Different thresholding methods on Nearest Shrunken Centroid algorithm

TL;DR

The paper addresses high-dimensional cancer classification with PAM by evaluating alternative thresholding strategies beyond the original soft thresholding. It introduces hard and order thresholding and a deep search procedure to select the thresholding parameter, assessing performance on ten multi-class gene expression datasets. Across datasets, hard and order thresholding improve model parsimony and often accuracy, while deep search substantially reduces the number of informative genes with minimal loss in predictive performance. Using SRD-based ranking, the authors find hard and order thresholding to be generally favorable for classification, with deep search further enhancing sparsity, offering practical guidance for parsimonious PAM classifiers in genomics.

Abstract

This article considers the impact of different thresholding methods to the Nearest Shrunken Centroid algorithm, which is popularly referred as the Prediction Analysis of Microarrays (PAM) for high-dimensional classification. PAM uses soft thresholding to achieve high computational efficiency and high classification accuracy but in the price of retaining too many features. When applied to microarray human cancers, PAM selected 2611 features on average from 10 multi-class datasets. Such a large number of features make it difficult to perform follow up study. One reason behind this problem is the soft thresholding, which is known to produce biased parameter estimate in regression analysis. In this article, we extend the PAM algorithm with two other thresholding methods, hard and order thresholding, and a deep search algorithm to achieve better thresholding parameter estimate. The modified algorithms are extensively tested and compared to the original one based on real data and Monte Carlo studies. In general, the modification not only gave better cancer status prediction accuracy, but also resulted in more parsimonious models with significantly smaller number of features.

Figures (9)

• Figure 1: Test error of OTh and HTh versus STh for SRBCT and Breast cancer data. The plotting symbol H (in red) is for HTh and O (in black) is for OTh. The numbers used in the plot are the frequencies of test errors out of 100 runs and the table gives a summary of the test errors in percentage.
• Figure 2: Overall comparison of STh, HTh, and OTh bases on SRD. The x-axis and the left y-axis represents SRD values scaled to between 0 and 100; the right y-axis gives the relative frequencies for the theoretical distribution. The XX1, Med, and XX19 mark the 5%, 50%, and 95% percentiles.
• Figure 3: Overall comparison of STh2, HTh2, and OTh2 bases on SRD. The x-axis and the left y-axis represents SRD values scaled to between 0 and 100; the right y-axis gives the relative frequencies for the theoretical distribution. The XX1, Med, and XX19 mark the 5%, 50%, and 95% percentiles.
• Figure 4: Overall comparison of STh, HTh, OTh, STh2, HTh2, and OTh2 bases on SRD. The x-axis and the left y-axis represents SRD values scaled to between 0 and 100; the right y-axis gives the relative frequencies for the theoretical distribution. The XX1, Med, and XX19 mark the 5%, 50%, and 95% percentiles.
• Figure S.1: Test error of OTh and HTh versus STh for Cancers and DLBCL data. The plotting symbol H (in red) is for HTh and O (in black) is for OTh. The numbers used in the plot are the frequencies of test errors out of 100 runs and the table gives a summary of the test errors in percentage.