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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Features after PCA are not normalized

You are supposed to normalise data before doing a PCA analysis. But when one has a PCA transformed dataset which contains 10 continuous features/variables, but the scale of feature one go from -6 to +...
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Relevant Dimension Estimation: Showing that $\sum_{i=1}^N s_i^2 = ||y||^2$

In relevant dimension estimation, we are given a Kernel Matrix $K \in \mathbb{R}^{n \times n}$, where $K_{ij} = k(x_i, x_j)$. We then compute the kernel eigenvector from the multiple solutions of the ...
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PCA loadings of one

I performed a PCA on the results of 4 different tests. Each test can only have whole integers as a score, and is measured on a scale of 0-5. From what I've read, you are not supposed to conduct a ...
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54 views

How to “mirror” PCA results [closed]

I have a practical visual problem. I would like to mirror the results of the PCA. In other words, everything that is on the left should go to the right and vice-versa. In my current graph, PCA 1 (see ...
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How to find the covariance matrix of a polygon?

Imagine you have a polygon defined by a set of coordinates $(x_1,y_1)...(x_n,y_n)$ and its centre of mass is at $(0,0)$. You can treat the polygon as a uniform distribution with a polygonal boundary. ...
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Different number of Eigen/Singular values from PCA and SVD

My understanding is that a SVD done on a raw data matrix M and a PCA done on its covariance matrix C should return the same eigen/singular values. I have a 2736 x 356 data matrix and am using the ...
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12 views

Why is more Covariance Matrix different in these two computations? [duplicate]

I am trying to break down a matrix into its principal components step-by-step using SVD in order to better understand the process. What I don't understand is why I'm getting different forms of the ...
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28 views

How to interpret two seemingly orthogonal axes in PCA plot

I have got the following PCA plot. I am not able to interpret the two seemingly orthogonal axes in this PCA plot. Do they imply something about the data? Why did PCA not take these two axes as the ...
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Does the order of columns matter in PCA for the results? Jumpy factor loadings? [duplicate]

I have six UK inflation time series, starting from Jan 1990 and ending in June 2019. These series as standardized on an expanding window and subsequently forward filled. I use these series to run a ...
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77 views

Regression shows high multicollinearity even after a PCA

I am comparing men and women using a measure of personality which has 24 variables. I did a oblimin rotated PCA for women and men separately so that they are truly representative of the population and ...
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127 views

When to prefer PCA over regularization methods in regression?

When dealing with the curse of dimensionality, regularization methods seem to be clear in their intuition. All "regularization" methods can be seen as a "squeezing" of one's variables towards ...
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51 views

What kind of statistical test is appropriate for the following example?

I ran an experiment varying the temperature and the quantity of chemicals added for the removal of 4 contaminants (A, B, C and D). The data obtained from this experiment was (in R): ...
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Questions about calculate the first k-th principal components of VR-PCA?

Variance-reduced PCA VR-PCA, focus on the first component calculation, what about the k-th PCs? Any idea? Thank you!
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Why does kmeans after SVD result in ideal clusters

I am clustering tweets which are related to eye fashion and they are extracted using keywords like mascara, eyeliner, eyeshadow, etc from twitter. I constructed a Tf-idf matrix (tweets x words) ...
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What is the formula for estimating confidence ellipses from a PCA projection with multiple groups?

I'm having a hard time finding a straightforward answer online. What formula is used to plot confidence intervals around PCA points for multiple groups? For PCA where all the samples come from the ...
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Parallel analysis for principle components analysis and Multi-dimensional scaling

Does the same method for conducting a parallel analysis for principal component analyses apply to find the cut-off point for multidimensional scaling? Under the pretense that PCA and linear MDS are ...
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identifying what has changed in the data year on year

I have a dataset from one year and the 'same' dataset for the next year. I would like to identify what has changed in the datasets between the years. Both datasets have the same columns. I currently ...
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Python Factor Analyzer and PCA

I am performing PCA and I need to extract squared loadings. I found this python library, Factor Analyzer, that can extract eigenvalues and squared loadings, etc., but the results are different from ...
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Data augmentation for animal measurements

I am looking for methods to do data augmentation for an animal study. What I want to do is generate a large number of data points by using a min and max measurements of the animal. So I have 2 ...
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164 views

PCA in R without deleting or imputing missing values

I want to perform a PCA on a dataset with missing values in R. the data set includes various variables (coralite area,diameter,distance between mouths ecc.)for different coral samples(250 samples and ...
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Dimension reduction for multivariate spatio-temporal data for hurricanes forecast

I have weather data for the 40 previous years and for each year I have information about the hurricane season (intensity, number of active days, casualties,...). My ultimate goal would be to forecast ...
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Problem with Principal component (PCA) and Partial least squares (PLS) using R

I'm trying to reduce highly dimensional data with factor methods. I'm using Principal component analysis and Partial least squares. From these methods I'm using the first component as a Common factor ...
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55 views

What do ellipses of PCA analysis (factoextra) mean?

