Linked Questions

17
votes
2answers
32k views

How to use SVD for dimensionality reduction to reduce the number of columns (features) of the data matrix? [duplicate]

My original data has many more columns (features) than rows (users). I am trying to reduce the features of my SVD (I need all of the rows). I found one method of doing so in a book called "Machine ...
8
votes
3answers
23k views

Understanding the output of SVD when used for PCA [duplicate]

I'm doing principal components analysis (PCA) on quite a bit of data (3000 variables, 100079 data points). I'm doing this mostly for fun; data analysis is not my day job. Normally, to do a PCA I ...
4
votes
1answer
12k views

How to use SVD for dimensionality reduction [duplicate]

After reading several "tutorials" on SVD I am left still wondering how to use it for dimensionality reduction. Here is my confusion in an applied setting. If I limit svd to only considering the first ...
7
votes
1answer
2k views

Interpreting matrices of SVD in practical applications [duplicate]

I have a question regarding the interpretation of the different matrices produced by singular value decomposition. Suppose a mxn matrix $A$ containing n images of m pixels. So each column of this ...
1
vote
1answer
2k views

Truncated SVD: how do I go from [Uk, Sk, Vk'] to low-dimension matrix? [duplicate]

I have a large word-frequency matrix (~6m unique words X ~4k documents) and I'm trying to use truncated singular value decomposition (SVD) to project it onto a matrix with fewer dimensions. I know how ...
5
votes
1answer
1k views

Why are the singular values of a standardized data matrix not equal to the eigenvalues of its correlation matrix? [duplicate]

Conceptually, aren't the eigenvalues of a correlation matrix and the singular values of the associated scaled data matrix supposed to be the same? The below illustration is saying that it isn't so. ...
0
votes
1answer
2k views

How do PCA/SVD Decorrelate the variables [duplicate]

I understood the "technique" for doing SVD and PCA. However, I couldn't understand these two claims: PCA/SVD decorrelate the variables They do so using orthogonal transformations For 1, PCA does ...
3
votes
2answers
2k views

Using the 'U' Matrix of SVD as Feature Reduction [duplicate]

This is a follow-up to the question asked regarding SVD and dimensionality reduction (question). In that question I asked how to use SVD for dimensionality reduction. Although not stated, the ...
0
votes
1answer
1k views

Solving PCA with correlation matrix of a dataset and its singular value decomposition [duplicate]

Suppose I have a $d \times n$ matrix $\mathbf X$ (each entry point has $d$ dimensions) and after some manipulation of data (i.e. summarizing the data $\mathbf X$) I get its $d \times d$ symmetric, ...
3
votes
0answers
1k 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 ...
1
vote
0answers
111 views

Is anything wrong with this approach to PCA? [duplicate]

I'm working on an implementation of PCA that works on very large data sets. Based on my understanding of the algorithm, the first step is to do an SVD of the input ...
1
vote
0answers
98 views

PCA Why covariance matrix? [duplicate]

At PCA why we find the Eigenvalues of the covariance matrix and not the eigenvalues of the matrix $A\times A^T$, where $A$ is the data matrix and $A^T$ its transpose? I saw a professor at YouTube who ...
0
votes
0answers
86 views

How SVD is used for dimensionality reduction? [duplicate]

Given a $M \times N$ data matrix $ D = (x_1, x_2, \cdots, x_M)^{T}$. Applying singular value decomposition to $D$ yields $$D = USV^{T} = (u_1, u_2, \cdots, u_M) \begin{pmatrix} s_1 &&0\\...
0
votes
0answers
67 views

How to re-construct a matrix from SVD [duplicate]

I have a Audio time-series, to which I'm trying to detect the most significant parts of the signal, i.e. the voiced parts and forget the unvoiced parts. $$ T = [0, 0, 1, 1, .....n] $$ I then ...
0
votes
0answers
63 views

The first principal component line minimizes the sum of the squared perpendicular distances between each point and the line [duplicate]

I am currently studying An Introduction to Statistical Learning, corrected 7th printing, by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. Chapter 6.3.1 Principal Components ...

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