# Questions tagged [dimensionality-reduction]

Techniques for reducing a large number of variables or dimensions spanned by data to a smaller number of dimensions while preserving as much information about the data as possible. Prominent methods include PCA, Factor Analysis, MDS, Independent Component Analysis, Multiple Correspondence Analysis, Isomap, etc. The two main subclasses of techniques: feature extraction and feature selection.

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### Matrix decomposition with constraints and weighted least squares

We have a matrix, $\mathbf{X}$, of probability distributions between 6 different results, so each row $\mathbf{x}_i$ sums to 1. We want to perform dimension reduction so that each row is a linear ...
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### Is the behavior of log-likelihood and number of parameters correct in probabilistic PCA?

I am studying the behavior of Probabilistic PCA as described by Tipping and Bishop (1999). I am using the R package "Rdimtools" to help. I am puzzled about the number of parameters in the ...
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### Efficient way to encode a set of large covariance matrices

I have a computational model that involves having a set of $K$ covariance matrices, $\{\Sigma_1, ..., \Sigma_K\}$ with each $\Sigma_i \in R^{n \times n}$. Storing all these full covariance matrices is ...
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1 vote
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### Applying PCA to Time-Series Emotional Data: Validity and Interpretation Concerns

I'm currently exploring the application of Principal Component Analysis (PCA) to time-series data representing various "facial emotional expression" states (e.g., anger, happiness, sadness, ...
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### Searching for a proper way to reduce the dimensionality of activations from a CNN

I am conducting an analysis to compare the similarities between different images across early and late layers in a CNN. The model I am working with is the pretrained DenseNet121 that comes 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 ...
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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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### Is my understanding of dimension reduction in Linear Discriminant Analysis correct?

Here is my understanding of how dimension reduction in LDA works: We have $n$ samples each with $p$ features assigned to $k$ classes. We use the sample mean $\mu_j$ of each class and the pooled ...
1 vote
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### Can you combine two 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 ...
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1 vote
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### Are imaginary eigenvalues a fatal flaw when doing a factor analysis?

I am running an exploratory factor analysis (EFA) in R, extracting three factors (determined via parallel analysis). ...
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### Reducing the number of observables in Factor Analysis

I have $k$ observables (e.g. questions in a questionnaire) and $n$ observational units (e.g. respondents of the questionnaire). Let's call the observation matrix $X$. Let's assume I have performed a ...
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1 vote
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### How can I rigorously quantify the increase performance due to additional parameters?

I am trying to evaluate a novel dimensionality reduction technique. Specifically, we start with a data set with around 1,000 features/covariates per observation. My technique maps this down to 12. ...
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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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### Domain mapping when performing dimensionality reduction

Consider the problem of performing dimensionality reduction from a vector space $V_{1}$ of dimension M to another one, $V_{2}$, of dimension N, where N<M. Is there a technique or theory which ...
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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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### Dimensional Reduction on multi dependent variable for propensity score matching

I have an analysis project and I am not quite sure about my analysis plan. The data context are about the treatment effect with confounding variables is well-established. But it have many dependent ...
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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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### interpreting t-sne scatter plot

I attempted to perform t-sne on some variables: Probability (%) of dying between age 30 and exact age 70 from illness (all)', 'Suicides per 100000 (all)', 'social_support', 'birth_health', 'freedom', '...
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### Linear Discriminant Analysis (LDA) with continuous value?

I wonder if LDA can be supervised with continuous value. If not, what are the closest variants for such applications?
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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. ...
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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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### Is this a dimensionality reduction problem?

I have an interesting (hopefully) data science problem and I want to post it here for discussion. Let's say we have a data set having ONE numerical column and FIVE categorical columns. For categorical ...
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### Does the ID class vector change in Kernel Linear Discriminant Analysis?

Assume that I have a matrix $X$ that has the size $m * n$ and a class ID vector with the length $n$. If I want to apply Kernel Linear Discriminant Analysis (KLDA) onto the matrix $X$ and vector $y$, ...
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