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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PCA regression coefficients recovery
Assume we have a simple linear model $$y = b^TX + \epsilon$$ for which we want to reduce the number of variables. We perform a PCA reduction on $X$ such that $$Z_{j} = \gamma^{T}_{j}(X-\mu)$$ where ...
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Factor analysis for ordinal data converted from binary ordinal data [closed]
Let’s begin with simple visualization:
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Purpose of expressing data in principal components
I have a rough understanding of the outline PCA. Given $n$ samples of $m$-dimensional data: $\vec{x}_1, \vec{x}_2, \dots, \vec{x}_n$, PCA aims to find an appropriate orthonormal basis called principal ...
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Feature Selection Using Principal Feature Analysis and Variables Factor Map
I am trying to select the most important features that explain the variability of my data using an unsupervised approach in python (would consider R though).
This is after I performed a PCA and ...
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Training data for classification with dimensionality reduction. How do we test the model prediction?
Hi I'm sorry if my question is a bit basic. But I need help with understanding classification with dimensionality reduction. Say I have a training matrix, X containing n $\times$ m. And m is a very ...
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help with principal component analysis using spatiotemporal data [closed]
I'm currently trying to run a PCA in R using the vegan and ggvegan packages. I have environmental data as well as spatial (site) and temporal (day, season, year) data. I'm attempting to show how much ...
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Why does princomp in R stats package use population sd if data is supplied but sample sd if covariance matrix is supplied?
In princomp of the R stats package, I noticed that the "scale" of the output varies based on whether the raw data or ...
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sklearn.decomposition PCA fit_transform() returns different results for the exact same array [duplicate]
If PCA is a deterministic algorithm, how come the results of two separate PCA operations on the exact same array are not even in close vicinity of each other?
EDIT:
It is not a sign problem (used abs()...
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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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Calculating RMSEC and RMSECV of PCA in R
I have been trying to calculate the root mean squares error of calibration (RMSEC) and the root mean squares error of cross validation (RMSECV) for a PCA model made in R using the mdatools package.
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Combining continuous and binary data in unsupervised learning
I am working on cluster detection applied to housing data. Each data point has some continuous features, such as house size, and some discrete ones, such as the number of garages (0 or 1).
At the ...
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Understanding clustering using oblique decision tree
I would like to understand the following post with regards to the code below.
https://www.kaggle.com/competitions/optiver-realized-volatility-prediction/discussion/276137#1559582
Initially, Principal ...
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How to apply PCA results on a Future Dataset?
I have a fundamental question regarding the applications of the results of PCA:
If we have already performed a successful PCA on a dataset of, say, real estate prices of a certain region over the last ...
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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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Scaling and centring in PCA of compositional data
I am following this review's approach for PCA using compositional data. It involves computing the centred log-ratio (CLR) transformation of the compositional data, and then running PCA on the ...
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Principal Component analysis (vector space or inner product space?)
(WARNING: This question might seem dumb)
I see that the optimization problem in PCA involves the notion of inner product. For example, to solve for the loadings in second principal component, the ...
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Link between CCA and PCA
I have two datasets, $X$ and $Y$. I calculate the PCA components of $X$ and also perform CCA on $X$ and $Y$. If I create a model with all the PCA components of $X$, and another model with all the CCA ...
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Time series forecast by Principal Component Analysis
Suppose that I have a series of $M$ time-observations of $N$ "quantities" $z_1(t_1),\dotsc,z_1(t_M)$, ... , $z_N(t_1), \dotsc,z_N(t_M)$. I want to estimate the values of $z_1(t_{M+1}), \...
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Which analysis should i use for group classification?
I have done this PCA analysis and found this score values, now I want to another analysis on this data to see that PC loaded in which "Region" (column 1). Now i did NMDS plot using bray-...
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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 ...
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What is multilinear principal components analysis?
I've gotten a lot of usage out of principal component analysis, and after recently learning the basics of performing canonical polyadic decomposition I was intrigued to learn that there exists a ...
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Which analysis should i use for group classification?
I have done this PCA analysis and found the score values. Now I want to do another analysis on this data to see that PC loaded in which "Region" (column 1). Now used a NMDS plot using Bray-...
