Unsupervised Feature Selection via Multi-step Markov Transition Probability

TL;DR

This paper introduces MMFS, a novel unsupervised feature selection method using multi-step Markov transition probabilities to better capture data relationships beyond adjacent points, improving data structure preservation.

Contribution

It proposes a new approach leveraging multi-step Markov transition probabilities for unsupervised feature selection, with three algorithms from positive and negative perspectives.

Findings

Effective in preserving data structure.

Outperforms state-of-the-art methods on real datasets.

Demonstrates robustness across multiple data scenarios.

Abstract

Feature selection is a widely used dimension reduction technique to select feature subsets because of its interpretability. Many methods have been proposed and achieved good results, in which the relationships between adjacent data points are mainly concerned. But the possible associations between data pairs that are may not adjacent are always neglected. Different from previous methods, we propose a novel and very simple approach for unsupervised feature selection, named MMFS (Multi-step Markov transition probability for Feature Selection). The idea is using multi-step Markov transition probability to describe the relation between any data pair. Two ways from the positive and negative viewpoints are employed respectively to keep the data structure after feature selection. From the positive viewpoint, the maximum transition probability that can be reached in a certain number of steps is used to describe the relation between two points. Then, the features which can keep the compact data structure are selected. From the viewpoint of negative, the minimum transition probability that can be reached in a certain number of steps is used to describe the relation between two points. On the contrary, the features that least maintain the loose data structure are selected. And the two ways can also be combined. Thus three algorithms are proposed. Our main contributions are a novel feature section approach which uses multi-step transition probability to characterize the data structure, and three algorithms proposed from the positive and negative aspects for keeping data structure. The performance of our approach is compared with the state-of-the-art methods on eight real-world data sets, and the experimental results show that the proposed MMFS is effective in unsupervised feature selection.