Questions tagged [pca]
Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.
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Why is the amount of Eigenvalue of the first Principal component much higher than the rest of the PCs?
I have the time series of 16 water quality parameters, and after standardizing them using the zscore method, I performed principal component analysis. These are my eigenvalues [7.62675203795075
2....
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Can I use a variable from Principal Component Analysis (PCA) as outcome Y in a linear regression [closed]
(1) I have a set of 3 predictors which predict an outcome Y (BF10 = 10). Each predictor alone does not predict Y (BFincl < 1)
(2) I would like to assess if another predictor can predict those 3 ...
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Posterior mean in Probabilistic PCA shifts towards 0 when $\sigma^2 > 0$
We know that in probabilistic PCA, where $$x = Wz + \mu + \epsilon, \epsilon \sim N(0, I)$$
The posterior can be derived to be $$z|x \sim N\left(M^{-1}W^T(x-\mu), \sigma^{-1}M\right)$$
where $M = W^TW ...
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Factor Analysis with Multiple Imputation
I have a dataset with 49 Items of a questionnaire (ordinal; 0,1,2,3,4) with 5 diagnostic group of samples (n1: 50, n2: 25; n3:30, n4:23, n5:60). However, the dataset have missings like for 10-12 ...
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Is this a reasonable way to check the quality of simulated data in MCMC inference?
I have a hierarchical Bayesian model that looks like this:
$\alpha_i \sim \mathcal{N}\left(\mu_\alpha, \sigma_\alpha\right) \tag{1}$
$\beta_i \sim \mathcal{N}\left(\mu_\beta, \sigma_\beta\right) \tag{...
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Variable weighted PCA
I have seen a lot of "weighted PCA" but they are really all on "observations". For example Weighted principal components analysis if you have K variables, N observations, the ...
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How to make an index with PCA?
I'm new to PCA and have a question about interpreting the results. In R, I can obtain the component loadings and scores. To create an index, should I just add these scores together? Are the scores ...
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Comparing the angle between PCA loading plots
I am analyzing temperature, precipitation, and snow depth in three datasets. I used PCA for the analysis, and I obtained angles of 13.1°, 19.6°, and 102.0° between precipitation and snow depth for ...
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Performing a PCA on data of different hierarchical levels
I (novice) plan to use a PCA on several different, related, i.e. non-orthogonal questionnaire measures. These measures have composite scores (item sums etc.) and some of them have sub-facets. Also, ...
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Confusion regarding PCA, FA, and PCR?
I learned here: Is PCA followed by a rotation (such as varimax) still PCA?
About the relationship between PCA and FA and how they each provide a perspective for looking at the same thing. However, at ...
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Creating an Index using PCA?
Apologies if this question seems basic—I'm new to PCA. In R, I've figured out how to obtain the component loadings and scores. To create an index, should I simply add these scores together? In other ...
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What is the interpretation of outlier-robust principal component analysis?
There's a set of methods called "robust" principal component analysis (here, "robust" means resistant to influence from outliers). One example is Hubert et al., "ROBPCA: A new ...
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When is multidimensional scaling exact for a graph?
For an undirected graph with one connected component and distance matrix given by the shortest path between nodes, I would like to embed the nodes in a high dimensional Euclidean space where all ...
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Reproducing PCA results of pca.fit_transform() using pca.fit()? [duplicate]
I have a data frame called data_principal_components with dimensions (306x21154), so 306 observations and 21154 features. Using PCA, I want to project the data into 10 dimensions.
As far as I ...
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What dimensions to expect of Principal Components Analysis? [duplicate]
In both Python and R, the matrix of eigenvectors of Principal Component Analysis (PCA) is a matrix of principal components with dimensions (Number of Observations x Number of Principal Components). ...
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