Tensor-Train Parameterization for Ultra Dimensionality Reduction
This work addresses dimensionality reduction for high-dimensional data, particularly in classification, but appears incremental as it builds on existing tensor-train and LPP techniques.
The paper tackles the limitations of Locality Preserving Projections (LPP) for high-dimensional data by proposing a tensor-train parameterization method (TTPUDR) that enhances robustness and preserves structural information, resulting in significant outperformance over past and state-of-the-art methods in classification tasks.
Locality preserving projections (LPP) are a classical dimensionality reduction method based on data graph information. However, LPP is still responsive to extreme outliers. LPP aiming for vectorial data may undermine data structural information when it is applied to multidimensional data. Besides, it assumes the dimension of data to be smaller than the number of instances, which is not suitable for high-dimensional data. For high-dimensional data analysis, the tensor-train decomposition is proved to be able to efficiently and effectively capture the spatial relations. Thus, we propose a tensor-train parameterization for ultra dimensionality reduction (TTPUDR) in which the traditional LPP mapping is tensorized in terms of tensor-trains and the LPP objective is replaced with the Frobenius norm to increase the robustness of the model. The manifold optimization technique is utilized to solve the new model. The performance of TTPUDR is assessed on classification problems and TTPUDR significantly outperforms the past methods and the several state-of-the-art methods.