# 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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### Does the average eigenvalue equals 1 in PCA applied to standardised data?

From what I understood when we are doing PCA, we can work both with raw or standardised data, depending on the situation we're in. Is it true that the average of the eigenvalues is equal to 1 when we ...
1 vote
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### Can I apply Kaiser Rule without knowing the eigenvalues?

Kaiser's rule suggests the number of principal components to be included in an analysis by looking at eigenvalues. If I'm given standard deviations only, instead of eigenvalues, can I still somehow ...
1k views

### Is it OK to tune the k parameter in PCA?

Principal Component Analysis (PCA) is used to reduce n-dimensional data to k-dimensional data to speed things up in machine learning. After PCA is applied, one can check how much of the variance of ...
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### Clustering sparse dataset with mix of continuous and categorical variables

I am trying to cluster sparse heterogeneous datasets containing demographics and diagnosis variables ( mix of categorical and numerical variables). How should I start my clustering endeavors ? start ...
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### Creating a standardized composite "score" made up of multiple continuous, dependent variables for analysis in SPSS

I am trying to evaluate how a surgical intervention (insertion of a spinal fusion cage), resulting in distance changes between two vertebral bodies, led to new symptoms (yes/no) in some patients but ...
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### Plotting all the points of PCA to only one PCA axis, first PC1 and then on the PC2

I am required to project all the points on PCA to PC1 axis and then on PC2 axis as to see whether there is a good separation between the points. Through this I have to determine which dimension can ...
1 vote
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### duplicated variables for different components

I'm presently evaluating the position of individuals of an 3 populations of an animal (according to their sexe) in function of the environmental factors (12) present in their habitat. To detect which ...
2k views

### Practical usefulness of PCA

I asked a similar question in the past, but I've thought about the message I am trying to convey a bit more and feel I can articulate it better. For context, I am on an introductory course in machine ...
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### How to use slopes in PCA?

I would like to use slope values in PCA. The problem I face is that the slopes I calculate per group could be within different ranges of values. We know that it is important to normalize your data ...
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### Can I perform multiple Kruskal-Wallis tests with different explanatory variables against the same response variable?

My data is observational data, and that's made it all kinds of ugly, and I can't decide what statistical test is needed. I have one response variable, which is categorical (Species 1, Species 2, or ...
2k views

### Principal Component Analysis with time series and index construction

I am doing a pca analysis to construct a financial stress index from different variables which I expect they will move together in a period of "financial stress". As I have read in different papers I ...
723 views

### Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
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### What does the quality of representation of a variable mean in PCA?

I understand that the quality of representation of an individual by a certain axis is measured by the cosine of the angle between the axis and the individual; the more the vector representing the ...
1 vote
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### Dealing with high dimension in principal component analysis

Does PCA work well or does it work at all in extremely high-dimensional problems, i.e. when the number of dimensions $p$ is larger than the sample size $N$? By 'work' I mean if it works mathematically....
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### PCA with variables in different Likert scales

Can I run PCA (principal components analysis) if my Likert variables are measured differently? E.g. one Likert variable is in the range 0-6, another one is in the range 0-10 and yet another one is in ...
1k views

### Checking Multicollinearity and building a classification model when dependent is a factor and other independent variables are numerical in r

Problem statement Y - Dependent variable is a factor (with levels A, B, and C) Independent variables are all numerical variables. Important: I have only 70 data points. End Goal: Building a ...
47k views

### Meaning of "reconstruction error" in PCA and LDA

I am implementing PCA and LDA for compression and classification respectively (implementing both an LDA for compression and classification). I have the code written and everything works. What I need ...
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### Is it okay to perform PerMANOVA on PCA values?

Is it acceptable to first perform principal components analysis on a dataset, and then use permutational MANOVA on those principal components values, rather than on the original values in the dataset? ...
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### PCA: How can the first principal component both maximize variance AND define the line that most closely fits the data?

I'm reviewing Chapter 6 from An Introduction to Statistical Learning. I'm having trouble understanding PCA and the provided example. Can someone explain how the first principal component direction ...
1 vote
527 views

### Differentiable PCA? [closed]

Is there a differentiable method for dimensionality reduction that is either based on PCA or has the properties of: Mathematically or algorithmically defined, e.g. not trained like an ML model or t-...
1 vote
533 views

I just started to read about PCA in machine learning , and got to know that the main goal to determine principal components is to maximize variance so that more information is retained.But, why does ...
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### Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
1 vote
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### How to find complete log likelihood for mixture of PPCA

In Appendix C of a paper by Michael E. Tipping and Christopher M. Bishop about mixture models for probabilistic PCA, the probability of a single data vector $\mathbf{t}$ is expressed as a mixture of ...
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While reading about PCA, I came across the following explanation: Suppose we have a data set where each data point represents a single student's scores on a math test, a physics test, a reading ...
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### FAMD explained variance of components very low

I am dealing with a dataset composed of 50 features. There are both categorical (some with many levels, others dichotomous) and numerical features, so I decided to use FAMD in order to reduce the ...
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1 vote
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### Latent Semantic Indexing vs. PCA

I am trying to understand how Latent Semantic Analysis works, reading demonstrations based on singular value decomposition. Let's denote $X$ a $N \times D$ document-term matrix. The $D$ rows of $X$ ...
1 vote
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### Euclidean distance between points in PCA space along different principal component dimensions

I've picked up this project half way through, and I'm working through the last guy's code, so please bear with me. So the original data consists of 500+ points in 150 dimensions, and I want to ...
1 vote
338 views

### Interpretation of a PCA plot

I have a PC1-PC2 plot generated by applying PCA to the combination of 2 sets of samples where red means one set and blue means the other set. I can see that the two sets of samples are very different ...
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### Optimal predictive factors

Assume I am interested in predicting a time series variable $y_t$ using a vector of possible predictors $X_t$ of dimension $N_x$. I am interested in finding the optimal $N_z < N_x$ predictive ...
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1 vote
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### How can I compare one full PCA model to two smaller ones?

I have nearly 30 variables going in to a large PCA, but the variables really fall into two conceptual categories. I want to test whether leaving all the variables to correlate freely with one another ...
1 vote