Different thresholding methods on Nearest Shrunken Centroid algorithm

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.

Keywords:

• High-dimensional classification
• Cross-validation
• Order thresholding
• Soft thresholding
• Hard thresholding
• Nearest Shrunken Centroid

AMS 2000 SUBJECT CLASSIFICATIONS:

• Primary 65C60
• secondary 62P10

Disclosure statement

The authors do not have any potential competing interest.

Additional information

Funding

This work was partially supported by a grant by Simons Foundation (#246077) to Haiyan Wang. We would also like to thank the anonymous reviewer whose comments have lead to a much improved version of this manuscript.