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 ...

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Which normalization procedure is suitable for Principal Component Analysis (PCA)?

I have a data-set that has features with different ranges, scales and measurement units so as proposed in literature I'm using Principal Component Analysis (PCA) with "correlation matrix". In this ...
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1answer
26 views

Is continuous inputs an assumption of factor analysis?

Should we use only continuous inputs for factor analysis (FA)? My data is a mix of continuous and categorical inputs: one of the inputs has only 600, 700 and 1000 as values. I found that principal ...
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6 views

Export contribution of every input in every principal component that explained variance percentage in Principal Component Analysis (PCA) in MATLAB [migrated]

How can I export a report like this in PCA function of MATLAB R2015a? 1 to 10 are PCA ...
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1answer
25 views

What are variable weights in principal component analysis (PCA) using MATLAB?

Can I set variable (inputs) weights in MATLAB for principal component analysis using pca() function? There is VariableWeights ...
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19 views

PCA to look at relationships between pretest - posttest changes?

I ran a pretest posttest experiment with two groups. I am interested in looking at how the changes in the measured variables (for example: levels of depression, levels of empathy, levels of anxiety) ...
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1answer
147 views

Why are principal component scores uncorrelated?

Supose $\mathbf A$ is a matrix of mean-centred data. The matrix $\mathbf S=\text{cov}(\mathbf A)$ is $m\times m$, has $m$ distinct eigenvalues, and eigenvectors $\mathbf s_1$, $\mathbf s_2$ ... ...
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40 views

PCA Algorithm & Residual in R

I'm studying the PCA algorithm. But I have a problem with the residuals. I did the same as in the manual below until step 5. From step 6, I don't quite understand the idea, as the dimensions of $Y$ ...
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29 views

Principal Component Analysis on Time series data and panel data

I am trying to build an index on infrastructure and compare the index over the years and between nations. Since the variables are highly correlated with each other, review has suggested me to proceed ...
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20 views

Observations get in a line in a PCA score plot. Something wrong with the data?

I ran a clustering and in the resultant PCA score plot some observations getting in a line drew my attention (I marked them with a red line) . How come they distribute like that? I doubt there is ...
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33 views

PCA on a rank-deficient matrix using SVD of the covariance matrix

I have a high-dimensional data matrix X where sample size is smaller than the variable size. I want to use PCA as a dimensionality reduction method, but I cannot ...
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11 views

Component score covariance matrix [on hold]

What does the component (factor) score covariance matrix in PCA or FA explain?
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23 views
+50

factorial analysis of 2 quantitative + 2 qualitative - inconsistent results

I have a dataset composed of 4 variables, 2 being numerical and 2 categorical (ordinal in fact). They all represent 4 types of indicators/measures of the same phenomenon . I want to analyse them in a ...
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94 views

What's wrong with this visualization of eigenvalues/vectors/PCA?

I have a dataset of 17 people, ranking 77 statements. I want to extract principal components on a rotated correlation matrix of correlations between people (as variables) across statements (as ...
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13 views

calculate the contribution of each variable to the T square score

We use T square chart to monitor the our drives testing parameters. We use $prcomp()$ in R. All PCs and T square can be well calculated. But when we detect a abnormality in our T square chart, we ...
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37 views

Is the use of PCA appropriate to validate a designed questionnaire?

I looked at the questions that may already have my answer but unfortunately it is not the case. I would like to ask again my question which has been revised to fit the rules. I am to measure 5 ...
2
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1answer
42 views

Rotation to get equal loadings in the first principal component or factor

I have the observations of $n$ variables $x_i(t)$ where $t$ is the time, and $i=1,2,\dots,n$ is the number of the variable. They're very correlated, so I wanted to use PCA. The first component ...
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1answer
46 views

Latent Semantic Indexing and Data Centering

In PCA it's common to center the data, i.e. preprocess the data matrix such that the columns have zero mean. PCA can be done via SVD, but in this case the data matrix also has to be mean-centered. If ...
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35 views

Principal Component Analysis [duplicate]

I am doing PCA using Matlab's pca() function and R's prcomp() function. They give identical principal components in some cases and same values and opposite sign in some other cases. Why is this ...
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7 views

Help: testing repeatability within a group, and conducting a PCA for observations within those perhaps-repeatable variables?

I'm trying to analyze behavioral observations of nesting birds within and across various field sites. I know that certain behaviors, such as latency to flight, amount of vocalizations, and defensive ...
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30 views

PCA: scores vs loadings in biplot

I was investigating the interpretation of a biplot and meaning of loadings/scores in PCA in this question: What are the principal components scores? According to the author of the first answer the ...
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1answer
14 views

how to modify covariance matrix of PC scores after rotation of axes

I have performed principal component analysis on a set of observations, retained four principal components and estimated covariance matrix of their scores. Then I have rotated the axes so that the ...
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0answers
10 views

commonalities and differences among groups in a matrix (based on features)

I have a (rather sparse) matrix with 7 columns and 66 rows. Each column represents a user group, each row represents a feature, and each cell represents a weighted value (see note below). I'd like to ...
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13 views

Is sign of loading and score immaterial for interpretation in PCA & Factor Analysis? [duplicate]

Is sign of loading and score immaterial and can be ignored for interpretation? Or is there a important significance for sign when used to interpret the result? I am assuming sign can be ignored ...
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1answer
156 views

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
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13 views

Implementing PCA using Incremental approach [migrated]

I am trying to implement the algorithm proposed in the paper in Section (III) here in R. It uses incremental eigendecomposition and incremental SVD for calculating IPCA. Instead of working on images ...
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1answer
41 views

Difference between PCA and spectral clustering for a small sample set of Boolean features

I have a dataset of 50 samples. Each sample is composed of 11 (possibly correlated) Boolean features. I would like to some how visualize these samples on a 2D plot and examine if there are ...
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19 views

How to plot a 'wachter plot' and compute a p-value for largest eigenvalue for a matrix?

