Principal component analysis is a technique to decompose an array of numerical data into a set of orthogonal vectors (uncorrelated linear combinations of the variables) called principal components. The first few principal components often suffice to grasp nearly all the multivariate variability of ...

learn more… | top users | synonyms (1)

3
votes
1answer
37 views

Reference for dimension reduction techniques

This is a follow-up question to Is PCA appropriate for comparing subsets of panel data?. It turns out that, yes, PCA is appropriate. But there are also many other ways to reduce n-dimensional data to ...
0
votes
0answers
21 views

Minimizing the Training data

I have a grey-box model of the form Y= a + b X1 + c X2. Where a, b and c are the coefficients based on regression. The regression variables X1 and X2 are determined based on ...
1
vote
0answers
37 views

How to create a composite of several variables without throwing information away

I want to create an index as a composite of several variables. It was recommend to me to use PCA. However, PCA discards too much information - essentially throwing away several of the variables in ...
0
votes
0answers
15 views

how to handle occlusion for face recognition?

If there some occlusion on face (such as sunglasses, mask, scarf), the recognition rate will decrease steeply? How to handle this case? I have do a survey, the PCA reconstruction method have been ...
0
votes
0answers
7 views

calculation of composite scores from factor analysis

We're designing a survey where we ask students to indicate their level of agreement (likert scale 1 - Strongly agree....5 - Strongly disagree. We ran factor analysis on the data and obtained 4 ...
1
vote
1answer
38 views

Is PCA appropriate for comparing subsets of panel data?

I have a large panel (5000+ subjects, 4 variables over 182 periods), and I've identified particular Granger-causal relationship in a large subset of those subjects (30% or so). I would like to somehow ...
0
votes
1answer
13 views

variable reduction

I have a set of features and a score in my dataset. Score is defined based on these features. What technique is used to see which of the features is more effective in the total score? I used anova and ...
0
votes
0answers
27 views

Can PCA scores be used as dependent variable?

I am working on a research project where I have several questions from a survey data that measures the same underlying quantity (my dv), possibly each with some measurement error. I was thinking about ...
2
votes
2answers
26 views

Dimensionality reduction (PCA) for plotting text documents on a graph

I have 50 text documents There are 500 possible words, after a stop list has been applied My term/document sparse matrix is therefore 50x500 I'd like to cluster these documents. One easy way to do ...
1
vote
0answers
27 views

Using a PCA to reduce response variables or multivariate multiple regression?

Does it make sense to use a PCA (principal component analysis) on a set of response Y variables and then conduct a multiple regression, or carry out a multivariate multiple regression all response ...
0
votes
1answer
15 views

Multivariate regression or PCA to reduce response variables?

I hope the title is self-explanatory, but essentially I want to know which method is better: does it make sense to use a PCA to reduce a number of response Y variables and then conduct a univariate ...
1
vote
0answers
20 views

Predict/impute one cell of matrix using all other cells

The question: I want to predict/impute one missing cell of a matrix using the contents of all other cells. Anyone have ideas on how to do this? The context: The matrix is n people's responses to m ...
0
votes
0answers
34 views

Can Principal Component analyses be applied to a counting trait?

I am analyzing a segregating population of plants coming from an hybridization process. The experiment consists in several field plots (according to an augmented design). In each plot a segregating ...
1
vote
1answer
100 views

Pull out most important variables from PCA

I would like to get the most important variables from a PCA result. I see two clusters in the plot. I now that is possible that there is no only one variable causing this, so maybe I would have to get ...
0
votes
0answers
21 views

Rotation of Mean Centred Variables in Principle Components Analysis

I'm looking to manually (Excel) perform PCA without any statistical packages such as R, but having trouble understanding how to rotate the original variables to find the maximum variance for the new ...
1
vote
0answers
21 views

Can I use non-linear PCA (CATPCA?) on my multivariate dataset that contains nominal AND ordinal data?

