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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eigenvector terminology [duplicate]

This is a basic question about PCA. The term eigenvector seems to be used in different scenarios and I would like some help improving the precision with which I use it. It is used for the unit ...
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Centering and scaling in Partial Least Squares

I am trying to understand, how data is centered and scaled in Partial Least Squares (PLS). I understand how it is done in Principal Component analysis (PCA). For example, in PCA test-data is centered ...
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PCA for Feature Engineering

PCA is finding features with high variance features and transforms (Gives more appropriate/variance captured features) For feature engineering, we tend to create features like rations and other ...
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PCA / PCR with longitudinal data

I have a panel data set with a more than 100 variables and want to perform a pricipal component analysis and eventually a pricipal component regression. My data has the form of: ...
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eigenvector question [closed]

In the scenario where an eigenvector (x) of a principal component subtends a descriptor coordinate with an angle alpha. What is the name of the x(cosalpha) or x(sinalpha) quantities (cosalpha or ...
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PCA / PCR with longitudinal data

I have a longitudinal data frame with a more than 100 variables and want to perform a pricipal component analysis and eventually a pricipal component regression in R. My data has the form of: ...
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Getting the arc-lengths of projections along a local principal curve in LPCM [closed]

I have been using the R package LPCM to obtain local principal curves (Einbeck, Tutz, and Evers 2005). I would want to obtain the arc-lengths of the projected points from the beginning of the curve, ...
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Getting distances from points to their principal curve projections in R princurve? [closed]

I have been using the R package, princurve, to calculate principal curves. Now I want to obtain the squared distances from the points I used to fit the principal curve to their projections in the ...
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creating index using pca

i want to create an index. it has 3 subindices A,B,C. each subindex further consists of 3 different variables A1,A2,A3,B1,B2,B3 and so on. in total there are 9 variables. i want to assign weights ...
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How to use sparse PCA loadings in a regression?

I'm using Dr Frank Harrell's code in RMS 2nd edition. He goes into sparse PCA. Does anyone know how to code a regression model after getting the sparse component grid? ...
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Should I apply PCA on every sample of a multivariate time series dataset and calculate mean values or should I reshape the 3D array into 2D?

I am relatively new to PCA and can't find a sufficient answer to my question. I have got a multivariate timeseries dataset of the shape [1200 (Samples), 100 (Timesteps), 18 (Variables)]. I want to ...
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How to interpret a PCA score plot?

I get a following score plot for the breast cancer dataset. The score plot has been clustered into two categories. I want to know what inferences could I draw from it?
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Do differences between ordinations prove a relationship between variables?

I have a large dataset that contains a variety of environmental characteristics (air temperature, tree cover, insect counts) as well as bird abundance data for each point. I was talking with my friend ...
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SPSS - How can I measure whether a questionnaire consistently decomposes along similar dimensions? [closed]

I've been using a 14-item questionnaire that measures thought content. Each row in my dataset represents a completed questionnaire, showing the scores on each item. I've been decomposing sets of ...
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Parallel analysis in R scree plot [closed]

I just plot a parallel analysis in R but I am not sure how to interpret the plot and how can I know how many factors do I need for a factor analysis.
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Use of PCA to model variance for dependent variables

I am working on a math problem with some friend and there is some disagreement on the meaning of what we are doing. We have 3 independent variables measured tens of thousands times and we have a model ...
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Correlated variables and similar loadings in first principal component

I'm doing a K-Means model for first time, thus very low experience. I read that it is not bad to discard variables through some PCA analysis. After standardizing the data, the loadings (weights) for ...
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Find the principal component and the proportion of the total population variance explained by each when the variance covariance matrix is given

I can understand the part where we have to find the principal component from the variane covariance matrix- find eigen values, make eigen vector and normalise. The principal component would be ...
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PCA: understanding how to use loading vectors of X to recapture the geometry of X

If we suppose that X is an n x d matrix, and then perform PCA to obtain loading vectors ...
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Does PCA centering guarantee projection optimality onto an affine set subject to dimensionality constraint?

Say I have $m$ points in $R^n$, not necessarily with sum 0, and I want to project them onto an affine set $S$ with $\dim(S)=d$ for a given $d$ so as to minimize the sum of the squared distances ...
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parallel lines (cluster) in PCA plots (PC1 vs PC2)

There are about 20 subjects, 3 treatment groups, and 1000+ genes in my data; the 1000+ genes were processed in two batches. Could anyone comment on why I am seeing parallel lines/clusters in the PCA ...
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PCA on individual image or a set of images

I have a set of $N$ hyperspectral images each of the shape $500 \times 500 \times 200$ where the width, height are $500$ and the number of bands is $200$. I want to use PCA to reduce the ...
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Ridge or multiple linear regression following PCA?

I have a real world clinical dataset with a severe issue of p >> n. I have thus decided to run PCA before modelling the data. This leads to a dataset with 150 samples with 85 features. I would ...
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What are the pre-requisite of a dataset's measurement type before Principal Component Analysis can be used? [duplicate]

Must all the measured data be discrete, continuous, nominal or ordinal? What are some of the transformation techniques that can be used?
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Sum of PCA principal components

Short I wonder is it possible to sum the principal components together to obtain a score? For example, PC1 + PC2. Details I got the below dataframe: admin_username sales sign book team_sales ...
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Python KernelPCA inverse_transform does not remove noise as it does with regular PCA function [closed]

Context: I am attempting noise reduction using PCA before entering features into a model. To do this, I am transforming the features into their principal components, removing the principal components ...
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Will PCA always fit a model at least as well as NMF?

