
handling a large number of tasks. Their building blocks which are “learning to learn” can be optimizers,
loss functions, initializations, Learning Rates, updated functions and architectures.
In general, for real physical modeling situations, the input patterns with and without tags are
derived from the same boundary distribution or they follow a common cluster structure. Thus,
classified data can contribute to the learning process, while correspondingly useful information related

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to the exploration of the data structure of the general set can be extracted from the non-classified
data. This information can be combined with knowledge originating from prior learning processes
or from completed prior classification tasks. Based on the above theory, meta-learning techniques can
discover the structure of the data, by allowing new tasks to be learned quickly. This is achieved by
using different types of metadata, such as the properties of the learning problem, the properties of
the algorithm used (e.g., performance measures) or the patterns derived from data from a previous
problem. This process employs knowledge from unknown cases sampled from real-world distribution
of examples, aiming to enhance the outcome of the learning task. In this way it is possible to learn,
select, change or combine different learning algorithms to effectively solve a given problem.
Meta-learning is achieved by conceptually dividing learning in two levels. The inner-most levels
acquire specific knowledge for specific tasks (e.g., fine-tuning a model on a new dataset), while the
outer-most levels acquire across-task knowledge (e.g., learning to transfer tasks more efficiently).
If the inner-most levels are using learnable parameters, outer-most optimization process
can meta-learn the parameters of such components, thereby enabling automatic learning of
inner-loop components.
A meta-learning system should combine the following three requirements [9,10]:
1. The system must include a learning sub-system.
2. Experience must be derived from the use of extracted knowledge from metadata related to
the dataset under consideration, or from previous learning tasks completed in similar or
different fields.
3. Learning biases should be dynamically selected.
Employing a generic approach, a credible meta-learning model should be trained in a variety of
learning tasks and it should be optimized for the best performance in generalizing tasks, including
potentially unknown ones. Each task is associated with a dataset D, containing attribute vectors and
class labels in a supervised learning problem. The optimal parameters of the model are [11]:
θ∗
= argmin
θ ED∼P(D)[Lθ(D)] (2)
It looks similar to a normal learning process, but each data set is considered as a data sample.
The dataset D is divided in two parts, a training set S and a set of predictions B for validation
and testing.
D = S, B (3)
The dataset D includes pairs of vectors and labels so which:
D = (xi, yi) (4)
Each label belongs to a known label set L.
Let us consider a classifier fθ. The parameter θ extracts the probability x, Pθ (y x) of a data point
to belong to class y, given by the attribute vector. Optimal parameters should maximize the likelihood
of identifying true labels in multiple training batches B ⊂ D:
θ∗
= argmaxθE(x,y)∈D[Pθ(y x)] (5)
θ∗
= argmaxθEB⊂D


(x,y)∈B
Pθ(y|x)


(6)
The aim is to reduce the prediction error in data samples with unknown labels, in which there is a
small set of “fast learning” support which can be used for “fine-tuning”.

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Fast learning is a trick which creates a “fake” dataset containing a small subset of labels (to avoid
exposing all labels to the model). During the optimization process, various modifications take place,
aiming to achieve rapid learning.
A brief step-by-step description of the whole process is presented below [11]:
1. Development of a subset of labels Ls ⊂ L
2. Development of a training subset SL ⊂ D and a forecast subset BL ⊂ D. Both of them include data
points with labels belonging to the subset Ls, y ∈ Ls, ∀ (x, y) ∈ SL, BL.
3. The optimization procedure uses BL to calculate the error and to update the model parameters via
back propagation. This is done in the same way as it is used in a simple supervised learning model.
In this way each sample pair (SL, BL) can be considered to be a data point. The model is trained so
that it can generalize to new unknown datasets.
The following function (Equation (7)) is a modification of the supervised learning model.
The symbols of the meta-learning process have been added:
θ∗
= argmaxθELs⊂L


ESL⊂D,BL⊂D


(x,y)∈BL
Pθ x, y, SL




(7)
There are three meta-learning modeling approaches, as presented below [11] and the Table 1:
a. Model-based: These are techniques based on the use of circular networks with external or
internal memory. They update their parameters quickly with minimal training steps. This can be
achieved through their internal architecture or by using other control models. Memory-augmented
neural networks and meta networks are characteristic cases of model-based meta-learning techniques.
b. Metrics-based: These are techniques based on learning effective distance measurements which
can offer generalization. The core concept of their operation is similar to that of the nearest
neighbors algorithms, where they aim to learn a measurement or a distance from objects.
The concept of a good metric depends on the problem, as it should represent the relationship
between inputs to the site, facilitating problem solving. Convolutional Siamese neural networks,
matching networks, relation networks and prototypical networks are characteristic metrics-based
meta-learning techniques.
c. Optimization-based: These are techniques based on optimizing the parameters of the model
for quick learning. LSTM Meta-Learners, temporal discreteness and the reptile plus Model-Agnostic
Meta-Learning (MAML) algorithms are typical cases of optimization-based meta-Learning.
Table 1. Meta-learning approaches.
Model-Based Metric-Based Optimization-Based
Key idea RNN; memory Metric learning Gradient descent
How is Pθ(y|x) modeled? Fθ(x,S) (xi,yi)∈S kθ(x, xi)yi Pgϕ(θ,SL)(y x)
kθ is a kernel function which calculates the similarity between xi and x.
The Recurrent Neural Networks (RNNs) which use only internal memory, and also the
Long-Short-Term Memory approaches (LSTM), are not considered meta-learning techniques [11].
Meta-learning can be achieved through a variety of learning examples. In this case, the supervised
gradient-based learning can be considered as the most effective method [11]. More specifically, the
gradient-based, end-to-end differentiable meta-learning, provides a wide framework for the application of
effective meta-learning techniques.
This research proposes an optimization-based, gradient-based, end-to-end differentiable meta-learning
architecture, based on an innovative evolution of the MAML algorithm [10]. MAML is one of the most

