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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Quantifying contributions of each variable to Mahalanobis distance for a final “Fitness-score”

Background Each year, all schoolchildren are assessed by four tests linked to physical fitness: balance, jump, sprint and shuttle run (the exact nature of these tests is irrelevant for the question). ...
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How to compare two PCAs

I am working on a deep learning research and came across the following problem: I have a network (let's call it A) that performs a certain task with X% ...
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134 views

SVM: Maximal number of components kernel PCA versus linear PCA

I'm comparing the Support Vector Machines (SVM) formulation of linear PCA with kernel PCA. I know that in linear PCA, the maximum number of principal components is equal to the dimension of the input ...
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Why is PCA (using sklearn library) increasing the size of my dataset? [on hold]

I used PCA on the Fashion MNIST dataset, with the intention of reducing the size of the dataset. ...
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How can I calculate principal components scores in a compositional data PCA?

I hope someone can help. Please let me know if my question is not clear. I have compositional data, where there are three variables which sum to 100% for each row, something like this: ...
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What are the advantages of kernel PCA over standard PCA?

I want to implement an algorithm in a paper which uses kernel SVD to decompose a data matrix. So I have been reading materials about kernel methods and kernel PCA etc. But it still is very obscure to ...
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Can I use the CLR (centered log-ratio transformation) to prepare data for PCA?

I am using a script. It is for core records. I have a dataframe which shows the different elemental compositions in the columns over a given depth (in the first column). I want to perform a PCA with ...
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Combined PCA and Quantization

I did some PCA on a dataset to reduce the size without compromising too much on their actual information. However, I learnt that quantization is also an effective technique to do this. I guess it is ...
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Does a correlation matrix of two variables always have the same eigenvectors?

I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same ...
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Confused about PCA transformation vectors

I'm trying to get the intuition of how PCA works. So far I understood that: I start from the input matrix $X = [X_{1},...,X_{p}]$ where each $X_{i}$ is composed by $n$ elements that are the $n$ ...
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Time series plots, polynomial coefficients and PCA

I have several time series plots that I have their polynomial coefficients (curve fitting using Matlab polyfit). Is it possible and valid to use Principal Component Analysis (PCA) to try to classify ...
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858 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 ...
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Should we normalize data after applying the PCA? [on hold]

I capped the outliers and applied a log transformation. Then, to remove the multicollinearity, I did a PCA and fitted those data to a multinomial logistic regression model. But it produced NaNs for ...
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367 views

Help understanding DCT compression for a vector

I have multiple 60-dimensional vectors on which I need to apply DCT and reduce to various dimensions. I'm trying to understand how this happens: https://www.cs.cf.ac.uk/Dave/Multimedia/Topic5.fig_47....
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Sampling and Standardization of data before applying dimentionality reduction?

I'm trying to solve a classification problem with 4 parameters, next_action - binary variable(0/1) total_visits- numerical value days_Since_last_visit - numerical lead_source- categorical variable (5 ...
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Are my PCA groups significantly different?

I am studying the feeding behaviour of deep sea fishes, and have produced a dataset containing percentages for 20 different fatty acids (totalling 100%) for 32 individual fish. I have performed PCA (...
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Clustering of multivariate data [closed]

Please I am about to cluster some data based which have about 15 different columns all of which are numbers(Some categorical while some are measurements) also some of my values are missing in some ...
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Using dimension reduction techniques for poverty/wealth indicator

I would like to create an indicator/index of a person's wealth (or socio-economic status, SES). I have about 20 variables that are a combination of education, household assets, access to money, and ...
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Principal Components Analysis, Reading PC Plot

For Question 2v, can someone please explain to me why each subject is located where they are in terms of the two principal components.
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Multiple factor analysis: Getting more number of factors than the number of dimensions/ features

I am trying to apply multiple factor analysis on a survey data, which has all sorts of features - numerical, categorical and ordinal. In total, there are 109 features. Now, when I did multiple factor ...
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In max-variance PCA, why is the variance of the projected data equals to $\sum_{j=1}^M\mathbf{u}^T_j\mathbf{S}\mathbf{u}_j$?

In my machine learning course we have been taught that given a new axis $\mathbf{u}_j$ and a datapoint $\mathbf{x}_n$, the projection is $z_j = \mathbf{u}^T\mathbf{x}_n$. The variance of $z_j$ can be ...
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138 views

Which rotation type for principal component regression?

