  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.
