Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of variables preserving as much information (as much variance) as possible.

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How to create an index of a several variables that best summarizes them?

I want to describe the "influence" of some internet content, where "influence" is loosely defined as its virality/popularity among the audience. For each link, I have information such as the number of ...
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PCA Transforming back to original space from a subset of principal components

I applied PCA on a 12000 x 500 data set (12000 data points with 500 features). PCA gave me 12000 x 20 data (20 features). Is there any way to transform the results back to the original data space? (To ...
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15 views

Is PCA the best method for my question/data?

I have a sample of 32 subjects who corrected grammar issues in 6 texts. Not all subjects saw all texts - a latin square design was adopted and each subject saw 2 texts. I'm interested in a general ...
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Inverse PCA Whitening - get the data back into its original space

I'm currently performing the following PCA-whitening in Python: ...
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Meaning of “reconstruction error” in PCA and LDA

I am implementing PCA, LDA, and Naive Bayes, for compression and classification respectively (implementing both an LDA for compression and classification). I have the code written and everything ...
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21 views

In PCA, are PC scores the same as factor scores?

Are PC scores and factor scores the same thing? If so, are PC scores just the original but centered scores multiplied by the i-th eigenvector? Is the corresponding i-th eigenvalue the variance of ...
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59 views

Can PCA be applied twice or more?

I have a very high-dimensional dataset with 27k features. I want to a reduce the dimensionality of the dataset. I want to use PCA to reduce the dimensionality to 2 as the toolbox I am using expects 2 ...
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Time series forecasting with many predictors

Suppose I want to forecast a time series $y$ using its own lags and a large set of potential candidate predictors $X$. The model could be specified as follows: $$y_t = a + \rho \cdot y_{t-1} + \beta ...
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PCA to decorrelate and classify timeseries

I have a labeled dataset where each subject belongs to one of two classes A or B, with A ...
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16 views

Performing PCA on a tetrachoric matrix in SPSS

I am currently working on a project where I have nine dependent variables, each binary, measuring similar outcomes. Accordingly, I'd like to perform a principal component analysis on them to reduce ...
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52 views

What does it mean when all eigenvalues of a correlation matrix are zero?

I am applying PCA to a dataset. After calculating eigenvalues of the covariance matrix I noticed that all eigenvalues are equal to zero. Can anyone please explain to me what does it mean when all ...
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15 views

Principal Component Regression In R using Caret [closed]

I am trying to build a model using Principal components Regression. I first build the model on the training data set using the Caret package : ...
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24 views

Normalization after PCA Whitening (for Deep Learning)

When training a Deep Learning model like an auto-encoder, is it necessary to normalize data again after it has been processed by PCA Whitening? Right now I zero-mean my data before PCA and use the ...
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After running kernel PCA on the training data, how to apply it to a new data point? [duplicate]

My data set has a training set of 1000 input with 6 features (data set size is 1000*6). I applied kernel PCA to the data set and reduced the number of features to 3. It means that the dimension of the ...
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1answer
29 views

Need guidance on image classification problem with large feature matrix

So I've got an interesting problem that I'm struggling with and I wanted to hear some ideas on possible solutions. The data is not public and I can't go into much detail. The problem involves a ...
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23 views

Units of measurement on a two-dimensional PCA scatterplot

I have a dataset that consists of the average consumption of 200~ types of food in grams per person per week for several countries, much like the dataset described at the bottom of this page Eating in ...
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9 views

Adding Factor Scores after PCA to create index

I am creating a single index and have narrowed my variables down to two Components using Principal Components analysis (varimax rotation). I have a ton of literature/theory that states that the two ...
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1answer
23 views

Removing a principal component [closed]

What is the aim of removing a principal component from a data matrix and how would you do that in R?
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26 views

Restoring original data after PCA using loadings and getting a wrong magnitude [duplicate]

I have a dataset containing 5 variables. I want to take 1st PC of that dataset. I calculated covariation matrix for centered data: S = X'X. Then I took largest ...
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17 views

Valid procedure for binary classification with cross validation

I have inherited a classification model for a binary parameter and have been asked if estimates can be improved. From this model, an equation has been put into some software for predicting this ...
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10 views

Choosing orientation for kernel principal component analysis

I have a matrix with orientation [1500x93]. The 1500 corresponds to 1500 time samples and the 93 corresponds to the X,Y and Z coordinates for 31 markers. I am performing principal component analysis ...
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8 views

Index Creation using Ordinal Variables and Principal Components

I am creating an index based off 5 ordinal variables [coded 0,1,2,3]. I ran a Factor Analysis / PCA on the data and it shows that they all fit on a single factor, explaining ~50% of the variance. I do ...
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14 views

Using Modified Z-score or Mahalanobis distance to detect outliers

I am working on a piece of MATLAB code that performs PCA and I would like to be able to detect points in the data that are outside the cluster, such as points with labels Part A1 and Part A7 in the ...
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51 views

When to use PCA vs. OLS

Let's say I want to build a factor model to explain (excess) stock returns--think Fama-French, for instance. Obviously one could use OLS to fit a model, but I've seen PCA used as well. What are the ...
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23 views

Inferences from PCA plot

I have done a dimensionality reduction of binary labelled data (0,1 labels) from 300 features to 2 features. The plot looks like - What kind of inferences can I make from this plot? Can I infer - ...
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51 views

Dimension reduction using PCA in Matlab

I have a $152 \times 27578$ matrix, $152$ samples and $27578$ features, and I used the PCA function for the dimension reduction in Matlab. ...
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PCA (with phi/tetrachoric correlation matrix) or LTM to study the correlation of (true) dichotomous variables?

