Dimensionality reduction by t-Distribution adaptive manifold embedding

High-dimensional data are difficult to explore and analyze due to they are highly correlative and redundant. Although previous dimensionality reduction methods have achieved promising performance, there are still some limitations. For example, the constructed distribution of data in the embedding space could not be approximated adaptively, and the parameters in these model lack of interpretation. To handle these problems, in this paper, a novel dimensionality reduction method named t-Distribution Adaptive Manifold Embedding (t-AME) is proposed. Firstly, t-AME constructs the pairwise distance similarity probability in the embedding space by Student-t distribution, and distributions generated by different degrees of freedom are learned according to the data itself to better match high-dimensional data distributions. Afterwards, to pull similar points together and push apart dissimilar points, an objective function with the corresponding optimization strategy is designed. Therefore, both the local and global structure of the original data could be well preserved in the embedding space. Finally, numerical experiments on synthetic and real datasets illustrate that the proposed method achieves a significant improvement over some representative and state-of-the-art dimensionality reduction methods.