Principal components of the colon-cancer matrix
Section of High-dimensional analysis, part of Statistical learning
Principal components of the colon-cancer matrix
| Type | Section |
| Taught in | High-dimensional analysis |
| Part | Statistical learning |
The first ten principal components were examined, for three reasons. One or more components might pick up variation associated with the class difference. One can look for outliers, including possibly mislabelled observations. The dimension reduction allows a full suite of classifiers to be constructed. A plot of the first component against the second offered almost no separation between the classes and indicated no outliers. Welch t-tests of each component between the classes gave
| Component | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| p-value | 0.479 | 0.339 | 1.8\times 10^{-7} | 0.0995 | 0.0958 | 0.0166 | 0.346 | 0.84 | 0.915 | 0.431 |
The third component appears very aligned with the class differences, and the sixth is also promising. Their scatter plot separates the classes substantially, with some overlap. A simple classifier such as quadratic discrimination in these two dimensions might separate them fairly accurately. The labels were used in choosing these dimensions, so the analysis would need to be redone with left-out data to estimate classification accuracy honestly. The genes with the largest magnitude in the third and sixth direction vectors were listed, the top 20 of each. There were no genes in common between these two lists.
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See also
Rank bound · Family-wise control implies false-discovery control · Benjamini–Hochberg · Benjamini–Hochberg controls the false discovery rate · Why classical methods fail when p > n · Rank of the sample covariance · Regression when p > n · Where high-dimensional columns come from