Deep reconstruction of 1D ISOMAP representations

Abstract

This paper proposes a deep learning priors-based data reconstruction method of 1D isometric feature mapping (ISOMAP) representations. ISOMAP is a classical algorithm of nonlinear dimensionality reduction (NLDR) or manifold leaning (ML), which is devoted to questing for the low dimensional structure of high dimensional data. The reconstruction of ISOMAP representations, or the inverse problem of ISOMAP, reestablishes the high dimensional data from its low dimensional ISOMAP representations, and owns a bright future in data representation, generation, compression and visualization. Due to the fact that the dimension of ISOMAP representations is far less than that of the original high dimensional data, the reconstruction of ISOMAP representations is ill-posed or undetermined. Hence, the residual learning of deep convolutional neural network (CNN) is employed to boost reconstruction performance, via achieving the priors between the low-quality result of general ISOMAP reconstruction method and its residual relative to the original data. In the situation of 1D representations, it is evaluated by the experimental results that the proposed method outbalances the state-of-the-art methods, such as nearest neighbor (NN), discrete cosine transformation (DCT) and sparse representation (SR), in reconstruction performance of video data. In summary, the proposed method is suitable for low-bitrate and high-performance applications of data reconstruction.