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Should I go with an unrotated factor analysis model?
I'm running a project on survey data where I have a bunch of very similar operationalizations of my DV (four different indices of my DV). Let's call it support for X behavior. All of them are ...
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PCA with unbalanced panel
As far as I know, to use Principal Component Analysis (PCA) on a panel of data, data must be balanced.
As an example, consider the returns of the constituents of S&P500 from 1967 to 2020. Because ...
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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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How do I interpret regression coefficients with PCA scores as dependent variable?
I am performing a PCA on four variables all measuring performance on a test in some way. Now I want to use the first principle component (test1_pca) as dependent variable in a linear regression, such ...
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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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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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PCA Questions on the principal() function of psych package
I recently learned PCA and have the following questions on the use of principal() function of psych package:
From 20 variables I decided to keep 4 components / factors.
I used principal() function ...
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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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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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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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Best book for learn principal component analysis
Which book could you recommend for me to study principal component analysis at an intermediate level?
I have studied multivariate statistics, but I want to delve into this topic.
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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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Should I do PCA reduction before applying Mclust()?
I am doing some work where I am meant to apply Mclust() to my data set, with 50000 samples.
I previously used PCA in order to reduce the dimension, which left me ...
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Can you combine to 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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Interpreting plot of PCA results (from 3 to 2 dimensions)
I'm having trouble understanding how to interpret/explain the end result of dimensionality reduction via PCA. Namely, I've attempted to code up a simple example in R but can't really say what happened....
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Frequency parameter of robust PCA for anomaly detection
I am using the R implementation of robust PCA here for anomaly detection.
I have a vector of time series data, and a vector of dates. The algorithm works fine when the length of the vector is a ...
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Can it Work to Run PCA only on a Subset of Highly Correlated Predictors prior to Regularization? (Cox)
I'm running Cox-LASSO (using glmnet as explained by Tay et al) on about 50 variables with about 300 observations. The variables fit into different categories like &...
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Principal Component's Direction for a Matrix
Can anyone give a brief mathematical derivation on how to calculate principal components in PCA for a given covariance matrix let's say -
\begin{pmatrix}
5 & 2\\
2 & 5
\end{pmatrix}
?
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How can I group several variables into 1 variable of interest?
I have a survey data and there are 2 questions (variables from the data at the same time and Likert scaled) that I would like to group them together in 1 variable. This is also, my one dependent ...
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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 ...
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How to balance PCA and LDA in subspace learning?
PCA is a generative model, by which input images or data can be reconstructed. LDA (Linear Discriminant Analysis) is a discriminative model, which extracts better features for classification. How to ...
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How to minimize influence of outliers in PCA for anomaly detection?
Let $\mathbf{X}$ be a dataset of size $n \times d$, where $n$ is the number of samples (days) and $d$ is the number of variables (daily observations). All observations are taken at the same times each ...
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Rank Neurons Importance of the latent space of an Autoencoder using PCA
I am trying to extract only the important neurons from the latent space of an Autoencoder to be converted later to a pattern for a model pattern recognizer.
PCA Loadings helps in finding the highest ...
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PCA: should standardization be applied on features or samples?
I am struggling a little bit with PCA.
I understand that standardization is an important part of the algorithm but I do not understand which elements should be standardized. Let's say I have a 10x100 ...
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I'm getting "jumpy" loadings in rollapply PCA in R. Can I fix it?
I have 10 years of daily returns data for 28 different currencies. I wish to extract the first principal component, but rather than operate PCA on the whole 10 years, I want to rollapply a 2 year ...
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Direction of PC1 and PC2 in Principal Component Analysis (PCA)
I am a bit confused by what is considered the direction for the principal
components in PCA.
For example: I do understand that the picture on the right hand side is correct.
However, is the the PC1 ...
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Generative model for random covariance matrices to fit hierarchical data
I have a multivariate dataset with M groups of data, each consisting of N iid measurements of p variables. Say I take the N measurements from a single widget, and M corresponds to the number of ...
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A method to categorize variations in time series of images
I am working with a time series of remote sensing images from a particular area.
Temporal standard deviation (SD) of these images showed high fluctuations at some regions with SD of 1.17 while some ...
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