In my multivariate dataset I have over 100 objects/cases that have been coded on 20 different variables. Several variables are ordinal and several variables are nominal. Is it possible to use ...
1
vote
1answer
46 views

Principal components using correlation matrix in R

My understanding is that prcomp and princomp work off the dataset itself (row of observations, across variables in the columns). ...
0
votes
0answers
17 views

Intuition behind which eigenvectors to use in PCA for orthogonal regression

I am learning PCA, and while this seems like an obvious question, I can't seem to understand some of the ideas behind which eigenvectors to use when performing orthogonal regression with PCA. My code ...
1
vote
0answers
29 views

Can seasonality be detected / explored with principal components analysis?

I have a rainfall data consisting of around 95 years for the rows and twelve months of the year for columns. So this is a 95x12 matrix, not a column vector. Can I derive any idea about the months to ...
3
votes
1answer
39 views

When is it appropriate to use PCA as a preprocessing step?

I understand that PCA is used for dimensionality reduction to be able to plot datasets in 2D or 3D. But I have also seen people applying PCA as a preprocessing step in classification scenarios where ...
0
votes
0answers
16 views

Is subtracting the mean from PCA necessary when using an SVD result that is feature scaled?

I've applied SVD to the original data matrix and eliminated insignificant columns and rows from U and V^T respectively using the Sigma values. I multiplied together my optimized U, Sigma, and V^T ...
1
vote
2answers
42 views

Is it important to convert “integer” variables (with 0 or 1 values) to factors?

I am working on a high-dimensional dataset (1776 variables). When I read the csv file, R loads variables (with 0 or 1 values) as class of "integer". Is it important to convert these variables to ...
0
votes
1answer
19 views

What is the range of values that can be expected in the result of Principal Component Analysis (PCA)?

I want to normalize all of my preprocessing techniques between 0 and 1 so I want to know what the PCA range of values is so that I can apply a proper normalization to it. I applied PCA by using the ...
0
votes
0answers
14 views

Reconstructing a vector after projection

Suppose one has a matrix of data $X$, which is $n$ observations by $p$ dimensions. Let $P_\perp$ be a projection onto some $k<p$ dimensional subspace. Suppose one computes the principal direction ...
0
votes
0answers
14 views

Feature selection from wavelet transformation in R

I am new to wavelets. Currently, I am developing a prediction model using time series data. I am using the wavelets package in R. I am taking part of the time ...
3
votes
2answers
92 views

Best practice for dimensionality reduction using Principal Component Analysis (PCA) and/or Linear Discriminant Analysis (LDA)

Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via ...
0
votes
0answers
23 views

Is there an ideal number of measures in PCA ?

Working on a problem of extracting a minimal sub-set of criteria in a siting problem, I resorted to PCA, I have only 26 individuals (measures), I naturally thought it would be wise to ask whether that ...
0
votes
0answers
25 views

Correlation tests – multivariate correlation matrix?

I just got comments from a reviewer to a submitted article and didn't understand what I should do very well. Here are the tests I performed: We first used principal components analysis (PCA) to ...
2
votes
4answers
237 views

Clustering binary categorical data

I have some data where I have certain classes (c1, c2, c3, c4 ...) and the data comprises of binary vectors where 1 and 0 denote that an entry belongs to a class or not. The number of classes will be ...
2
votes
4answers
69 views

Impractically long running time PCA command in R RStudio

I am using R in RStudio on OS X ver. 10.9.2 on 1.7 GHz Intel Core i7 with 8 GB RAM. I am trying to run a PCA command (prcomp) and plots on a dataset with ...
3
votes
1answer
75 views

Not normalizing data before PCA gives better explained variance ratio

I normalized my dataset then ran 3 component PCA to get small explained variance ratios ([0.50, 0.1, 0.05]). When I didn't normalize but whitened my dataset then ran 3 component PCA, I got high ...
1
vote
0answers
26 views

Representing a distance matrix in the plane [duplicate]

I've worked with observations as vectors with both continuous and categorical variables. In both cases one can use dimensionality reduction techniques such as PCA (in the latter case through ...
0
votes
0answers
31 views

PCA proof needed for proportion of variance explained by L PCs = mean R-square from regression on PC scores