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successful and at the same time simple optimization algorithms which belongs to the meta-learning
approach. One of its great advantages is that it is compatible with any model which learns through the
Gradient Descent (GRD) method. It is comprised of the Base-Learner (BL) and the Meta-Learner (ML)
models, with the second used to train the first. The weights of the BL are updated following the GRD
method in learning tasks of the k-shot problem, whereas the ML applies the GRD approach on the
weights of the BL, before the GRD [10].
In Figure 1 you can see a depiction of the MAML algorithm.
Algorithms 2020, 13, 61 23 of 24
Figure 1. Model-Agnostic Meta-Learning algorithm.
It should be clarified that 𝜃 denotes the weights of the meta-learner. Gradient 𝐿 comprises of
the losses for task 𝑖 in a meta-batch. The 𝜃 ∗ are the optimal weights for each task. It is essentially
an optimization procedure on a set of parameters, such that when a slope step is obtained with respect
to a particular task i, the respective parameters 𝜃ᵢ
∗
are approaching their optimal values. Therefore,
the goal of this approach is to learn an intrinsic feature which is widely applicable to all tasks of a
distribution p(T) and not to a single one. This is achieved by minimizing the total loss across tasks
sampled from the distribution 𝑝(𝑇).
In particular, we have a base-model represented by a parametric function 𝑓 with parameters
𝜃ᵢ and a task 𝑇 ∼𝑝(𝑇). After applying the Gradient Descent, a new feature vector is obtained denoted
as 𝜃 :
𝜃 = 𝜃 − 𝛼∇ 𝐿 (𝑓 ) (8)
We will consider that we execute only one GD step. The meta-learner optimizes the new
parameters using the initial ones, based on the performance of the 𝑓 model, in tasks which use
sampling from the 𝑃(𝑇). Equation (9) is the meta-objective [10]:
min 𝐿 𝑓 = min 𝐿 𝑓 − 𝛼∇ 𝐿 (𝑓 )
~ ( )~ ( )
(9)
The meta-optimization is performed again with the Stochastic Gradient Descent (SGD) and it
updates the parameters 𝜃 as follows:
𝜃 ← 𝜃 − 𝛽∇ 𝐿 𝑓
~ ( )
(10)
It should be noted that we do not actually define an additional set of variables 𝜃 whose values
are calculated by considering one (or more) Gradient Descents from 𝜃 relative to 𝑡𝑎𝑠𝑘 i. This step is
known as the Inner Loop Learning (INLL), which is the reverse process of the Outer Loop Learning (OLL),
and it optimizes Equation (10). If, for example, we apply INLL to fine-tune 𝜃 for process 𝑖, then
according to Equation (10) we are optimizing a target with the expectation which the model applies
to each task, following corresponding fine-tuning procedures.
The following Algorithm 1 is an analytical presentation of the MAML algorithm [10].
Algorithm 1. MAML.
Require: 𝑝(𝑇): distribution over tasks
Require: 𝛼, 𝛽: step size hyperparameters
1: randomly initialize 𝜃
2: while not done do
3: Sample batch of tasks 𝛵 ~𝑝(𝑇)
4: for all 𝛵 do
5: Evalluate ∇ 𝐿 (𝑓 ) with respect to K examples
Figure 1. Model-Agnostic Meta-Learning algorithm.
It should be clarified that θ denotes the weights of the meta-learner. Gradient Li comprises of
the losses for task i in a meta-batch. The θ∗
i
are the optimal weights for each task. It is essentially an
optimization procedure on a set of parameters, such that when a slope step is obtained with respect
to a particular task i, the respective parameters θ∗
i
are approaching their optimal values. Therefore,
the goal of this approach is to learn an intrinsic feature which is widely applicable to all tasks of a
distribution p(T) and not to a single one. This is achieved by minimizing the total loss across tasks
sampled from the distribution p(T).
In particular, we have a base-model represented by a parametric function fθ with parameters θi
and a task Ti∼p(T). After applying the Gradient Descent, a new feature vector is obtained denoted as
θi
:
θi = θ − α θLTi
( fθ) (8)
We will consider that we execute only one GD step. The meta-learner optimizes the new parameters
using the initial ones, based on the performance of the fθ model, in tasks which use sampling from the
P(T). Equation (9) is the meta-objective [10]:
min
θ
Ti∼p(T)
LTi
fθi
= min
θ
Ti∼p(T)
LTi
fθ − α θLTi
( fθ) (9)
The meta-optimization is performed again with the Stochastic Gradient Descent (SGD) and it
updates the parameters θ as follows:
θ ← θ − β θ
Ti∼p(T)
LTi
fθi
(10)
It should be noted that we do not actually define an additional set of variables θi
whose values
are calculated by considering one (or more) Gradient Descents from θ relative to task i. This step
is known as the Inner Loop Learning (INLL), which is the reverse process of the Outer Loop Learning
(OLL), and it optimizes Equation (10). If, for example, we apply INLL to fine-tune θ for process i, then
according to Equation (10) we are optimizing a target with the expectation which the model applies to
each task, following corresponding fine-tuning procedures.
The following Algorithm 1 is an analytical presentation of the MAML algorithm [10].

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Algorithm 1. MAML.
Require: p(T): distribution over tasks
Require: α, β: step size hyperparameters
1: randomly initialize θ
2: while not done do
3: Sample batch of tasks Ti ∼ p(T)
4: for all Ti do
5: Evalluate θLTi
( fθ) with respect to K examples
6: Compute adapted parameters with gradient descent: θi
= θ − α θLTi
( fθ)
7: end for
8: Update θ ← θ − β θ
Ti∼p(T)
LTi
fθi
9: end while
Figure 2 is a graphical illustration of the operation of the MAML algorithm.
Algorithms 2020, 13, 61 24 of 24
Figure 2 is a graphical illustration of the operation of the MAML algorithm.
Figure 2. Graphical presentation of the MAML.
It should be clarified that the intermediate parameters 𝜃ᵢ’ are considered fast weights. The INLL
considers all of the 𝑁 gradient steps for the final estimation of the fast weights, based on the fact
that the outer learning loop calculates the outer task loss 𝐿 𝑓 . However, though the inner
learning loop makes 𝑁 iterations, the MAML algorithm employs only the final weights to perform
the OLL. However, this is a fairly significant problem, as it can create instability in learning when N
is large.
The field of few-shot or Zero-shot Learning, has recently seen substantial advancements. Most
of these advancements came from casting few-shot learning as a meta-learning problem. MAML is
currently one of the best approaches for few-shot learning via meta-learning. It is a simple, general,
and effective optimization algorithm that does not place any constraints on the model architecture or
loss functions. As a result, it can be combined with arbitrary networks and different types of loss
functions, which makes it applicable to a variety of different learning processes. However, it has a
variety of issues, such as being very sensitive to neural network architectures, often leading to
instability during training. It requires arduous hyperparameter searches to stabilize training and
achieve high generalization, and it is very computationally expensive at both training and inference
times.
3. Related Work
Although the MAML algorithm and its variants do not use parameters other than those of the
base-learner, network training is quite slow and computationally expensive as it contains second-
degree derivatives. In particular, the meta-update of the MAML algorithm includes gradient nested
Figure 2. Graphical presentation of the MAML.
It should be clarified that the intermediate parameters θi
are considered fast weights. The INLL
considers all of the N gradient steps for the final estimation of the fast weights, based on the fact that
the outer learning loop calculates the outer task loss LTi
( fθi
). However, though the inner learning
loop makes N iterations, the MAML algorithm employs only the final weights to perform the OLL.
However, this is a fairly significant problem, as it can create instability in learning when N is large.
The field of few-shot or Zero-shot Learning, has recently seen substantial advancements. Most
of these advancements came from casting few-shot learning as a meta-learning problem. MAML is
currently one of the best approaches for few-shot learning via meta-learning. It is a simple, general, and
effective optimization algorithm that does not place any constraints on the model architecture or loss
functions. As a result, it can be combined with arbitrary networks and different types of loss functions,
which makes it applicable to a variety of different learning processes. However, it has a variety of issues,
such as being very sensitive to neural network architectures, often leading to instability during training.
It requires arduous hyperparameter searches to stabilize training and achieve high generalization, and
it is very computationally expensive at both training and inference times.