I would like to perform a principal component regression (PCR), but feel a little confused about the rotation type to be used in the principal component analysis (PCA) step. First I perform a PCA to ...
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535 views

Permutation test for factor analysis

We have a survey instrument and are interested in assessing dimensionality of it. Looking at plots of multidimensional scaling, it appears as though there are, perhaps, 3 distinct dimensions to the ...
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Image feature extraction using an Autoencoder combined with PCA

Background: I have fairly large dataset of biomedical images (around 10,000 images) of 1920x1920 pixels (after cropping parts of black borders out). My task is to extract the 200 most important ...
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Boundary point errors in PCA projection using sklearn

I am preparing a small example of a projection using python, numpy and sklearn to perform <...
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170 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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Correlation between matrix variables and its PCA scores

Suppose a matrix $X$ and $T$ the score matrix obtained from a PCA decomposition of $X$. Denote as $x_i$ and $t_i$ the columns of $X$ and $T$ respectively. Is there any reason for which $cor(x_i, ...
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135 views

How to use principal component to fit linear regression for pairwise relation in R

I have been struggling with this problem for several months. I would really appreciate if someone could help me solve this. I am working on a pairwise relationship as shown in the data below (...
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57 views

One strong variable load on components in principal component analysis?

Hello and good day to you. I am using Principle Component Analysis (PCA) with Varimax rotation to analyze variables on my research. There are 20 variables and 6 components were extracted. From the ...
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24 views

Why the first principal component is mostly negative while the second component is mostly positive?

I am running PCA for a fleet management data frame $X$, where each column is a city, each row is a date, there are 50 cities and 500 dates. I run PCA on $A=X^{T}X$. Then the first component $v_{1}$ ...
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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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How to pick the model that minimizes the mean absolute error when the amount of observations is small

I am given a data set with 1 target variable and 12 features for only 18 observations. My goal is to build a model that has the smallest expected prediction error. I am allowed to use simple methods ...
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How to create 3 variable scatter plot after accounting the variation in First Principal Component

I am performing PCA with three variables with 300 obs for the example given in the text book "Analyzing multivariate data" by James Lattin et al. The authors have drawn a scatter plot after they ...
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Why is VAE a nonlinear extension of PCA (and has the “interpolation” property")?

In many research fields there is a great need of finding a PCA-like nonlinear counterpart. I know PCA has two main properties: the first is dimension reduction, it can detect the correlation between ...
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372 views

Multiple T Tests

On one of my questionnaires, which measure learning behaviours, after PCA, I have 4 subgroups, Efficacy/Perseverance/Effort/Achievement - I have run a T-Test and I have 4 sets of data comparing my ...
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Advantage & disadvantage of PCA vs kernel PCA

PCA is used for dimensional reduction. I learned today that PCA cannot be used for nonlinear data. When nonlinear, you have to use kernel PCA (KPCA). It seems that since KPCA is more applicable to ...
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Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
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630 views

How do I use principal components as predictors in linear regression?

I followed the instructions from this open Stanford lecture on PCR. I have a couple of questions, but first I'll post the code with my comments. ...
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Why the huge difference between the results from pca and spares pca using R [closed]

I am using "elasticnet" package to do the sparse PCA in R. I could get the percent of explained variance of each PC. However the explained variance from sparse pca is much smaller than that from ...
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How to get adjusted explained variance of PC using Sparse PCA in R

I am using "elasticnet" package to do the sparse PCA. However I could only get the percent of explained variance of each PC. I am wondering can I get the adjusted explained variance of each PC using "...
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How to understand “factor loadings” in PCA? [duplicate]

I have seen that some people are talking about "factor loadings" in PCA. It is a topic that I do not manage to understand, despite some googling. I managed to obtain some code that generates the ...
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139 views

Can I use cross validation on a subset of the training set to select hyperparameters?

I am using R, and I had a dataset with 400000 rows and 800 columns, training a random forest model with only 100 trees on this dataset will take me about 1 and half hour on my laptop. So I went on and ...
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PCA explained variance that increases linearly

I'm wondering what it says about the data when, instead of dropping off dramatically the variance explained by the number of components continues increasing in a reasonably linear manner. For ...
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427 views

Using PCA, clustering, and LDA together

After reading about both algorithms (Principal Component analysis and Linear Discriminant analysis), I started using them combined in a way which appeared intuitive to me. I have a data set that I ...
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What statistical analysis to use to relate multispectral seed data to other conventional tests?

I'm a PhD student at the University of São Paulo, Brazil, and I'm conducting experiments with multispectral analysis of soybean seeds. I have reflectance data for 8 different soybean seed samples, ...
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497 views

Is it correct to standardise (z-score) features within samples before PCA?

Given a data set where we have different measured features in the same units for each subject. For example, numbers of different cell types (features) in a tumour (subject), where we have n tumours ...
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18 views

principal component analysis on reduced data

I have the following experience about PCA and I don't understand why. I first do PCA on the original dataset, say, a collection of three-dimensional vectors $(x_1,x_2,x_3)$. The first principal ...
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192 views

PCA explained variance and clustering

Social scientist here with little background in stats. I have a question regarding a PCA I've carried out on my data. I have 17 variables catching different properties of neighbourhoods (geometrical ...
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FastICA results not exactly consistent on repetition

I have asked this on stack overflow but couldn't get an answer. I am using the fastICA implementation in R. Example code: ...