If I perform PCA/NMF on a dataset, and then use the reduced models to reconstruct the original dataset, it seems to me that PCA should typically outperform NMF, simply due to the fact that NMF has the ...
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Does the fraction of explained variance in the first PCA component necessarily drop if you remove features from the dataset?

When performing PCA on a certain dataset and logging the fraction of total variance explained by the components, will this fraction drop for the first component if one or more features (that were ...
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MCA vs PCA - results for one factor are the same, but negative! [duplicate]

quick question regarding principal component analysis (PCA) and multiple correspondence analysis (MCA). I am trying to extract scores to create index variables from ordinal data. I first used PCA, but ...
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How to work with Proportion of variance explained in PLS Regression?

I have some very basic questions regarding PLS. I ran PLS using SPSS on small dataset. n=312, Dependent variable=1; Independent Variables=9. Here is the output of Proportion of Variance Explained. As ...
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Curse of dimensionality: How PCA improves my model?

After having read about the curse of dimensionality, I have been looking into a filtered version of the Superconductivity dataset. The number of dimensions is 81, so initially I thought that reducing ...
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what could be wrong with a Principal Component analysis that uses regression on dummy variables? (I am not looking for workarounds) [duplicate]

I have already checked the suggested links and they do not answer my questions; my question is simple and does not need to be reinterpreted. So please do not close the question until it receives its ...
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What would we violate if we use principal component analysis on datasets containing only dummy variables?

I have 23 dummy variables that are generated through a multiple-answer question. Respondents could choose more than one option. I ran a PCA and could see meaningful components emerging. I then ...
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GMM clustering with binary and multicollinear data

I am using GMM clustering on bank data. The data have both categorical and numerical attributes. The categorical data were converted to numerical using binary encoding. I have a couple of questions: ...
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Can PCA provide contextual correlation between features and a target label?

I was exploring some of the projects I've done years ago in high school, and my current understanding of Principal Component Analysis differs from what I have performed back then. Experiment: Our ...
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Why doesn't my VAE encoder (for dimension reduction) model work? [duplicate]

...
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How to mathematically interpret orthogonal rotation in principal components analysis for more than 2 factors

When performing orthogonal rotations for a loading matrix in principal components analysis, the mathematical interpretation is relatively simple - rotate the two axes while keeping them perpendicular. ...
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Is it okay to use PCA then with LSTM

I am currently trying to see if there is any validity to this procedure: Using PCA on data in tabular data Then transforming the new "PCA data" into a multivariate time series Using an LSTM ...
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How can I do continuum regression in R?

I am looking for a R package that does continuum regression. More concrete I need a function that does continuum regression s.t. I can evaluate the values afterwards. At least extracting MSE or RMSE ...
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PCA graph: Formal analysis of how each loading effects individual players?

Here is a PCA example, with environment variables loaded in blue, species in red, and sites in black. I am trying to make two specific interpretations. I want to know if they are right and if there is ...
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PCA versus mixed effects model: Incorporating relationship between loadings?

I have species abundances with associations between environmental variables. I realize the RDA will only be able to tell you the strength of the relationship of all the species abundances with the ...
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PCA Minimizing Reconstruction Error

In PCA, we want to fit the best $k$-dimensional subspace to given data $x_1,\dots,x_n\in\mathbb{R}^d$. Specifically, we want to approximate each $x_i$ by $\mu + V_k\alpha_i$, where $\mu \in \mathbb{R}^...
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Need help interpreting featureplot legend

Previously, I asked this question on StackOverflow and was directed here: https://stackoverflow.com/questions/71797502/need-help-interpreting-featureplot-legend I am using the FeaturePlot command ...
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Is my sample sufficient for PCA?

I’m working on a project for my stats class and I’m wondering if my sample size is sufficient for PCA; I keep seeing mixed recommendations so I figured I’d ask. My sample size is 50 (unit of analysis ...
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Should we use PCA or Categorical PCA or Multiple Response Analysis if categorical variable is ordinal numeric?

The dataset I use includes several categorical variables where values are ordinal numeric. For example, I have a variable X1 of which possible values are as follows: Value Description of value 1 Bad ...
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Principal component analysis and statistical significance

I've been drawn into a discussion at work on interpretation of principal component analyses. My "adversary" claims that the PCA score plot shows "statistically significant" ...
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PCA as a Cure for the Curse of Dimensionality

I would like some clarification as to how principal component analysis mitigates the Curse of Dimensionality problem. My particular interest is in curbing overfitting in my modelling, or more ...
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Is it possible to "warp" samples of different dimensions for sparse PCA?

It's my understanding that for $n$ samples each with $k$ dimensions I can utilize dimensionality reduction methods (ie. PCA, or in my case, sparse PCA) in a straightforward way. But what if my samples ...
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Why is sum of squares equal to eigenvalue in PCA?

We fit a line or a hyperplane to a set of points. We project the points onto the hyperplane. The sum of squared distances of the projected points to origin is equal to the eigenvalue. Why is that?
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How many percent of variance can each variable explain in principal components analysis?

In a dataset with 5 variables, how many percent of variance of the dataset can each variable explain at most?
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