Structure Regularized Method Based Semi-supervised Dimensionlity Reduction

As an important machine learning topic,dimensionality reduction has been widely studied and utilized.So a great number of dimensionality reduction methods have been developed.When only a small number of labeled samples are available,supervised dimensionality reduction methods often tend to perform not optimal because of over fitting.In such cases,unlabeled samples could also be useful improving the performance,so that semi-supervised dimensionality reduction has been attracting much attention.In this paper,we consider an robust semi-supervised dimensionality reduction algorithmic,The method can simultaneously reduce the dimension of data and the structural characteristics of learning data,we say the proposed algorithm is structure regularized semi-supervised dimensionality reduction.Firstly,the proposed framework implements structure learning where the data structures(including essential distribution structure and the data segment)are found via a combination of alternating direction method of multipliers and clustering;both the intrinsic data structure and data segment are formulated as regularization terms for dimensionality reduction.The results of the dimensionality reduction can also affect the structure learning step in the following iterations.By leveraging the interactions between structure learning and dimensionality reduction,we are able to capture more accurate structure of data and reduce to right dimensionality,making the classification results is much better.Our algorithm is based on two projective space: Non-orthogonal projection space and the Orthogonal projection of space constraints.Lots of experiments demonstrate the effectiveness of our method.