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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84 views

Clustering users with very sparse data

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

Positioning multivariate data in a 2-dimensional space (with PCA)

I have multidimensional data. (11 columns - attributes , 150K rows - number of data). It is slightly sparse-alike data, for example, which means one datum has numeric values like (0, 0, 6.5, 0, 0, 7.5,...
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How to conduct a principal component analysis on data set with large number of zeros

I have data for percentage cover of plant species in 500 sites. There are columns for 30 different species in the data set and I would like to drastically reduce this down to a manageable number of ...
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How to find out when one of a set of recurrent data is behaving unusually

My problem is finding out a week in which week the data about our sales are "strange". We sell 8 products through a third party vendor V. V sends us, each week, the amount sold for each product. ...
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Why do people use PCA when it has so many issues?

(This is a soft question) Recently I'm learning Principal Component Analysis, and it appears to have a lot of issues: You have to transform the data to roughly the same scale before applying PCA, but ...
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scikit learn PCA - transform results - explain why transform does not match dot product of components on original data

I have a timeseries of first differences onto which i apply PCA using scikit to get the first PC ...
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Two questions regarding factors/loadings in PCA (Factor analysis)

Sorry if these end up being kind of naive questions, but I'm only starting to get into this type of data analysis technique: -When I decide to remove a specific variable from my Rotated Component ...
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Does $\text{cov}(a_1' X, a_2' X) = 0$ imply $a_1 \cdot a_2 = 0$?

Let $X$ be a $p$-dimensional random vector with $p$ principal components $y_1, y_2, \dots, y_p$. By definition, a restriction put on the second principal component $y_2 = a_2'X$ is $$ \text{cov}(y_1, ...
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Why do PCA and PCoA give the same components but different explained variances?

I'm quite familiar with Principal Component Analysisis, as I use it to study genetic structure. Lately, I was revisiting some of the functions I was using in R (...
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Is this an example of where I shouldn't scale before doing PCA / PLS?

I'm working with NMR spectra (it's a common chemical test). There are various peaks of the signal across a range of ppm values. I'm trying to relate the NMR spectra of various samples to a ...
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Appropriate dimensionality reduction technique for a small, but high-dimensional sample

I am attempting to conduct some multivariate analysis on a dataset I've been given with a sample size (n) of 23 and a feature number (p) of ~800. I would like to use dimensionality reduction, but ...
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PCA as scaled average of original variables

Let $X_i=(x_{i1},...,x_{ip})$ be a vector of $p$-dimensional $n$ observations. Suppose that we apply principal component analysis and find the $p$ principal components. Also, suppose that the $p$ ...
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How to calculate the critical DmodX value from a PCA?

R has a DModX Calculation for PCA. I've seen references in some online texts that a critical DModX can be used to flag samples which are significantly poor fit to the model. The R documentation states ...
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38 views

Principal component analysis in two dimensions

During my studies, I stumbled upon the following exercise: We have the following joint probability distribution: $$p(x,y) = p(x) p(y|x)$$ $$p(x) = \mathcal{N}(0,1), p(y \mid x) = \frac{1}{2} \delta(y ...
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Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
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How to decide if a rotation is necessary in a factor anaysis?

I have a (self-report) scale with 18 items. The scale as a whole is very reliable ($\alpha = .92$); however, the original authors report two sub-scales. Here is the interesting thing that I don't ...
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Principal Component Analysis - Why Use Eigenvectors of the covariance matrix? [duplicate]

In PCA we start with a dataset and we reduce its dimensions by giving it new features that are each a linear combination of the original features of the dataset, and only keeping the ones with maximum ...
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Is there a PCA quality metric to compare data subsets?

I would like to see if on a subset of the data (selected by a range of a particular feature) 2-component PCA does particularly well. Is there a quality metric - apart from explained variance - which ...
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Percentage of variance explained by rotated factors (PCA, Stata)

I am carrying out an exercise in Principal Component Analysis in Stata. I have created my own rotated factors after carrying out the PCA, and am looking to check the percentage of variance that is ...
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When to use PCA vs LDS vs nMDS for microbiota dataset?

I'm trying to understand the certain situations in which you would use the 3 above ordinance/rank tests over the other in terms of microbiota count data. Typically, I have been told to use nMDS over ...
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When doing pca on a specific cnn feature map, is the pca substance always the same regardless of the input?

Lets say I have a pretrained CNN, and I extract the feature map from one of the layers for some input data x. I do the same thing for for a second set of input data y, which is very different from ...
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Interesting Way To Implement Factor Analysis From PCA

Is it possible to modify the PCA algorithm so that it actually implements factor analysis? We can assume that the uniquenesses are known. I'm aware that for a $d$-dimensional data $x$, PCA takes the ...
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Correlated component scores after PCA with varimax rotation in Stata

I have a dataset with 6 personality traits for 155 individuals that are highly correlated. To get rid of multicollinearity (and potential noise in the original variables) in my regression analysis, I ...
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Can the sum of the variation explained by PCA ever not match the total variance of the original data matrix?

