Linked Questions
86 questions linked to/from Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
3
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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 : $\overline{Y_{.,j}}$...
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2
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0
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1k
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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 $\...
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2
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1
answer
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interpretation of $A^T A$ [duplicate]
Is there a statistical/information theoretic interpretation of this matrix in the context where A represents observations of data (and this matrix which shows up in e.g. solving linear systems and ...
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1
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0
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130
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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 ...
user35349
1368
votes
27
answers
961k
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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 ...
- 14k
62
votes
4
answers
73k
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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 ...
- 629
57
votes
4
answers
75k
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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 ...
- 757
61
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3
answers
85k
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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 ...
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36
votes
2
answers
33k
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Is there any relationship among cosine similarity, pearson correlation, and z-score?
I'm wondering if there is any relationship among these 3 measures. I can't seem to make a connection among them by referring to the definitions (possibly because I am new to these definitions and am ...
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37
votes
3
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59k
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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 (...
- 669
43
votes
1
answer
62k
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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 ...
- 431
33
votes
1
answer
47k
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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 ...
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39
votes
2
answers
21k
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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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17
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3
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What are the assumptions of factor analysis?
I want to check if I really understood [classic, linear] factor analysis (FA), especially assumptions that are made before (and possibly after) FA.
Some of the data should be initially correlated and ...
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32
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2
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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 $\bf X$ ...
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