Algorithms 2020, 13, 61 8 of 25
3. Related Work
Although the MAML algorithm and its variants do not use parameters other than those of the
base-learner, network training is quite slow and computationally expensive as it contains second-degree
derivatives. In particular, the meta-update of the MAML algorithm includes gradient nested in gradient,
or second-degree derivatives, which significantly increases the computational cost. In order to solve
the above problem, several approximation techniques have been proposed to accelerate the algorithm.
Finn et al. [12] developed the MAML by ignoring the second derivatives, calculating the slope in
the meta-update, which they called FOMAML (First Order MAML).
More specifically, MAML optimizes the:
min
θ
ET∼p(T) LT Uk
T(θ) , (11)
where Uk
T
is the process by which k samples are taken from task T and θ is updated. This procedure
employs the support set and the query set, so the optimization can be rewritten as follows:
min
θ
ET∼p(T) LT,Q(UT,S(θ)) (12)
Finally, MAML uses the slope method to calculate the following:
gMAML = LT,Q(UT,S(θ)) = UT,S(θ)L T,Q θ , (13)
where θ = UT,S(θ) and UT,S
is the Jacobian renewal matrix of UT,S where the FOMAML considers
UT,S
as unitary, so it calculates the following:
gFOMAML = L T,Q θ (14)
The resulting method still calculates the meta-gradient for the parameter values after updating θ ,
which is an effective post-learning method from a theoretical point of view. However, experiments have
shown that the yield of this method is almost the same as the one obtained by a second derivative. Most
of the improvement in MAML comes from the gradients of the objective at the post-update parameter
values, rather than the second-order updates from differentiating through the gradient update.
A different implementation employing first degree derivatives was studied and analyzed by
Nichol et al. [13]. They introduced the reptile algorithm, which is a variation of the MAML, using only
the first derivative. The basic difference from FOMAML is that the last step treats θ−θ as a slope and
feeds it into an adaptive algorithm such as ADAM. Algorithm 2 presents reptile.
Algorithm 2. Reptile algorithm.
Initialize θ, the vector of initial parameters
1: for iteration = 1, 2, . . . , do
2: Sample task T, corresponding to Loss LT on weighs vector θ
3: Compute θ = Uk
T
(θ), denoting k steps of gradient descent or Adam algorithm
4: Update θ ← θ + ε θ − θ
5: end for
MAML also suffers from training instability, which can currently only be alleviated by arduous
architecture and hyperparameter searches.
Antoniou et al. proposed an improved variant of the algorithm, called MAML++, which
effectively addresses MAML problems, by providing a much improved training stability and removing
the dependency of training stability on the model’s architecture. Specifically, Antoniou et al. [14] found
that simply replacing max-pooling layers with stridden convolutional layers makes network training

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unstable. It is clearly shown in Figure 3 that in two of the three cases, the original MAML appears to be
unstable and irregular, while all 3 MAML++ models appear to converge consistently very quickly,
with much higher generalization accuracy without any stability problems.
MAML also suffers from training instability, which can currently only be alleviated by arduous
architecture and hyperparameter searches.
Antoniou et al. proposed an improved variant of the algorithm, called MAML++, which
effectively addresses MAML problems, by providing a much improved training stability and
removing the dependency of training stability on the model’s architecture. Specifically, Antoniou et
al. [14] found that simply replacing max-pooling layers with stridden convolutional layers makes
network training unstable. It is clearly shown in Figure 3 that in two of the three cases, the original
MAML appears to be unstable and irregular, while all 3 MAML++ models appear to converge
consistently very quickly, with much higher generalization accuracy without any stability problems.
Figure 3. Stabilizing MAML.Figure 3. Stabilizing MAML.
It was estimated that the instability was caused by a gradient degradation (gradient explosion or
vanishing gradient) which was due to the depth of the network. Let us consider a typical four-layer
Convolutional Neural Network (CNN) followed by a single linear layer. If we repeat the Inner Loop
Learning N times, then the inference graph comprises 5N layers in total, without any skip connections.
Since the original MAML only uses the final weights for the Outer Loop Learning, the
backpropagation algorithm has to go through all layers, which causes gradient degradation. To solve
the above problem, the Multi-Step Loss (MSL) optimization approach was adopted. It eliminates the
problem by calculating the external loss after each internal step, based on the outer loop update, as in
Equation (15) below:
θ = θ − β θ
B
i=1
N
j=1
wjLTi
fθi
j
, (15)
where β is a Learning Rate; LTi
( fθi
j
) denotes the outer loss of task i when using the base-network
weights after the j-inner-step update; and wj denotes the importance weight of the outer loss at step j.
The following, Figure 4, is a graphical display of the MAML++ algorithm, where the outer loss is
calculated after each internal step and the weighted average is obtained at the end of the process.
In practice, all losses are initialized with equal contributions to the overall loss, but as repetitions
increase, contributions from previous steps are reduced, while the ones of subsequent steps keep
increasing gradually. This is to ensure that as training progresses, the final step loss receives more
attention from the optimizer, thereby ensuring that the lowest possible loss is achieved. If the annealing
is not used, the final loss might be higher compared to the one obtained by the original formulation.
Additionally, due to the fact that the original MAML overcomes the second-order derivative cost by
completely ignoring it, the final general performance of the network is reduced. The MAML++ solves
this problem, by using the derivative order annealing method. Specifically, it employs the first order
grade for the first 50 epochs of training and then it moves to the second order grade for the rest of the
training process. An interesting observation is that this derivative-order annealing does not create
incidents of exploding or diminishing gradients, and so the training is much more stable.
Another drawback of MAML is the fact that it does non-use batch normalization statistic accumulation.
Instead, only the statistics of the current batch are used. As a result, smoothing is less effective, as the
trained parameters must include a variety of different means and standard deviations from different
tasks. A naive application would accumulate current batch statistics at all stages of the Inner Loop
Learning update, which could cause optimization problems, and it could slow or stop optimization
altogether. The problem stems from the erroneous assumption that the original model and all its