I observed the following relation and would like to know where I can find a general proof for this: Assume a data matrix $A = [a_{ij}]_{t x k}$. 1) Perform principal component analysis (PCA) using ...
2
votes
0answers
53 views

Factor analysis - CATPCA combined with conventional PCA

I have some concerns regarding factor analysis and especially about combining the factor analysis for an ordinal scale (categorical data) - CATPCA with conventional PCA. Basically, I need to enter my ...
0
votes
0answers
27 views

Principal component analysis, psychometrics, and number of items required

I saw that questions regarding sample sizes and PCA are asked here quite frequently. However, I was not able to find exactly the information I need. I plan to do a psychometric study and conduct a ...
0
votes
0answers
29 views

Effect sizes from regression analysis and factor loadings

To do a meta analysis, I try to calculate effect sizes. In an article by Shah and Ward, the authors do a regression analysis after combining various factors by a CPA to four factors. The factor ...
1
vote
2answers
73 views

R and SPSS differences in pca loadings

I performed two principal components analyses: in R and in SPSS - using the same dataset and the same variables. I got the same results - at least to some point. The eigenvalues are the same (I used ...
4
votes
1answer
52 views

Principal component regression analysis using SPSS

I have done multiple regression analysis (MLR) of my data and find out $R^2$ and $r$, and then to remove multicollinearity problem I used PCA. This analysis generated PC equal to my variables, I ...
2
votes
1answer
26 views

Method to compare ratings from multiple different sources with missing data

I want a method to compare ratings from multiple sources and find a single measure that best reflects all the ratings. To give a specific example, let's call it "The fellowship review committee ...
1
vote
1answer
94 views

What is the difference between loadings and correlation loadings in pca and pls?

One common thing to do when doing Principal Component Analysis (pca) is to plot two loadings against each other to investigate the relationships between the variables. In the paper accompanying the ...
-1
votes
1answer
57 views

factor analysis for given data with help of matlab

suppose that we have following data i have done covariance matrix and eigenvalue decomposition ...
0
votes
0answers
38 views

PCA eigenvalues meaning

When projecting the data set on the Eigen vectors of the co-variance matrix , the eigenvalues represent how much each example varies away from the mean of the data set in the projected direction , ...
0
votes
1answer
35 views

Question about PCA data recovery equation

In PCA , consider a 4 x 3 data matrix ( 4 examples each with 3 features ). After getting the 3 eigenvectors (a/b/c) and projecting data on the first 2 vectors, the equation looks like this : [ first ...
1
vote
0answers
20 views

Stock Returns Covariance Prediction - Number of Principal Components

I am working on the following problem. Given N days of stock returns, I compute the covariance matrix for stocks. I then use Probabilistic PCA to "shrink" the covariance matrix. I am trying different ...
0
votes
1answer
72 views

PCA on Binary Data

I having binary data set (yes/no), so can I apply PCA on that. Is it mathematically correct to do that. In my opinion Binary variable can only be subjected to logical operations, so how it can be ...
0
votes
0answers
28 views

Asymptotic principal component analysis

I understand how principal component analysis works. However, in a financial time series sense, I do not understand why the number of observations should be larger than the number of dimensions. I am ...
0
votes
1answer
40 views

Calculate principal components

Given the following data: ...
1
vote
1answer
48 views

Understanding PCA - How to calculate scores

I'm looking for advice to whether or not the following method is good and is standard for calculating PCA of the data. So the examples that I will give will be small. Given a matrix of $A = [4, 6, ...
1
vote
0answers
26 views

Principled approach for PCA on correlated variables?

Related to Should one remove highly correlated variables before doing PCA?, PCA is used a lot in population genetics to essentially cluster individuals into ethnic group based on their genetic markers ...
0
votes
1answer
20 views

Literature for Cross Validation on Sparse Data?

I've read a lot about Cross Validation to estimate prediction error, specifically for selecting the number of components in a PCA model (I'm not doing SVD/PCA, but it's very similar), but I can't find ...