Linked Questions

5
votes
1answer
5k views

How to understand “factor loadings” in PCA? [duplicate]

I have seen that some people are talking about "factor loadings" in PCA. It is a topic that I do not manage to understand, despite some googling. I managed to obtain some code that generates the ...
1
vote
1answer
3k views

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 ...
1
vote
0answers
2k 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?
-1
votes
2answers
739 views

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?
3
votes
0answers
741 views

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 ...
0
votes
1answer
483 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?
0
votes
1answer
345 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 ...
1
vote
0answers
330 views

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 ...
0
votes
0answers
292 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 ...
2
votes
0answers
175 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 ...
0
votes
1answer
150 views

Principal component anaylsis, what do obtained coefficients tell me? [duplicate]

I have already posted my problem in stackoverflow, I am not sure if this might be problematic, and I am not sure, if the post is shown in both communities. If so I will delete. I am trying to apply ...
0
votes
0answers
103 views

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 ...
0
votes
0answers
83 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 ...
0
votes
0answers
46 views

How to get an intuition to draw the eigenvectors for PCA? [duplicate]

For exam preperation I want to know how to get an intuition to draw in the eigenvectors corresponding to the smallest and largest eigenvalue. Student friends say "just get the direction of the largest ...
0
votes
0answers
44 views

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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