Algorithms 2020, 13, 61 10 of 25
updated iterations have similar attribute distributions. Thus, the current statistics could be shared
across all updates to the internal loop of the network. Obviously, this assumption is not correct. A
better alternative solution, which is employed by MAML++, is the storage of per-step batch normalization
statistics and the reading of per-step batch normalization weights and biases for each repetition of the inner
loop. One issue that affects the speed of generalization and convergence is the use of a shared Learning
Rate for all parameters and all steps of learning process update.
Since the original MAML only uses the final weights for the Outer Loop Learning, the
backpropagation algorithm has to go through all layers, which causes gradient degradation. To solve
the above problem, the Multi-Step Loss (MSL) optimization approach was adopted. It eliminates the
problem by calculating the external loss after each internal step, based on the outer loop update, as
in Equation (15) below:
𝜃 = 𝜃 − 𝛽∇ ∑ ∑ 𝑤 𝐿 𝑓 , (15)
where β is a Learning Rate; 𝐿 𝑓 denotes the outer loss of task i when using the base-network
weights after the j-inner-step update; and 𝑤 denotes the importance weight of the outer loss at step
j.
The following, Figure 4, is a graphical display of the MAML++ algorithm, where the outer loss
is calculated after each internal step and the weighted average is obtained at the end of the process.
Figure 4. MAML++ visualization.
In practice, all losses are initialized with equal contributions to the overall loss, but as repetitions
increase, contributions from previous steps are reduced, while the ones of subsequent steps keep
increasing gradually. This is to ensure that as training progresses, the final step loss receives more
attention from the optimizer, thereby ensuring that the lowest possible loss is achieved. If the
annealing is not used, the final loss might be higher compared to the one obtained by the original
formulation. Additionally, due to the fact that the original MAML overcomes the second-order
derivative cost by completely ignoring it, the final general performance of the network is reduced.
The MAML++ solves this problem, by using the derivative order annealing method. Specifically, it
employs the first order grade for the first 50 epochs of training and then it moves to the second order
grade for the rest of the training process. An interesting observation is that this derivative-order
Figure 4. MAML++ visualization.
The consistent Learning Rate requires multiple hyperparameter searches, in order to find the right
rate for a particular set of data. This is computationally expensive and time consuming, depending on
how the search is shared. Use the shared Learning Rate for all parameters and all the steps of updating
the learning process. In addition, while gradient is an effective data fitting tactic, a constant Learning
Rate can easily lead to overfitting under the few-shot regime. An approach to avoid potential overfitting
is the identification of all learning factors in a way that maximizes the power of generalization rather
than the over-fitting of the data.
Li et al. [15] proposed a Learning Rate for each parameter in the core network where the internal
loop was updated, as in the following equation (Equation (16)):
θ = θ − α ◦ θLTi
( fθ), (16)
where α is a vector of learnable parameters with the same size as LTi
( fθ) and denotes the element-wise
product operation. We do not put the constraint of positivity on the Learning Rate (LER) denoted as
“α.” Therefore, we should not expect the inner-update direction to follow the gradient direction.
A clearly improved approach to the above process is suggested by MAML++ which employs
per-layer per-step Learning Rates. For example, if it is assumed that the core network comprises L layers
and the Inner Loop Learning consists of N stages of updating, then there are LN additional learnable
parameters for the Inner Loop Learning Rate.
MAML uses the ADAM algorithm with a constant LER to optimize the meta-objective. This means
which more time is required to properly adjust the Learning Rate, which is a critical parameter of the

Algorithms 2020, 13, 61 11 of 25
generalization performance. On the other hand, MAML++ employs the cosine annealing scheduling
on the meta-optimizer, which is defined based on the following Equation (17) [16].
β = βmin +
1
2
(βmax − βmin)(1 + cos (
T
Tmax
π)), (17)
where βmin denotes the minimum Learning Rate, βmax denotes the initial Learning Rate, T is the number
of current iterations and Tmax is the maximum number of iterations. When T = 0, the LER β = βmax.
On the other hand, if T = Tmax, then β = βmin. In practice, we might want T to be Tmax.
In summary, this particular MAML++ standardization enables its use in complex Deep Learning
architectures, making it easier to learn more complex functions, such as loss functions, optimizers or
even gradient computation functions. Moreover, the use of first-class derivatives offers a powerful
pre-training method aiming to detect the parameters which are less likely to cause exploding or
diminishing gradients. Finally, the learning per-layer per-step LER technique avoids potential overfitting,
while it significantly reduces the computational cost and time required to build a consistent Learning
Rate throughout the process.
4. Design Principles and Novelties of the Introduced MAME-ZsL Algorithm
As it has already been mentioned, the proposed MAME-ZsL algorithm employs MAML++ for
the development of a robust Hyperspectral Image Analysis and Classification (HIAC) model, based on
ZsL. The basic novelty introduced by the improved MAME-ZsL model, is related to a neural network
with Convolutional (CON) filters, comprising very small receptive fields of size 3 × 3.
The Convolutional stride and the spatial padding were set to 1 pixel. Max-pooling was performed
over 3 × 3 pixels windows with stride equal to three. All of the CON layers were developed using the
Rectified Linear Unit (ReLU) nonlinear Activation Function (ACF), except for the last layer where the
Softmax ACF [3] was applied, as it performs better on multi-classification problems like the one under
consideration (18).
σj(z) =
ezj
K
k=1 ezk
, j = 1, . . . , K (18)
The Sigmoid approach offers better results in binary classification tasks. It is a fact that in the
Softmax, the sum of probabilities is equal to 1, which is not the case for the Sigmoid. Moreover, in
Softmax the highest value has a higher probability than the others, while in the Sigmoid the highest
value is expected to have a high probability but not the highest one.
The fully Convolutional Neural Network (CNN) was trained based on the novel AdaBound
algorithm [17] which employs dynamic bounds on the Learning Rate and it achieves a smooth transition
to stochastic gradient descent. Algorithm 3 makes a detailed presentation of the AdaBound [17]:
Algorithm 3. The AdaBound algorithm.
Input: x1 ∈ F, initial step size α, β1t
T
t=1, β2 lower bound function ηl, upper bound function ηu
1: Set m0 = 0, u0 = 0
2: for t = 1 to T do
3: gt = ft(xt)
4: mt = β1tmt−1 + (1 − β1t)gt
5: ut = β2ut−1 + (1 − β2)g2
t and Vt = diag(ut)
6: ˆηt = Clip a√
Vt
, ηl(t), ηu(t) and ηt =
ˆηt
√
t
7: xt+1 =
f,diag(η−1
t )
(xt − ηt·mt)
8: end for

