Linked Questions

1
vote
0answers
390 views

Is there a name for “uncentered covariance matrix”? [duplicate]

If I have an $n\times p$ data matrix $X$ with $n$ observations, one in each row, and $p$ variables, one in each column, then I can call $XX^T$ "gram matrix", but is there also a name for $X^TX$ or $\...
2
votes
1answer
242 views

What does the matrix $\frac{1}{n-1} X^{t}X$ represent? [duplicate]

Let be $Y$ the matrix of observations with $n$ lines and $m$ columns. Let be $X$ the centered matrix, where $X_{i,j} = Y_{i,j} - \overline{Y_{.,j}}$ , $i = 1:n$, $j = 1:m$ Edit : $\overline{Y_{.,j}}$...
1
vote
0answers
90 views

Reading and interpreting the scatter matrix [duplicate]

The scatter matrix is defined as $$S = \sum_{j=1}^n (\mathbf{x}_j-\overline{\mathbf{x}})(\mathbf{x}_j-\overline{\mathbf{x}})^T$$ The trace (sum of the diagonal elements) of this matrix is ...
0
votes
0answers
27 views

The least squares estimator for beta in matrix notation in connection to normal equations and orthogonal projection in linear algebra [duplicate]

Somebody posted this link here about DERIVATION OF THE LEAST SQUARES ESTIMATOR FOR BETA IN MATRIX NOTATION-(https://economictheoryblog.com/2015/02/19/ols_estimator/). My question is 'How does THE ...
990
votes
28answers
585k views

Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
34
votes
3answers
38k views

Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?

I have been researching the meaning of positive semi-definite property of correlation or covariance matrices. I am looking for any information on Definition of positive semi-definiteness; Its ...
38
votes
3answers
30k views

Would PCA work for boolean (binary) data types?

I want to reduce the dimensionality of higher order systems and capture most of the covariance on a preferably 2 dimensional or 1 dimensional field. I understand this can be done via principal ...
32
votes
3answers
48k views

PCA on correlation or covariance: does PCA on correlation ever make sense? [closed]

In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components (from their respective eigenvectors). These give different results (...
29
votes
1answer
30k views

Best factor extraction methods in factor analysis

SPSS offers several methods of factor extraction: Principal components (which isn't factor analysis at all) Unweighted least squares Generalized least squares Maximum Likelihood Principal Axis Alpha ...
29
votes
1answer
40k views

Doing principal component analysis or factor analysis on binary data

I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I ...
30
votes
1answer
29k views

How does centering make a difference in PCA (for SVD and eigen decomposition)?

What difference does centering (or de-meaning) your data make for PCA? I've heard that it makes the maths easier or that it prevents the first PC from being dominated by the variables' means, but I ...
22
votes
2answers
16k views

Why PCA of data by means of SVD of the data?

This question is about an efficient way to compute principal components. Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ ...
26
votes
1answer
12k views

Converting similarity matrix to (euclidean) distance matrix

In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment ...
17
votes
1answer
14k views

What is the proper association measure of a variable with a PCA component (on a biplot / loading plot)?

I am using FactoMineR to reduce my data set of measurements to the latent variables. The variable map above is clear for me to interpret, but I am confused when ...
15
votes
2answers
7k views

Understanding distance correlation computations

As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers: ...

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