# 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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### Scaling and centring in PCA of compositional data

I am following this review's approach for PCA using compositional data. It involves computing the centred log-ratio (CLR) transformation of the compositional data, and then running PCA on the ...
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### Which analysis should i use for group classification?

I have done this PCA analysis and found the score values. Now I want to do another analysis on this data to see that PC loaded in which "Region" (column 1). Now used a NMDS plot using Bray-...
10 views

### Which analysis should i use for group classification?

I have done this PCA analysis and found this score values, now I want to another analysis on this data to see that PC loaded in which "Region" (column 1). Now i did NMDS plot using bray-... 49 views

### Should I go with an unrotated factor analysis model?

I'm running a project on survey data where I have a bunch of very similar operationalizations of my DV (four different indices of my DV). Let's call it support for X behavior. All of them are ...
6 views

### CCA for Change Over Time

I initially was thinking of using PCA but have shifted towards CCA due to using species abundance and those abundances not being linear. I want to see how environmental variables are associated with ...
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### Is it possible to have better results by PCA PCs in compare to Laplacian eigenmap

Suppouse I have a data set of the form $p = 200$ and $N = 35$. I am interesting in the multiple linear regression model train, for this reason I need somehow simplify my data. I decided to use two ...
1 vote
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### Are population principal components scale invariant?

Are population principal components scale invariant? The answer is no. I'm not sure whether my understanding regarding the first two is correct; please, correct me if I'm wrong. Also, I don't ...
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### Should I do PCA reduction before applying Mclust()?

I am doing some work where I am meant to apply Mclust() to my data set, with 50000 samples. I previously used PCA in order to reduce the dimension, which left me ...
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### Can you combine to principal components into one variable when carrying out a principal component analysis?

I am getting into and trying to learn how to use principal component analyses (PCA), and got stuck on a few things that I thought someone here might be able to help me with. What I am trying to do: I ...
23 views

### Can it Work to Run PCA only on a Subset of Highly Correlated Predictors prior to Regularization? (Cox)

I'm running Cox-LASSO (using glmnet as explained by Tay et al) on about 50 variables with about 300 observations. The variables fit into different categories like &...
1 vote
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### How to balance PCA and LDA in subspace learning?

PCA is a generative model, by which input images or data can be reconstructed. LDA (Linear Discriminant Analysis) is a discriminative model, which extracts better features for classification. How to ...
68 views

### Direction of PC1 and PC2 in Principal Component Analysis (PCA)

I am a bit confused by what is considered the direction for the principal components in PCA. For example: I do understand that the picture on the right hand side is correct. However, is the the PC1 ...
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### Generative model for random covariance matrices to fit hierarchical data

I have a multivariate dataset with M groups of data, each consisting of N iid measurements of p variables. Say I take the N measurements from a single widget, and M corresponds to the number of ...
1 vote
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### A method to categorize variations in time series of images

I am working with a time series of remote sensing images from a particular area. Temporal standard deviation (SD) of these images showed high fluctuations at some regions with SD of 1.17 while some ...
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### Generalized Low-Rank Models in a Regression Format

I've been using principle component regression (PCR) to model data, and was interested in using generalized low rank models (GLRM) in its place. Using PCR, I am able to easily get the coefficients for ...
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If I have five variables, each with four sub-questions, In each sub-question, I have: 1 = I usually don't do this at all 2 = I usually do this a little bit 3 = I usually do this a medium amount 4 = I ...
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### Do we need to scale our features before applying ICA, like in PCA?

I am reasonably certain that we don't need to scale data before applying ICA, like we do for the PCA. In PCA we do this because it assumes normal distribution of the features, and in ICA we don't ...
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### Comparing scree plots or explained variance of two groups with different number of features after PCA

I want to define the dimensionality of a group as the number of PC features that can explain 80% of the variance in the group dataset. This intuition seems to work for a single group, however, if I ...
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### Geometric Intuition Behind Whitening for ICA

I know there are a couple posts asking about why we whiten the data for ICA. I understand why we whiten to fix scaling invariants between the sources and to increase the computationally efficiency. ...
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### Is FAMD (Factor Analysis of Mixed Data) truly a factor analysis technique? or it is a dimension reduction technique?

PCA is distinct from factor analysis; it's a dimension reduction technique. PCA does not account for individual variable noise. On the other hand, FAMD (Factor Analysis of Mixed Data) combines PCA and ...
29 views

### Interpretation of pca plot [duplicate]

I am looking at an example of using PCA: https://wiki.q-researchsoftware.com/wiki/Principal_Components_Analysis_Biplot Specifically, Example 2 has data What are the points I'm looking at the biplot? ...
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### Precise definition of a principal component in PCA

To the following question regarding how PCA is performed, two well-detailed answers are given: one by ameoba and one by Andre P. In the first, ameoba takes an $n\times p$ centred matrix $X$ and ...
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### Principal component analysis for "uneven" data

Suppose I have data consisting of three layers. Layer $i$ consists of $n_i$ 2D points, $i=1,2,3$. Here $n_1$, $n_2$ and $n_3$ may be different. I would like to somehow apply the Principal Component ...
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### Variances explained by each feature on PC in PCA

I came across this article with an associated Python codebase. In brief, there is a section "Understanding How Features Contribute to PCs ", where... One method for understanding which ...
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### Can participants be columns in a data frame for PCA?