For example if using skikit PCA when might the following not hold assuming we have a data matrix with 4 columns (features): ...
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Question about PCA

Correct me if I am wrong anywhere. I understand PCA is used to determine what component(s) of a given dataset could be of more use than the other. By #1, I understand, for a structured dataset (with ...
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Scaling Variables in PCA, yet all on the same scale

I know this topic of scaling and normalizing variables for PCA has been posted on a lot, 1, 2, 3. However, I am performing PCA on coordinate data that is measured all on the same scale, i.e. (x,y) ...
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Calculating PCA coefficients using SVD, PCA (sklearn) and Covariance Matrix

I am trying to understand PCA implemented in different methods on python. I am failing to get equal PCA coefficients in each of the methods. By PCA coefficients I mean data projected in the principle ...
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2answers
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PCA in production - use with incoming data

I have a large training dataset that I used to fit a model. Before fitting the model I applied PCA. Now the model is fit and ready to be deployed to production, where it will make predictions one ...
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1answer
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Is it possible to specifiy the components to use in PCR (in R)?

For a class project, my group and I are looking to play around with PCR since we didn't get a chance to dive into much details in class. We were going to look at a few different ways to select the ...
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Guidance on analysing my PCA plot / NLP methodology,

I have been analysing documents which also contains chapters. I use TF-IDF to generate the word embeddings and then take the cosine similarity of a document chapter at year ...
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110 views

High dimensional clustering (K-means and DBSCAN)

My research is all about comparing the K-means and DBSCAN(Density-Based Spatial Clustering with Application of Noise) and I used python with the aid of jupyter notebook. I have 28 variables and 3048 ...
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1answer
193 views

Calculate first principal component direction and scores

Given that x1 = (9, 9, −18)^T and x2 = (18, 9, 9)^T with eigendecomposition of its sample covariance matrix Σ = cov(X) How do I calculate the first two principal component direction and the ...
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Finding dependence of output variables on input variables

I want to perform a regression using neural networks. My input has 5 parameters [a, b, c, d, e] and the output is 4 variables [x, y, z, w]. Total number of observations I have is 1000. I wanted to ...
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Is it reasonable to include both principal component analysis (PCA) and Structural Equation Modeling (SEM) into a single regression?

Seems a bit silly to do both. Using PCA cleans up the way the model looks, bu reducing number of variables, but it seems like you would suffer an (unnecessary) loss of information.
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Hierarchical Factor Analysis - Analyzing the factor structure of an identified factor

Problem Summary After performing an exploratory factor analysis one of the resulting factors "contains" a lot of variables which make its interpretation very hard. Since all the other factors have a ...
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1answer
48 views

The relation of eigenvalue and PCs in PCA

In R, I got the result of PCA and eigenvalues and vectors and three eigenvalues above 1 were checked. If so, is it valid data from PCA results to PC1 ~ 3? Here is my eigen values and vectors, ...
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1answer
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Eigenvalues as weighting factors for projection results on corresponding eigenvectors in PCA

In the paper Novel PCA-based Color-to-gray Image Conversion, the authors project the three-dimensional $(R, G, B)$ value of each pixel onto a one-dimensional grayscale space via a curious application ...
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1answer
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Linear and Non-Linear dimensionality reduction with missing variables

I'm trying to compare the two types of reduction by applying it to a list of ingredients for about 1000 sponge cakes. The ingredient lists do however have miss certain ingredients out for some cakes, ...
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PCA whitened data

Let $X$ be a feature matrix of size $m\times d$. I understand that the standard PCA whitening process follows three steps. (Centerization) ${X} \to \hat{X}:=({X} - \mu)$, where $\mu$ is a matrix of ...
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1answer
120 views

First Component in PCA

I was doing the Andrew Ng's ML course, and one of the solutions mentioned The first principal component is aligned with the direction of maximal variance. I didn't get what it is trying to say.
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Why we try to capture variability?

I am new to Statistics and I have a Mathematics background. In Statistics, particularly in Linear Regression and Principal Component Analysis (PCA) so far what I have understood is that the main idea ...
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1answer
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Top principal components versus most significant random forest variables

I was working on making a supervised learning model starting with a database of about 100 features and 1000 data entries. My goal is to predict a certain target variable. I tried three different ...
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Visualising sentence vectors by averaging word vectors

I have $82114$ sentences for which I have found the vector representation by summing over individual word vectors(using Word2Vec). Now I have a vector representation for each sentence in my dataset. ...
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1answer
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Computing the trace of the sample covariance of projected data

Problem For a given dataset $\{x_1, \dots, x_n \}$ where $x_i \in \mathbb{R}^d$, assuming that we project each $x_i$ onto a unit vector $u$, and denote the projected data point as $\tilde{x}_i = (x_i^...
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How to identify and reduce question overlap and redundancies in a survey? (remove questions asked for a more concise survey, w/o losing information)

Suppose I have a survey that contains 30 items. The items ask about the relationship between the respondent and their family, in many different realms. For example, the strength of the connection ...
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Dimensionality reduction before clustering cosine data values causes a change of scale

In my experiment, I am doing hierarchical agglomerative clustering of texts (parameters: cosine, average). My features matrix is very sparse, so I considered PCA as dimensionality reduction technique. ...
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Plot of two ordinal variables?

It is common to represent various (ordinal, social) attributes on a pair of axes as in the examples below. In general, what is this sort of graph/representation called? It is, perhaps, useful to ...
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1answer
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Selecting Mutually Exclusive PC from a PCA Analysis in R

I have run a PCA Analysis on some code and it produced a PCA analysis; however, I want to identify which PC are mutually exclusive and use them in a logistic regression. According to the PCA analysis ...
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Dimension Reduction on Data with both Spatial and Non-Spatial Variables to Train a Logistic Regressor for Cross Sectional Time Series Data

I need some help on how to process and analyse a study of mine. I'm running a study on mice to look at the effect of diet on cells over a series of time. My mice are divided into two groups, one group ...