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Compared to other methods, AdaBound has two major advantages. It is uncertain whether there
exists a fixed turning point to distinguish the simple ADAM algorithm and the SGD. The advantage of
the AdaBound is the fact that it addresses this problem with a continuous transforming procedure,
rather than with a “hard” switch. The AdaBound introduces an extra hyperparameter to perform
the switching time, which is not very easy to fine-tune. Moreover, it has a higher convergence speed
than the stochastic gradient descent ones. Finally, it overcomes the poor generalization ability of the
adaptive models, as it uses dynamic limits on the LER, aiming towards higher classification accuracy.
The selection of the appropriate hyperparameters to be employed in the proposed method, was
based on the restrictions’ settings and configurations, which should be based on the consideration
of the different decision boundaries of the classification problem. For example, the obvious choice
of classifiers with the smallest error in training data is considered as improper for generating a
classification model. The performance based on a training dataset, even when cross-validation is
used, may be misleading when first seen data vectors are used. In order for the proposed process
to be effective, individual hyperparameters were chosen. They not only display a certain level of
diversity, but they also use different operating functions, thus allowing different decision boundaries
to be created and combined in such a way that can reduce the overall error.
In general, the selection of features was based on a heuristic method which considers the way the
proposed method faces each situation. For instance:
• Are any parametric approaches employed?
• What is the effect of the outliers? (The use of a subgroup of training sets with bagging can provide
significant help towards the reduction of the effect of outliers or extreme values)
• How is the noise handled? For instance: if it is repeatedly non-linear, it can detect linear or
non-linear dispersed data; it tends to perform very well with a lot of data vectors. The final
decision is made based on the performance encountered by the statistical trial and error method.
5. Application of the MAME-ZsL in Hyperspectral Image Analysis
Advances in artificial intelligence, combined with the extended availability of high quality data
and advances in both hardware and software, have led to serious developments in the efficient
processing of data related to the GeoAI field (Artificial Intelligence and Geography/Geographic Information
Systems). Hyperspectral Image Analysis for efficient and accurate object detection using Deep Learning
is one of the timely topics of GeoAI. The most recent research examples include detection of soil
characteristics [18], detailed ways of capturing densely populated areas [19], extracting information
from scanned historical maps [20], semantic point sorting [21], innovative spatial interpolation
methods [22] and traffic forecasting [23].
Similarly, modern applications of artificial vision and imaging (IMG) systems significantly extend
the distinctive ability of optical systems, both in terms of spectral sensitivity and resolution. Thus,
it is possible to identify and differentiate spectral and spatial regions, which although having the
same color appearance, are characterized by different physico-chemical and/or structural properties.
This differentiation is based on the emerging spatial diversification, which is detected by observing in
narrow spectral bands, within or outside the visible spectrum.
Recent technological developments have made it possible to combine IMG (spatial variation in
RGB resolution) and spectroscopy (spectral analysis in spatially emitted radiation) in a new field called
“Spectral Imaging” (SIM). In the SIM process, the intensity of light is recorded simultaneously as a
function of both wavelength and position. The dataset corresponding to the observed surface contains
a complete image, different for each wavelength. In the field of spectroscopy, a fully resolved spectrum
can be recorded for each pixel of the spatial resolution of the observation field. The multitude of
spectral regions, which the IMG system can manage, determines the difference between multispectral
(tens of regions) and Hyperspectral (hundreds of regions) Imaging. The key element of a typical
spectral IMG system is the monochromatic image sensor (monochrome camera), which can be used to
select the desired observation wavelength.

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It can be easily perceived that the success of a sophisticated Hyperspectral Analysis System (HAS)
is a major challenge for DL technologies, which are using a series of algorithms attempting to model
data characterized by high-level of abstraction. HAS use a multi-level processing architecture, which is
based on sequential linear and non-linear transformations. Despite their undoubtedly well-established
and effective approaches and their advantages, these architectures depend on the performance of
training with huge datasets which include multiple representations of images of the same class.
Considering the multitude of classes which may be included in a Hyperspectral image, we realize that
this process is so incredibly time consuming and costly, that it can sometimes be impossible to run [1].
The ZsL method was adopted based on a heuristic [24], hierarchical parameter search
methodology [25]. It is part of a family of learning techniques which exploit data representations to
interpret and derive the optimal result. This methodology uses distributed representation, the basic
premise of which is that the observed data result from the interactions of factors which are organized in
layers. A fundamental principle is that these layers correspond to levels of abstraction or composition
based on their quantity and size.
Fine-Grained Recognition (FIG_RC) is the task of distinguishing between visually very similar
objects, such as identifying the species of a bird, the breed of a dog or the model of an aircraft. On
the other hand, FIG_RC [26] which aims to identify the type of an object among a large number of
subcategories, is an emerging application with the increasing resolution which exposes new details in
image data. Traditional fully supervised algorithms fail to handle this problem where there is low
between-class variance and high within-class variance for the classes of interest with small sample
sizes. The experiments show that the proposed fine-grained object recognition model achieves only
14.3% recognition accuracy for the classes with no training examples. This is slightly better than a
random guess accuracy of 6.3%. Another method [27] automatically creates a training dataset from
a single degraded image and trains a denoising network without any clear images. However, the
performance of the proposed method shows the same performance as the optimization-based method
at high noise levels.
Hu et al., 2015, proposed a time-consuming and resource depended model [28] which learns to
perform zero-shot classification, using a meta-learner which is trained to produce corrections to the
output of a previously trained learner. The model consists of a Task Module (TM) which supplies an
initial prediction, and a Correction Module (CM) updating the initial prediction. The TM is the learner
and the CM is the meta-learner. The correction module is trained in an episodic approach, whereby
many different task modules are trained on various subsets of the total training data, with the rest
being used as unseen data for the CM. The correction module takes as input a representation of the
TM’s training data to perform the predicted correction. The correction module is trained to update the
task module’s prediction to be closer to the target value.
In addition [29] proposes the use of the visual space as the embedding one. In this space, the
subsequent nearest neighbor search suffers much less from the harness problem and it becomes more
effective. This model design also provides a natural mechanism for multiple semantic modalities (e.g.,
attributes and sentence descriptions) to be fused and optimized jointly in an end-to-end manner. Only
the statistics of the current environment are used and the trained process must include a variety of
different statistics from different tasks and environments.
Additionally, [30] propose a very promising approach with high-grade accuracy, but the model
is characterized by high bias. In the case of image classification, various spatial information can be
extracted and used, such as edges, shapes and associated color areas. As they are organized into
multiple levels, they are hierarchically separated into levels of abstraction, creating the conditions for
selecting the most appropriate features for the training process. Utilizing the above processes, ZsL
inspires and simulates the functions of human visual perception, where multiple functional levels and
intermediate representations are developed, from capturing an image to the retina to responding in
stimuli. This function is based on the conversion of the input representation to a higher level one,
as it is performed by each intermediate unit. High-level features are more general and unchanged,

Algorithms 2020, 13, 61 14 of 25
while low-level ones help to categorize inputs. Their effectiveness is interpreted on the basis of
the “universal approximation theorem,” which deals with the ability of a neural structure to approach
continuous functions and the probabilistic inference which considers the activation of nonlinearity as a
function of cumulative distribution. This is related to the concepts of optimization and generalization
respectively [25].
Given that in deep neural networks, each hidden level trains a distinct set of features, coming
from the output of the previous level, further operation of this network enables the analysis of the
most complex features, as they are reconstructed and decomposed from layer to layer. This hierarchy,
as well as the degradation of information, while increasing the complexity of the system, also enables
the handling of high-dimensional data, which pass through non-linear functions. It is thus possible to
discover unstructured data and to reveal a latent structure in unmarked data. This is done in order to
handle more general problematic structures, even discerning the minimal similarities or anomalies
they entail.
Specifically, since the aim was the design of a system with zero samples from the target class, the
proposed methodology used the intermediate representations extracted from the rest of the image
samples. This was done in order to find the appropriate representations to be used in order to classify
the unknown image samples.
To increase the efficiency of the method, bootstrap sampling was used, in order to train different
subsets of the data set in the most appropriate way. Bootstrap sampling is the process of using
increasingly larger random samples until the accuracy of the neural network is improved. Each sample
is used to compile a separate model and the results of each model are aggregated with “voting”;
that is, for each input vector, each classifier predicts the output variable, and finally, the value with
the most “votes” is selected as the response variable for which particular vector. This methodology,
which belongs to the ensemble methods, is called bagging and has many advantages, such as reducing
co-variance and avoiding overfitting, as you can see in the below Figure 5 [31].
Algorithms 2020, 13, 61 31 of 24
“voting”; that is, for each input vector, each classifier predicts the output variable, and finally, the
value with the most “votes” is selected as the response variable for which particular vector. This
methodology, which belongs to the ensemble methods, is called bagging and has many advantages,
such as reducing co-variance and avoiding overfitting, as you can see in the below Figure 5 [31].
Figure 5. Bagging (bootstrap sampling) (https://www.kdnuggets.com/).
The ensemble approach was selected to be employed in this research, due to the particularly
high complexity of the examined ZsL, and due to the fact that the prediction results were highly
volatile. This can be attributed to the sensitivity of the correlational models to the data, and to the
complex relationship which describes them. The ensemble function of the proposed system offers a
more stable model with better prediction results. This is due to the fact that the overall behavior of a
multiple model is less noisy than a corresponding single one. This reduces the overall risk of a
particularly bad choice.
It is important to note that in Deep Learning, the training process is based on analyzing large
amounts of data. The research and development of neural networks is flourishing thanks to recent
advancements in computational power, the discovery of new algorithms and the increase in labeled
Figure 5. Bagging (bootstrap sampling) (https://www.kdnuggets.com/).
The ensemble approach was selected to be employed in this research, due to the particularly high
complexity of the examined ZsL, and due to the fact that the prediction results were highly volatile.
This can be attributed to the sensitivity of the correlational models to the data, and to the complex
relationship which describes them. The ensemble function of the proposed system offers a more stable
model with better prediction results. This is due to the fact that the overall behavior of a multiple

