  In the field of data mining, how to deal with high-dimensional data is an
inevitable problem. Unsupervised feature selection has attracted more and more
attention because it does not rely on labels. The performance of spectral-based
unsupervised methods depends on the quality of constructed similarity matrix,
which is used to depict the intrinsic structure of data. However, real-world
data contain a large number of noise samples and features, making the
similarity matrix constructed by original data cannot be completely reliable.
Worse still, the size of similarity matrix expands rapidly as the number of
samples increases, making the computational cost increase significantly.
Inspired by principal component analysis, we propose a simple and efficient
unsupervised feature selection method, by combining reconstruction error with
$l_{2,p}$-norm regularization. The projection matrix, which is used for feature
selection, is learned by minimizing the reconstruction error under the sparse
constraint. Then, we present an efficient optimization algorithm to solve the
proposed unsupervised model, and analyse the convergence and computational
complexity of the algorithm theoretically. Finally, extensive experiments on
real-world data sets demonstrate the effectiveness of our proposed method.
