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Principal axes, what are they and how to decide them? [duplicate]

I am reading a book about data mining and am currently in a chapter about Principal Component Analysis. But I am not sure from the explanation in the book what the principal axes are and how to find ...
1k views

*Why* are eigenvectors the principal components in Principal Component Analysis? [duplicate]

I am confused as to why eigenvalues are the principal components. What is the intuition behind finding the eigenvectors of the covariance matrix for PCA?
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How does PCA represent all data with just a few principal components? [duplicate]

How does principal component analysis (PCA) model data of admittedly higher dimensionality with just a few principal components?
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What exactly is a Principal component and Empirical Orthogonal Function? [duplicate]

I am trying to enhance the contrast in the images I get after scanning a surface using Thermography (Principal Component Thermography ~Rajic, which is basically an application of Principal Component ...
302 views

Co-variance matrix, Eigen vector and Eigen values [duplicate]

What does eigen vector with largest eigen value mean and how it has effect on covariance matrix?
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Principal Component Analysis (PCA) for binary data [duplicate]

First of all, I would like to note that I have read similar topics in CrossValidated but I am not fully satisfied. I have a dataset which consists of an $N\times M$ binary matrix. 1 means that an ...
264 views

How are eigenvectors and principal components related? [duplicate]

Possible Duplicate: Making sense of principal component analysis, eigenvectors & eigenvalues I am currently going through a PCA tutorial. However, I am a bit confused. For PCA, we calculate ...
181 views

Can someone explain the simple intution between Principal component 1, 2, … etc in PCA? [duplicate]

I see that in PCA the first principal component maximizes the variances amongst all the points within the data set. What exactly does this mean, what does it show and what does every other principal ...
148 views

Why the principal components correspond to the eigenvalues? [duplicate]

Suppose ${\bf{X}} = ({X_1},{X_2},\ldots,{X_n})$ are the original components (also random variables) and ${{\bf{w}}_j} = ({\omega _1},{\omega _2},\ldots,{\omega _n})$ are loadings for the $j$th ...
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Does PCA create new features or give weights to old ones? [duplicate]

I know that Principal Component Analysis (PCA) is the eigenvector of the covariance matrix. It is used as a tool for dimensional reduction. What I am confused about is whether the PCA give weights to ...
44 views

Computing 1st principal direction of 3 points in 2D [duplicate]

I am a little bit confused on the first principal directions. Say I have three points in a two dimensional euclidean space: (1,1), (2,2), and (3,3) and I want to calculate the first principal ...
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How PCA locates the origin (centre of data points) in the new space? [duplicate]

I am reading a document on PCA. I got some idea that PCA is a dimensionality reduction technique. It performs this tasks by shifting the data points in the new space. The centre of points in the old ...
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Examples (and how to generate them) of various conceptually different datasets to throw at PCA to gain better intuition for it [duplicate]

I've developed a solid understanding of principal component analysis to the point where I can actually write my own implementation of it in python. I fear this is the easy part where the hard part is ...