  Feature selection methods are widely used in order to solve the 'curse of
dimensionality' problem. Many proposed feature selection frameworks, treat all
data points equally; neglecting their different representation power and
importance. In this paper, we propose an unsupervised hypergraph feature
selection method via a novel point-weighting framework and low-rank
representation that captures the importance of different data points. We
introduce a novel soft hypergraph with low complexity to model data. Then, we
formulate the feature selection as an optimization problem to preserve local
relationships and also global structure of data. Our approach for global
structure preservation helps the framework overcome the problem of
unavailability of data labels in unsupervised learning. The proposed feature
selection method treats with different data points based on their importance in
defining data structure and representation power. Moreover, since the
robustness of feature selection methods against noise and outlier is of great
importance, we adopt low-rank representation in our model. Also, we provide an
efficient algorithm to solve the proposed optimization problem. The
computational cost of the proposed algorithm is lower than many
state-of-the-art methods which is of high importance in feature selection
tasks. We conducted comprehensive experiments with various evaluation methods
on different benchmark data sets. These experiments indicate significant
improvement, compared with state-of-the-art feature selection methods.