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model is less noisy than a corresponding single one. This reduces the overall risk of a particularly
bad choice.
It is important to note that in Deep Learning, the training process is based on analyzing large
amounts of data. The research and development of neural networks is flourishing thanks to recent
advancements in computational power, the discovery of new algorithms and the increase in labeled data.
Neural networks typically take longer to run, as an increase in the number of features or columns
in the dataset also increases the number of hidden layers. Specifically, we should say that a single
affine layer of a neural network without any non-linearities/activations is practically the same as a
linear model. Here we are referring to deep neural networks that have multiple layers and activation
functions (non-linearities as Relu, Elu, tanh, Sigmoid) Additionally, all of the nonlinearities and
multiple layers introduce a nonconvex and usually rather complex error space, which means that we
have many local minimums that the training of the deep neural network can converge to. This means
that a lot of hyperparameters have to be tuned in order to get to a place in the error space where the
error is small enough so that the model will be useful. A lot of hyper parameters which could start
from 10 and reach up to 40 or 50 are dealt with via Bayesian optimization, using Gaussian processes
to optimize them, which still does not guarantee good performance. Their training is very slow, and
adding the tuning of the hyperparameters into that makes it even slower, whereas the linear model
would be much faster to be trained. This introduces a serious cost–benefit tradeoff. A trained linear
model has weights which are interpretable and gives useful information to the data scientist as to how
various features should have roles for the task at hand.
Modern frameworks like TensorFlow or Theano perform execution of neural networks on GPU.
They take advantage of parallel programming capabilities for large array multiplications, which are
typical of backpropagation algorithms.
The proposed Deep Learning model is a quite resource-demanding technology. It requires
powerful, high-performance graphics processing units and large amounts of storage to train the models.
Furthermore, this technology needs more time to train in comparison with traditional machine learning.
Another important disadvantage of any Deep Learning model is that it is incapable of providing
arguments about why it has reached a certain conclusion. Unlike in the case of traditional machine
learning, you cannot follow an algorithm to find out why your system has decided which it is a tree on
a picture, not a tile. To correct errors in Deep Learning, you have to revise the whole algorithm.
6. Description of the Datasets
The datasets used in this research include images taken from a Reflective Optics System Imaging
Spectrometer (ROSIS). More specifically, the Pavia University and Pavia Center datasets were
considered [32]. Both datasets came from the ROSIS sensor during a flight campaign over Pavia
in southern Italy. The number of spectral bands is 102 for the Pavia Center and it is 103 for Pavia
University. The selected Pavia Center and Pavia University images have an analysis of 1096 × 1096
pixels and 610 × 610 pixels respectively. Ultrasound imaging consists of 115 spectral channels ranging
from 430 to 860 nm, of which only 102 were used in this research, as 13 were removed due to noise.
Rejected specimens which in both cases contain no information (including black bars) can be seen in
the following figure (Figure 6) below.

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University. The selected Pavia Center and Pavia University images have an analysis of 1096 × 1096
pixels and 610 × 610 pixels respectively. Ultrasound imaging consists of 115 spectral channels ranging
from 430 to 860 nm, of which only 102 were used in this research, as 13 were removed due to noise.
Rejected specimens which in both cases contain no information (including black bars) can be seen in
the following figure (Figure 6) below.
(a) Sample band of Pavia Centre dataset (b) Ground truth of Pavia Centre dataset
(c) Sample band of Pavia University dataset (d) Ground truth of Pavia University dataset
Figure 6. Noisy bands in Pavia Centre and University datasets.
The available samples were scaled down, so that every image has an analysis of 610 × 610 pixels
and geometric analysis of 1.3 m. In both datasets the basic points of the image belong to nine
categories which are mainly related to land cover objects. The Pavia University dataset includes nine
Figure 6. Noisy bands in Pavia Centre and University datasets.
The available samples were scaled down, so that every image has an analysis of 610 × 610 pixels
and geometric analysis of 1.3 m. In both datasets the basic points of the image belong to nine categories
which are mainly related to land cover objects. The Pavia University dataset includes nine classes, and
in total, 46,697 cases. The Pavia Center dataset comprises nine classes with 7456 cases, whereas the
ﬁrst seven classes are common in both datasets (Asphalt, Meadows, Trees, Bare Soil, Self-Blocking Bricks,
Bitumen, Shadows) [33].
The Pavia University dataset was divided into training, validation and testing sets, as is presented
in the following table (Table 2) [32].
Table 2. Pavia University dataset.
Class No Class Name All Instances
Sets
Training Validation Test
1 Asphalt 7179
√
- -
2 Meadows 19,189
√
- -
3 Trees 3588
√
- -
4 Bare Soil 5561
√
- -
5 Self-Blocking Bricks 4196
√
- -
6 Bitumen 1705
√
- -
7 Shadows 1178
√
- -
8 Metal Sheets 1610 -
√
-
9 Gravel 2491 - -
√
Total 46,697 42,596 1610 2491
The Pavia Center dataset was divided into training, validation and testing sets, as is presented
analytically in the following table (Table 3) [32].