I am very new to statistical analysis, so I apologize in advance if this question is too naïve. I would like to know whether participants be columns in data frames for PCA, but I first want to offer ...
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### Is there a difference between Principal Component and weighted mean using PC loadings? How to get Principal Component on scale of original variables?

I was interested in doing a Principal Component analysis but returning a Principal Component on the scale of the original variables. Principal component analysis in R defaults to scaling and centering,...
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### Why am I getting negative components with my custom NIPALS algorithm

I've recently been learning about the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm for computing the principal components of a dataset. I am trying to code a NIPALS class from scratch ...
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### How can to visualize/plot correlation matrix as a distance matrix of points in space?

It seems to me that the various options for visualizing the correlation matrix in R are quite unintuitive for laymen. They focus on the graphical representation of the correlation matrix as different ...
52 views

### PCA and scree plot and slope

This may be really a simple question. I know that if there are correlated variables, they may not be good to use for modeling. We have to use the PCA such that each PC is orthogonal to one meaning ...
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### What is Bayesian PCA and its cousin?

When I think of the phrase "Bayesian PCA" I think of two things, but these two things are what I have contrived rather than conventional notions. I would appreciate guidance on what these ...
1 vote
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### Comparing the PCA modes from two different covariances

Suppose I have a set of $n$ vectors $x_i$ arranged as columns of a matrix $X$ and I want to perform PCA to reduce the number of dimensions needed to explain some set of observations. I have developed ...
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### Using cross correlation and an uncorrelated eigenvector basis to minimize exposure

I have the following problem: We are looking at stock market data and have a historic price dataset $X$ with two stock types: \begin{equation} X = \begin{bmatrix} x_1 & x_2 \end{bmatrix} = \begin{...
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### Running all possible fixed effects combinations, LMER, PCA [duplicate]

my data looks like that: ...
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### Running all possible fixed effects combinations for linear mixed effects models

my data looks like this: ...
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### Kernel + Mutliple SVM's + Platt Scaling = 1 layer neural network?

I have built my own Support Vector Machine by using quadratic programming and I'm using Kernel PCA with SVM. The output is tanh e.g Platt scaling. When I combinde ...
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### Why does Kernel PCA works with validation data?

Assume that you have a matrix $X$ and you want to do Principal Component Analysis on that data. But the data contains nonlinearities, so you decided to use Kernel Principal Component Analysis instead. ...
1 vote
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### Nonlinear Sparse PCA

Given data $x_1, \dots, x_n \in\mathbb{R}^d$, I am looking for a nonlinear dimensionality reduction technique $f: \mathbb{R}^d \rightarrow \mathbb{R}^q$ that only uses a limited number of dimensions ...
1 vote
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### PCA with soil cover of plant species

8 plots (quadrants 3 x 3 meters), 4 invaded with an alien plant, 4 without the alien plant. I have measured the soil cover (as %) of the species found in these 8 plots. If I make a PCA with log (n+1)...
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### How do I measure the "dispersions" of a group of time series

I have a group of time series $X_1, X_2, ... X_n$. I want to measure how much they have "dispersed" over time. i.e. are they moving "more together" in 2023, comparing to 2022. $n$ ...
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### Analysis of the bias resulting from PCA [closed]

Suppose that we generate some dataset from $y = X \beta + \epsilon,$ where $\epsilon$ is some independent error, and the rows of $X$ come from some distribution (unspecified for now). Suppose you run ...
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### PCA with gram matrix produces different results from PCA done using covariance matrix?

I was trying PCA on a dataset (#samples=24, #dims=42) via eigendecomposition using numpy. I read that for matrices where the number of features exceeds the number of samples, we should use the gram ...
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### Comparing two algorithms, one is parameter free while the other is not

I wish to compare two algorithm for subspace approximation (similar to PCA). One algorithm is parameter free, while the other is not. I use cross validation to set value to this parameter, and then ...
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### Identifying stress in financial stress index constructed using PCA using Hodrick-Prescott filter

I am reading: https://www.econstor.eu/bitstream/10419/128519/1/ewp-356.pdf The footnote on page 19 says: The trend was derived using the Hodrick-Prescott method where the smoothing parameter λ is set ...
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### Difference between conducting PCA on $XX^\top$ vs $X^\top X$?

PCA: For a given set of centered data $\mathscr D =\{x_i\}_{i=1}^N \subset \mathbb R^d$, i.e. the data has $N$ examples with dimension $d$. Then the principal directions of PCA can be obtained from ...
1 vote
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### How to project kernel PCA?

I have an $m\times n$ matrix $X$. To apply a Kernel PCA to my $X$ matrix I need to warp it into a function $K = \Phi(X)$. The problem here is that $K$ get the size $m \times m$. If I'm doing ...
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### Functional Principal Component Analysis - Explaining Functional Principal Component Scores

I was wondering if someone can help with explaining Functional Principal Component Scores? I am working with a dataset which reflects participants in a weight loss management trial (longitudinal data)....
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### Can you only apply PCA feature reduction only when there are linear relationship between the variables?

My coworker and I were discussing this. He insists that PCA only makes sense just when you know at least one variable is linear combination of the rest but I think it can be applied whenever there are ...
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### Can I conduct a PCA on binary presence-absence data?

I have presence-absence data for 53 wildlife species at 60 different sites. I am a bit confused as to whether a PCA would be appropriate for this sort of data. If so, is there a specific R package I ... 