I need to use PCA analysis and want to plot a 'wachter plot' ,which seems like the 'scree plot',and little of literatures metion how to reduplicate the 'wachter plot'; like this: or: some ...
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1answer
46 views

Principal component analysis / multinomial logistic regression

I'm trying to see how level of scepticism impacts willingness to change diet. To measure sceptism I've used a 7 point likert scale. The study I'm basing my research on used a principal components ...
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0answers
15 views

What are the main differences between principal component analysis PCA and factor analysis [duplicate]

I have used PCA in my thesis and would like to argue (in best way) during viva the choice in addition to the fact that PCA analyses the variance of the observed items whereas FA analyses covariance.
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34 views

Plot eigenvectors on scatter plot

I have a problem and need some assistance. I have a scatter plot of two variables $x, y$, and I want to plot the eigenvectors on it. I tried one methods plotting each eigenvector as a line equation ...
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1answer
38 views

Which are the most important predictors (and how great is their impact) of a continuous dependent variable?

I have a continuous outcome (dependent) variable, which is body weight and I'm wondering which of my 20 candidate predictors (independent variables) are the most important ones for prediting body ...
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16 views

Create a 'biplot' (using factor analysis?) showing effect of each input variable on a two-output solution

I have a couple hundred datapoints, each of which has 6 input variables which run through a complex simulation to give two output variables. Because I have two output variables, I can create a nice ...
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6answers
233 views

Why do real-world high dimensional data often have much lower inherent dimensionality?

In a previous year exam about data analysis, there was a question that I'm confused about. Here's the question: Explain why it is natural to expect that in real-world high dimensional data the ...
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2answers
65 views

Meaning of principal components

I have difficulty understanding the meaning of the Principal Components (PC) - On one hand, PC are computed by finding loading vectors that maximize the variance, but on the other hand I read ...
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1answer
26 views

Distances in PCA space

I'm working on a project involving PCA, and my knowledge up till now with this method is quite good. My work involves finding nearest neighbors (having the least Euclidean distance) to a particular ...
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0answers
12 views

Adding point and lines to 3D scatter plot in R [migrated]

I want to visualize concentration ellipsoids in 3d scatter plot in respect of principal components (principal components as axes of these ellipsoids). I used function scatter3d with option ellipsoid = ...
0
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2answers
48 views

Retaining second principal component as a single index

I am using PCA to create an index for my research. In my original dataset, I have 4 main items, (Suppose A,B,C,and D) and one of the items have 4 subitems (for instance, B has 4 subitems, let's say, ...
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1answer
20 views

Fit multidimensional feature into design matrix

I'm having trouble understanding how I can have a multidimensional feature in my design matrix. I understand the concepts of PCA, but I'd rather avoid it. I have the feeling that I'm missing out on ...
1
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1answer
38 views

Isn't an oblique rotation against the whole spirit of principal component analysis?

I am studying principal component analysis (PCA) as a method to deal with multicollinearity. And when studying the rotation method -- which, if my understanding is correct, is the center of the PCA ...
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0answers
24 views

Stratum on subset of data: drop if too small?

We have genotype data for ~20000 samples with 4 principal components and 10 strata - study centres. Formula for an example analysis would be: ...
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1answer
45 views

How do you get the principal components of one matrix along the principal directions of another matrix?

I have a data matrix, A, on which I have performed principal component analysis (PCA) using the prcomp function in R. This gives me the ...
0
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1answer
27 views

Inconsistent Performance of PCA Results from SPSS

I've completed PCA with my dataset (16 variables) and extracted 3 factors. I then created an Excel spreadsheet where I can enter in user provided data and calculate the scores for each of the three ...
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0answers
16 views

Convert principal components based on covariance into principal components based on correlation

I am wondering if there is any way to mathematically express the change in direction of the principal components from the $2\times2$ covariance matrix to the correlation matrix. In other words, if ...
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0answers
35 views

Generalization error of PCA and kernel PCA

I've been recently reading Shawe-Taylor et al. 2005, On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel PCA, where the authors analyze the squared residual of kernel ...
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1answer
29 views

Naive Bayes Binary Classification with Binary Features

I have a dataset with two classes $C_0$ and $C_1$. I have around $10$ to $20$ features that take binary values (either $0$ or $1$). My dataset has around $10000$ instances, with only a hundred of ...
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0answers
23 views

Is it possible to use PCA twice, first on several subsets of data, and then again on the main components of those subsets?

I am interested in understanding if it is possible to use PCA twice, first on several subsets of data, and then again on the main components of those data subsets. I'm not entirely sure if this will ...
1
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1answer
33 views

Does PCA of high-dimensional data yield inaccurate reconstruction?

I have a data $1600\times5000$ matrix $X$ containing 1600 datapoints in 5000-dimensional space. Using MATLAB's built-in pca function, I get the loadings in ...
2
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1answer
56 views

Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations?

Disclaimer: I understand that this question has been answered on CV, but I am asking about the particular implementation, which AFAIK, is not answered yet. I have a $20\times100$ matrix $X$, ...
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1answer
25 views

Nested PCA : is it the same to reduce dimension one time by m and to reduce m times by 1?

My data is initially represented in a vector space $E$ of dimension $n$. I want to reduce the dimension by $m$, so I apply a PCA process to obtain a vector space $E'$ of dimension $n-m$. If I had ...
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51 views

Interpretation of biplot in PCA

Blue points all appear in the lower right-hand quadrant in the plane formed by the first two principal components. Is it a good interpretation of the biplot (right panel) to say that blue points ...