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Table 3. Pavia Center dataset.
Sets
1 Asphalt 816
√
- -
2 Meadows 824
√
- -
3 Trees 820
√
- -
4 Bare Soil 820
√
- -
√
- -
6 Bitumen 808
√
- -
7 Shadows 476
√
- -
8 Water 824 -
√
-
9 Tiles 1260 - -
√
Total 7456 5372 824 1260
Metrics Used for the Assessment of the Modeling Effort
The following metrics were used for the assessment of the modeling effort [33,34]:
(a) Overall Accuracy (OA): This index represents the number of samples correctly classified,
divided by the number of testing samples.
(b) Kappa Statistic: This is a statistical measure which provides information on the level of
agreement between the truth map and the final classification map. It is the percentage of agreement
corrected by the level of agreement, which could be expected to occur by chance. In general, it is
considered to be a more robust index than a simple percent agreement calculation, since k takes into
account the agreement occurring by chance. It is a popular measure for benchmarking classification
accuracy under class imbalance. It is used in static classification scenarios and for streaming data
classification. Cohen’s kappa measures the agreement between two raters, where each classifies N
items into C mutually exclusive categories. The definition of κ is [35,36]:
κ =
p0 − pe
1 − pe
= 1 −
1 − p0
1 − pe
, (19)
where po is the relative observed agreement among raters (identical to accuracy), and pe is the
hypothetical probability of chance agreement. The observed data are used to calculate the probabilities
of each observer, to randomly see each category. If the raters are in complete agreement, then κ = 1.
If there is no agreement among the raters other than what would be expected by chance (as given by
pe), then κ ≈ 0.
The Kappa Reliability (KR) can be considered as the outcome from the data editing, allowing
the conservancy of more relevant data for the upcoming forecast. A detailed analysis of the KR is
presented in the following Table 4.
Table 4. Kappa Reliability.
Kappa Reliability
0.00 no reliability
0.1–0.2 minimum
0.21–0.40 little
0.41–0.60 moderate
0.61–0.80 important
≥0.81 maximum

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(c) McNemar test: The McNemar statistical test was employed to evaluate the importance of
classification accuracy derived from different approaches [31]:
z12 =
f12 − f21
f12 + f21
, (20)
where fij is the number of correctly classified samples in classification i, and incorrect one are in
classification j. McNemar’s test is based on the standardized normal test statistic, and therefore the
null hypothesis, which is “no significant difference,” rejected at the widely used p = 0.05 (|z| > 1.96)
level of significance.
7. Results and Comparisons
The training of the models was performed using a Learning Rate of 0.001. Loss function is the
cross-entropy error between the predicted and true class. The cross-entropy error was used as the
Loss function between the predicted and the true class. For the other parameters of the model, the
recommended default settings were set as in [37].
A comparison with the following most widely used supervised Deep Learning models was
performed to validate the effectiveness of the proposed architecture.
(a) 1-D CNN: The architecture of the 1-D CNN was designed as in [38], and it comprises the input
layer, the Convolutional Layer (COL), the max-pooling layer, the fully connected layer and the
output one. The number of the Convolutional Filters (COFs) was equal to 20, the length of each
filer was 11 and the pooling size had the value of 3. Finally, 100 hidden units were contained in
the fully connected layer.
(b) 2-D CNN: The 2-D CNN architecture was designed as in [39]. It includes three COLs which were
supplied with 4×4, 5×5 and 4×4 CON filters respectively. The COL except of the final one were
followed by max-pooling layers. Moreover, the numbers of COFs for the COLs were to 32, 64 and
128, respectively.
(c) Simple Convolutional/deconvolutional network with the simple Convolutional blocks and the
unpooling function, as it is described in [40,41].
(d) Residual Convolutional/deconvolutional network: Its architecture used residual blocks and a
more accurate unpooling function, as it is shown in [42].
The following Tables 5 and 6 show the classification maps which have emerged for the cases of
the Pavia University and Pavia Center datasets. Moreover, they present a comparative analysis of the
accuracy of the proposed MAME-ZsL algorithm, with the performance of the following classifiers;
namely: 1-D CNN, 2-D CNN, Simple Convolutional/Deconvolutional Network (SC/DN), Residual
Convolutional/Deconvolutional Network (RC/DN).
A single dataset including all records of the Pavia University and Pavia Center datasets was
developed, which was employed in an effort to fully investigate the predictive capacity of the proposed
system. It was named General Pavia Dataset (GPD), and it was divided into training (Classes 1–7),
validation (Classes 8 and 9) and testing subsets (Classes 10 and 11). It is presented in the following
Table 7.

Algorithms 2020, 13, 61 19 of 25
Table 5. Testing classiﬁcation accuracy and performance metrics.
Pavia University Dataset
Class Name 1-D CNN 2-D CNN SC/DN RC/DN MAME-ZsL
Metal Sheets
OA κ McN OA κ McN OA κ McN OA κ McN OA κ McN
99.41% 0.8985
33.801
100% 1
32.752
97.55% 0.8356
30.894
97.77% 0.8023
29.773
78.56% 0.7292
30.856
Gravel
OA κ OA κ OA κ OA κ OA κ
67.03% 0.7693 63.13% 0.7576 60.31% 0.7411 61.46% 0.7857 54.17% 0.7084
Pavia Center Dataset
Water
77.83% 0.8014
32.587
79.97% 0.8208
32.194
80.06% 0.8114
31.643
82.77% 0.8823
30.588
62.08% 0.7539
31.002
Tiles
81.15% 0.8296 76.72% 0.7994 80.67% 0.7978 78.34% 0.8095 65.37% 0.7111
Table 7. The general Pavia dataset.
Sets
1 Asphalt 7995
√
- -
2 Meadows 20,013
√
- -
3 Trees 4408
√
- -
4 Bare Soil 6381
√
- -
√
- -
6 Bitumen 2513
√
- -
7 Shadows 1654
√
- -
8 Metal Sheets 1610 -
√
-
9 Water 824
√
-
10 Gravel 2491 - -
√
11 Tiles 1260 -
√
Total 47,968 42,596 2434 3751

