This work proposes a middle ground in the form of a scalable information-theoretic generalization of CCA, termed max-sliced mutual information (mSMI).

The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language processing, and speech analysis. Despite its popularity, CCA can encounter challenges in explaining correlations between two variable sets within high-dimensional data contexts. Thus, this paper studies Sparse Canonical Correlation Analysis (SCCA) that enhances the interpretability of CCA. We first show that SCCA generalizes three well-known sparse optimization problems, sparse PCA, sparse SVD, and sparse regression, which are all classified as NP-hard problems. This result motivates us to develop strong formulations and efficient algorithms. Our main contributions include (i) the introduction of a combinatorial formulation that captures the essence of SCCA and allows the development of exact and approximation algorithms; (ii) the establishment of the complexity results for two low-rank special cases of SCCA; and (iii) the derivation of an equivalent mixed-integer semidefinite programming model that facilitates a specialized branch-and-cut algorithm with analytical cuts. The effectiveness of our proposed formulations and algorithms is validated through numerical experiments.

Traditional SSVEP-based brain-computer interface (BCI) systems rely heavily on external visual stimulus equipment, limiting their practicality in real-world settings. This study proposes an augmented reality steady-state visually evoked potential (AR-SSVEP) system to address the lack of patient initiative and the high workload on therapists. Firstly, we design four HoloLens 2-based EEG classes and collect EEG data from seven healthy subjects for analysis. Secondly, we build upon the conventional CNN-BiLSTM architecture by integrating a multi-head attention mechanism (MACNN-BiLSTM). We extract ten temporal-spectral EEG features and feed them into a CNN to learn high-level representations. Then, we use BiLSTM to model sequential dependencies and apply a multi-head attention mechanism to highlight motor-intention-related patterns. Finally, the SHAP (SHapley Additive exPlanations) method is applied to visualize EEG feature contributions to the neural network's decision-making process, enhancing the model's interpretability. These findings enhance real-time motor intention recognition and support recovery in patients with motor impairments.

We propose a new technique, Singular V ector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less.

Neural Information Processing Systems http://nips.cc/

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.

In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems.

CFCNet learns to capture, to the largest extent, the semantically correlated features between RGB and depth information.

Alternating least-squares (ALS) is a simple yet effective solver for canonical correlation analysis (CCA). In terms of ease of use, ALS is arguably practitioners' first