Morten Hjorth-Jensen
13 lines
863 B
Plaintext
13 lines
863 B
Plaintext
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!split
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===== The Algorithm before the Theorem =====
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Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here.
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* Set up the datapoints for the design/feature matrix $\bm{X}$ with the predictors/features $p$ referring to the column numbers and the entries $n$ being the row elements.
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* Center the data by subtracting the mean value for each column.
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* Compute then the covariance/correlation matrix.
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* Find the eigenpairs of the covariance matrix with eigenvalues $[\lambda_0,\lambda_1,\dots,\lambda_{p-1}]$ and eigenvectors $[\bm{s}_0,\bm{s}_1,\dots,\bm{s}_{p-1}]$.
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* Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.
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* Keep only those $l$ eigenvalues larger than a selected threshold value, discarding thus $p-l$ features since we expect small variations in the data here.
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