Algorithms 2020, 13, 61 20 of 25
As it can be seen from Table 8, the increase of samples has improved the results in the case of the
trained algorithms and in the case of the ZsL technique. It is easy to conclude which the proposed
MAME-ZsL is a highly valued Deep Learning system which has achieved remarkable results in all
evaluations over their respective competing approaches.
The experimental comparison does not include other examples of Zero-shot Learning. This
fact does not detract in any case from the value of the proposed method, taking into account that
the proposed processing approach builds a predictive model which is comparable to supervised
learning systems. The appropriate hyperparameters in the proposed method are also identified
by the high reliability and overall accuracy on the obtained results. The final decision was taken
based on the performance encountered by the statistical trial and error method. The performance of
the proposed model was evaluated against state-of-the-art fully supervised Deep Learning models.
It is worth mentioning that the proposed model was trained with instances only from seven classes
while the Deep Learning models were trained with instances from all eleven classes. The presented
numerical experiments demonstrate that the proposed model produces remarkable results compared to
theoretically superior models, providing convincing arguments regarding the classification efficiency
of the proposed approach. Another important observation is that it produces accurate results without
recurring problems of undetermined cause, because all of the features in the considered dataset are
efficiently evaluated. The values of the obtained kappa index are a proof of high reliability (the
reliability can be considered as high when κ ≥ 0.70) [35,36].
The superiority of the introduced, novel model focuses on its robustness, accuracy and
generalization ability. The overall behavior of the model is comparable to a corresponding supervised
one. Specifically, it reduces the possibility of overfitting, it decreases variance or bias and it can fit
unseen patterns without reducing its precision. This is a remarkable innovation which significantly
improves the overall reliability of the modeling effort. This is the result of the data processing
methodology which allows the retention of the more relevant data for upcoming forecasts.
The following Table 8 presents the results obtained by the analysis of the GPD.
The above, Table 8, also provides information on the results of the McNemar test, to assess the
importance of the difference between the classification accuracy of the proposed network and the
other approaches examined. The improvement of the overall accuracy values obtained by the novel
algorithm (compared to the other existing methods) is statistically significant.
Finally, the use of the ensemble approach in this work is related to the fact that very often in
multi-factor problems of high complexity such as the one under consideration, the prediction results
show multiple variability [43]. This can be attributed to the sensitivity of the correlation models to
the data. The main imperative advantage of the proposed ensemble model is the improvement of
the overall predictions and the generalization ability (adaptation in new previously unseen data).
The ensemble method definitely decreases the overall risk of a particularly poorer choice.
The employed bagging technique offers better prediction and stability, as the overall behavior of
the model becomes less noisy and the overall risk of a particularly bad choice that may be caused from
under-sampling is significantly reduced. The above assumption is also supported by the dispersion
of the expected error, which is close to the mean error value, something which strongly indicates the
reliability of the system and the generalization capability that it presents.
As it can be seen in Tables 5–8, the ensemble method appears to have the same or a slightly lower
performance across all datasets, compared to the winning (most accurate) algorithm. The highly overall
accuracy shows the rate of positive predictions, whereas k reliability index specifies the rate of positive
events which were correctly predicted. In all cases, the proposed model has high average accuracy and
very high reliability, which means that the ensemble method is a robust and stable approach which
returns substantial results. Tables 7 and 8 show clearly that the ensemble model is very promising.

Algorithms 2020, 13, 61 21 of 25
General Pavia Dataset (OA Is the Overall Accuracy)
Metal Sheets
99.44% 0.8992
30.172
100% 1
33.847
99.09% 0.8734
31.118
97.95% 0.8137
30.633
81.16% 0.8065
31.647
Water
81.15% 0.8296 80.06% 0.8137 81.82% 0.8123 84.51% 0.8119 65.98% 0.7602
Gravel
67.97% 0.7422 64.17% 0.7393 61.98% 0.7446 63.98% 0.7559 54.48% 0.7021
Tiles
85.11% 0.8966 80.29% 0.8420 81.26% 0.8222 79.96% 0.8145 69.12% 0.7452

Algorithms 2020, 13, 61 22 of 25
8. Discussion and Conclusions
This research paper proposes a highly effective geographic object-based scene classification system
for image Remote Sensing which employs a novel ZsL architecture. It introduces serious prerequisites
for even more sophisticated pattern recognition systems without prior training.
To the best of our knowledge, it is the first time that such an algorithm has been presented in
the literature. It facilitates learning of specialized intermediate representation extraction functions,
under complex Deep Learning architectures. Additionally, it utilizes first and second order derivatives
as a pre-training method for learning parameters which do not cause exploding or diminishing
gradients. Finally, it avoids potential overfitting, while it significantly reduces computational costs
and training time. It produces improved training stability, high overall performance and remarkable
classification accuracy.
Likewise, the ensemble method used leads to much better prediction results, while providing
generalization which is one of the key requirements in the field of machine learning [38]. At the
same time, it reduces bias and variance and it eliminates overfitting, by implementing a robust model
capable of responding to high complexity problems.
The proposed MAME-ZsL algorithm follows a heuristic hierarchical hyperparameter search
methodology, using intermediate representations extracted from the employed neural network and
avoiding other irrelevant ones. Using these elements, it discovers appropriate representations which
can correctly classify unknown image samples. What should also be emphasized is the use of bootstrap
sampling, which accurately addresses noisy scattered misclassification points which other spectral
classification methods cannot handle.
The implementation of MAME-ZsL, utilizing the MAML++ algorithm, is based on the optimal
use and combination of two highly efficient and fast learning processes (Softmax activation function
and AdaBound algorithm) which create an integrated intelligent system. It is the first time which this
hybrid approach has been introduced in the literature.
The successful choice of the Softmax (SFM) function instead of the Sigmoid (SIG) was based on the
fact that it performs better on multi-classification problems, such as the one under consideration, and
the sum of its probabilities equals to 1. On the other hand, the Sigmoid is used for binary classification
tasks. Finally, in the case of SFM, high values have the highest probabilities, whereas in SIG this is not
the case.
The use of the AdaBound algorithm offers high convergence speed compared to stochastic gradient
descent models. Moreover, it exceedes the poor generalization ability of the adaptive approaches, as it
has dynamic limits on the Learning Rate in order to obtain the highest accuracy for the dataset under
consideration. Still, this network remarkably implements a GeoAI approach for large-scale geospatial
data analysis which attempts to balance latency, throughput and fault-tolerance using ZsL. At the same
time, it makes effective use of the intermediate representations of Deep Learning.
The proposed model avoids overfitting, decreases variance or bias, and it can fit unseen patterns,
without reducing its performance.
The reliability of the proposed network has been proven in identifying scenes from Remote Sensing
photographs. This suggests that it can be used in higher level geospatial data analysis processes, such
as multi-sector classification, recognition and monitoring of specific patterns and sensors’ data fusion.
In addition, the performance of the proposed model was evaluated against state-of-the-art supervised
Deep Learning models. It is worth mentioning that the proposed model was trained with instances
only from seven classes, while the other models were trained with instances from all eleven classes.
The presented numerical experiments demonstrate that the introduced approach produces remarkable
results compared to theoretically superior models, providing convincing arguments regarding its
classification efficiency.
Suggestions for the evolution and future improvements of this network should focus on comparison
with other ZsL models. It is interesting to see the difference between ZsL, one-shot and five-shot
learning methods, in terms of efficiency.

Algorithms 2020, 13, 61 23 of 25
On the other hand, future research could focus on further optimization of the hyperparameters of
the algorithms used in the proposed MAME-ZsL architecture. This may lead to an even more efficient,
more accurate and faster classification process, either by using a heuristic approach or by employing a
potential adjustment of the algorithm with spiking neural networks [44].
Additionally, it would be important to study the extension of this system by implementing more
complex architectures with Siamese neural networks in parallel and distributed real time data stream
environments [45].
Finally, an additional element which could be considered in the direction of future expansion,
concerns the operation of the network by means of self-improvement and redefinition of its parameters
automatically. It will thus be able to fully automate the process of extracting useful intermediate
representations from Deep Learning techniques.
Author Contributions: Conceptualization, K.D. and L.I.; investigation, K.D.; methodology, K.D. and L.I.; software,
K.D. and L.I.; validation, K.D. and L.I.; formal analysis L.I.; resources, K.D. and L.I.; data curation, K.D. and L.I.;
writing—original draft preparation, K.D.; writing—review and editing L.I.; supervision, L.I. All authors have read
and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
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GeoAI: A Model-Agnostic Meta-Ensemble Zero-Shot Learning Method for Hyperspectral Image Analysis and Classiﬁcation

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