I am doing a study were I have to initially do an exploratory analysis by grouping diseases that coexist in my study population. For that I have x diseases/variables that are (true) dichotomous ...
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31 views

How to compare PCA with KPCA for dimension reduction?

Both linear principal component analysis (PCA) and kernel principal component analysis (KPCA) are unsupervised dimension reduction methods. I have a dataset with $4000$ training samples and $40000$ ...
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Relationship between eigenvectors of $\frac{1}{N}XX^\top$ and $\frac{1}{N}X^\top X$ in the context of PCA

In Christopher Bishop's book Pattern Recognition and Machine Learning, the section on PCA contains the following: Given a centred data matrix $\mathbf{X}$ with covariance matrix ...
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62 views

Prove that $XX^\top$ and $X^\top X$ have the same eigenvalues

I'm not sure how to do the following exercise. Could someone help me by either suggesting the knowledge I should have to solve this, or pointing me out in the right direction? I have tried to expand ...
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22 views

Calculating Objects Scores in CATPCA when you have missing values?

I am doing a survey for my workplace and I am analysing the Likert questions using a CATPCA. The problem I have is that the respondents were permitted to answer 'N/A' or 'I don't know' which have been ...
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96 views

How does Principal Component Analysis help me understand my data?

I have a dataset which contains 10000 examples. Each example has 100 dimensions. These dimensions have the same scale. I clustered all examples using their 100-dimensional vectors and drew the elbow ...
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1answer
60 views

Off-diagonal elements of a correlation matrix after removing the first principal component

I have some data with more variables than observations, that I'd like to subject to a principal components analysis. For didactic reasons (to give an intuition for factor retention criteria under ...
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CATPCA Missing values

I have posted a question on stackexchange and you answered me very well before. Thank you. I have another CATPCA question and I want to ask to find out how missing values are used if you select ...
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Doing PCA with varimax rotation in R [migrated]

My code has gone south. I'm importing a data 578x17 sheet from csv using the: ...
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102 views

Relationship between cointegrating relationship found via PCA and that found via a Johansen test

Thanks to the explanation given here: PCA on prices or returns I understand how PCA can be used to derive cointegrating relationships. However there is of course another well known method to ...
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43 views

Different clustering for different rotation of PCA

i´m working on an application which is used for clustering. The process is done in SPSS. As the input-data can have a large number of variables/colummns as a pre-clustering step the PCA is run (via ...
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PCA (varimax normalized): are factor scores negative or positive?

When doing a Principal Component Analysis, with varimax rotations, we can get the factor scores based on correlations for each variable. These scores are either positive or negative, does it still ...
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Apply PCA on classification data, category wise or on complete dataset?

I have a classification related image data with 15 different classes and each class has five feature sets. Those five feature sets comprise of colour features, sift features etc.. upto 5 different ...
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PCA on prices or returns

This question has been addressed here: Can Principal Component Analysis be used on stock prices / non-stationary data? In his answer Jon Egil wrote please make sure you analyse returns not ...
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Maximizing the utility of performing PCA

Besides for generating a biplot and screeplot, are there any other useful graphical outputs that I can obtain from running PCA on a multivariate dataset? So, to sum up, my question really comes down ...
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55 views

random forests for optimal variable selection/feature selection

Gurus, I just came across this tutorial (http://blog.datadive.net/selecting-good-features-part-iii-random-forests/) about using "random forests" for optimal variable selection/feature selection. The ...
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How to compute the variances of PCA-transformed variables?

In principal component analysis (PCA), what is the covariance matrix in the new space of reduced dimensionality, i.e. the covariance matrix after multiplying the data by the eigenvector matrix? I ...
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Principal component analysis to reduce the number of observations

Principal Component Analysis (PCA) seems great to reduce the number of variables, but is it also good to reduce the number of observations? Here is an example: reflectance measurements were taken ...
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Data size reduction using Principal component analysis

I have a 5113 x 2 matrix with only two dimensions and I need to use PCA to reduce the size of my data retaining both of my dimensions. I need to reduce size of my input data such that the file size ...
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1answer
17 views

Groups of highly correlated variables within Regressions - dimension reduction by variable groups

Dear Cross Validated Users, I am addressing myself to you with a question for which I couldn't find an answer despite intensive googling. I want to run a regression with a multitude of independent ...
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28 views

what is the best approach for factor analysis when the data has more attributes than inputs? [closed]

i think i should ask the question like this: i am having a data set of 20 participants with 89 attributes , almost all of the attributes have values between 5 to 0 and there exist more than 20 ...
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What is effect on PCA of having too many zeros in the data?

I want to use Principal Components Analysis to derive dietary patterns. However, my data have many zeros (no intakes) for many observations. I'm unable to find relevant literature to know how biased ...
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1st PC irregular in Supervised Principal Component Analysis

I am using superpc package to carry out supervised principal component analysis on my data. I am using the following link as reference http://statweb.stanford.edu/~tibs/superpc/tutorial I am using ...
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PCA scores from SAS (what's going on in the background) [duplicate]

I'm having a hard time explaining what's going on in the background (stats) when SAS creates component scores after running a PCA. I understand that the default method for SAS component scores is the ...