Dimensionality reduction is a hot research topic in pattern recognition. Traditional dimensionality reduction methods can be separated into linear dimensionality reduction methods and nonlinear dimensionality reduction methods. Linear dimensionality reduction methods usually utilize Euclidean distances to explore global geometric structures, and nonlinear dimensionality reduction methods can preserve local manifold structures in learned low-dimensional subspaces. However, redundant information and noises of the raw high-dimensional data restrict the classification performance of these methods. To solve the problem, we propose a novel orthogonal dimensionality reduction method based on twin eigen decomposition called orthogonal locality and globality preserving projections (OLGPP). Orthogonality, as a commonly used criterion in pattern recognition, is insensitive to the redundant information and the noises. OLGPP not only combines the advantages of global Euclidean structures and local manifold structures, but also is insensitive to the redundant information and noises of the raw high-dimensional data by embedding the orthogonality criterion. Additionally, the objective function based on twin eigen decomposition can be solved sequentially to obtain analytical solutions. On four well-known datasets, we design extensive experiments to evaluate the performance of OLGPP. From the experimental results, OLGPP has the optimal experimental results, and its average recognition rates are about 10% higher than the classic local dimensionality reduction method (i.e., locality preserving projection), which proves OLGPP is an effective dimensionality reduction method.

Multi-set canonical correlation analysis (MCCA) is a famous multi-modal coherent subspace learning method. However, sample-based between-modal and within-modal covariance matrices of MCCA usually deviate from real covariance matrices due to noise information and limited sample size. The deviation will weaken the performance of MCCA, especially in image recognition. Aiming at this challenging issue, we correct singular values of sample covariance matrices with the employment of Cauchy estimate theory and further obtain Cauchy covariance matrices that are closer to real covariance matrices. On the basis of Cauchy covariance matrices, we develop a novel multi-modal subspace fusion method, i.e. Cauchy multi-set canonical correlations. By maximizing Cauchy correlations between different modalities and constraining Cauchy scatters of within-modal data, the method can learn a Cauchy coherent fusion subspace with well discriminative power from a few images. Experiment results have shown the effectiveness of the proposed method, promising to the aims of this research.

Rotating machinery is one of the important parts of industrial production equipment, and it is of great practical significance for fault diagnosis. Aiming at the problem of classification difficulty caused by feature interleaving in complex working conditions and high-dimension of rotating machinery fault samples, a rotating machinery fault diagnosis method based on multi-structure fusion discriminative projection (MFDP) is proposed. MFDP constructed intraclass and interclass hypergraph structures with multivariate relationships, fully revealing the higher-order association information among multiple samples. Besides, a tangential graph structure of MFDP is further constructed by combining the tangential affine of local samples to preserve the local tangential information of the manifold space. In the method, a unified objective optimization model of the discriminative hypergraph structures and local tangential graph structures is developed, and by solving the model, we can obtain fault structure features with well intraclass compactness and interclass separability. Extensive experiments on the Case Western Reserve University bearing dataset and Connecticut gear dataset show that the method has a good diagnostic accuracy of rotating machinery in different working conditions.

Dual-Path RNN(DPRNN) has achieved great progress in single-channel speech separation. However, RNN-based model needs to pass information through intermediate states and it does not allow parallel computing. Meanwhile, inter-chunk modeling of DPRNN only modeled between multiples of the chunk length, which means the underutilization of contextual information. To address these problems, we propose a multi-scale dual-path temporal convolutional network, DPTCN-ATPP. DPTCN-ATPP utilizes a stacked of one-dimensional dilated convolutions (1-D CNNs) instead of RNN to learn local and global information. Besides, DPTCN-ATPP applies parallel encoders to extract multi-scale input features. Finally, DPTCN-ATPP introduces the ATPP block to summarize multi-scale deep features. The experiment results show that DPTCN-ATPP achieves 19.6dB and 19.8dB on the metrics of scale-invariant source-to-noise ratio(SI-SNR) and source-to-distortion (SDR) respectively, outperforming baseline DPRNN and single-scale TCN (Conv-TasNet).