Biological question: do plants that have been attacked by insects differ in their characteristics from plants that have not been attacked by insects? Data frame includes six numerical variables ...
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R prcomp and KNN different correct classification rate

I'm performing a classification task using KNN and PCA to pre-process the data. The dataset contains 101 continuous variables and the column of the labels (here the link to download the data filebin....
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Statistical technique to combine scores from multiple tests

In my experiment I have two groups, one group has an anxiety disorder (N = 22), the other does not (N = 11) (I know low sample size). They were tested in a battery of psychological tests and also ...
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Interpretation of Eigenvalue vs. Singular Value plot

I'm doing some preliminary analysis on the feature matrix for a certain dataset (rows are observations, columns are feature dimensions). I have computed the SVD and PCA decompositions for this matrix ...
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pca gives a new set of variables to us?

did I understand pca correctly? if we have 9 features we call PCA to find corresponding components, then for example we use 2 first PCA, now we have a data set with 2 variables? and they are linear ...
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Subtraction between features before performing PCA and training a classification model

In my dataset, I've created moving averages for historical indicators. Is it pertinent to perform subtraction between those moving averages before PCA? My stats/calculus feeling: as PCA is a ...
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Eigenvectors - principle lines of force

In the article about PCA and coavariance matrix I've read the following: Finding the eigenvectors and eigenvalues of the covariance matrix is the equivalent of fitting those straight, principal-...
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38 views

EOF/ PCA: do I need to detrend my multivariate time series before finding Empirical Orthogonal Functions?

I am familiar with Principal Component Analysis, but I have recently been asked to find the Empirical Orthogonal Functions of a multivariate time series and I am not sure if what I need to do is just ...
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Centering input data for Robust PCA (RPCA)?

I know that before running Principal component analys, the input data needs to be centered around its mean (subtract the mean from each keypoint) before running the algorithm. Do I need to center my ...
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136 views

Principal component analysis on RGB images

I've implemented a method to compute PCA on grayscale images. I haven't seen PCA on RGB images yet, which left me wondering if it is possible to perform it. With RGB images, is PCA done for each color ...
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Clustering or classification to demonstrate that a yeast disease model is similar to a human disease

I have a yeast model which is suppose to model a human disease. We ran an experiment to determine gene expression in this model, and have list of genes that were differentially expressed between the ...
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Can I obtain original data by multiplying varimax-rotated principal components with varimax-rotated unit length loadings?

I have perform conventional Empirical Orthogonal Function (EOF) analysis to my data set and obtain loadings (eigenvector scaled by square root of eigenvalue) and corresponding principal component. ...
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Do we lose the bias after PCA?

I'm starting to learn about PCA, and this question just popped into my head. Warning: It may be trivial, since I"m still just starting to learn - sorry! Let's say we've got a whole bunch of $(x,y,z)$ ...
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Determine missing eigenvalues given only correlations between variables and components

Given that I just have a correlation matrix ($X$ Variables vs. $Y$ Principal Components), and that I am trying to find 2 missing eigenvalues (e.g., missing $\lambda_1$ and $\lambda_5$) from the total $...
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508 views

Using PCA vs Linear Regression

I'm looking to analyzing data from a study and previous studies that are similar have used either PCA or hierarchical linear regression to analyze the data. I've used both PCA and linear regression ...
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Estimation of NegEntropy

I am trying to evaluate the different ICA algorithms. To do that, one of the measure which I use, is to estimate the non-gaussianity using NegEntropy. I am trying to find a formula/function which can ...
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Should a factor analysis (for construct validity) be performed in a section of a test that is meant to measure knowledge in a specific subject?

As a part of a study, a survey to measure the impact of an environmental education project is being developed, and to do so, factor analysis and principal component analysis are being performed for ...
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Is it possible that PCA works better without data scaling? [duplicate]

I am a beginner. I have a dataset of 1700 samples with 4 features and I have to perform Hierarchical Clustering (the agglomerative version) and I need to decide whether or not to scale the data and ...
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58 views

Variance vs Variation

So far both terms have always meant the same thing for me, however, I started wondering, do they mean the same thing? The first 3 principal components explain 80% of the variance. The first 3 ...
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Feature Selection Pipeline - Combining PCA and SelectKBest with Chi2 Test

This example applies a Feature Union using both PCA and SelectKBest: https://scikit-learn.org/stable/auto_examples/compose/plot_feature_union.html#sphx-glr-auto-examples-compose-plot-feature-union-py ...
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Understanding PCA from a linear transformation perspective

I've came across several great questions and answers here regarding PCA, but I would like to have a look at it from a linear transformation perspective. Let's say I have a (demeaned) data matrix $X$ ...
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What does the PCA().transform() method do?

I've been taught to think of the PCA as change of basis technique with a cleverly chosen basis. Let's say my initial data is a $m\times n$ matrix $X$ where $m$ is a number of features and $n$ is a ...
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How to analyze difference in answers between groups across multiple Likert questions? Categorical PCA and Chi Sq?

I'm analyzing this dataset from UCI ML Repo. It's on the perception of Wikipedia amongst university professors/instructors. I'm looking to test the differences between departments in their answers to ...
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How do I classify multiple time series into different buckets?

I have 60 different time series, denoted $\{y_{i,t}\}_{i=1}^{60}$. So $i$ denotes the time series in question, and $t$ obviously denotes the time period from $t=1$ to $t=T$, where $t \in \mathbb{N}_{+}...
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Factorizing a matrix of distributions [closed]

Let's say we have a matrix $X \in \mathbb{R}^{m \times n}$, then the (R-truncated) SVD allows to approximate: $X_{i,j} \approx \sum\limits_{r=1}^{R} \sigma_r \times U_{r,i} \times V_{r, j}$ Now I ...
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121 views

How to determine number of profile in a dataset derivated from repeated measures?

I'm currently working on datasets which have been derivated from repeated measures over time (blood concentrations). Actually the descriptors of these datasets are descripting the shape of the curves (...
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82 views

Clustering users with very sparse data

I have a dataframe of the form ...
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32 views

How to measure correlation between two groups of variables?

I have a data set that contain 75 variables of football players . These 75 variables basically measures two different types of information. 30 of those variables related to bio metric information ...