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- W3201839482 abstract "We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p times p$ covariance matrix $Sigma$ exhibits a spiked eigenvalues structure and the vector $zeta$, given by the difference between the whitened mean vectors, is sparse with sparsity at most $s$. We propose an adaptive classifier (adaptive with respect to the sparsity $s$) that first performs dimension reduction on the feature vectors prior to classification in the dimensionally reduced space, i.e., the classifier whitened the data, then screen the features by keeping only those corresponding to the $s$ largest coordinates of $zeta$ and finally apply Fisher linear discriminant on the selected features. Leveraging recent results on entrywise matrix perturbation bounds for covariance matrices, we show that the resulting classifier is Bayes optimal whenever $n rightarrow infty$ and $s sqrt{n^{-1} ln p} rightarrow 0$. Experimental results on real and synthetic data sets indicate that the proposed classifier is competitive with existing state-of-the-art methods while also selecting a smaller number of features." @default.
- W3201839482 created "2021-10-11" @default.
- W3201839482 creator A5056784746 @default.
- W3201839482 creator A5085147413 @default.
- W3201839482 date "2021-10-05" @default.
- W3201839482 modified "2023-09-27" @default.
- W3201839482 title "Classification of high-dimensional data with spiked covariance matrix structure." @default.
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