The motor imagery (MI) classification has been a prominent research topic in brain-computer interfaces based on electroencephalography (EEG). Over the past few decades, the performance of MI-EEG classifiers has seen gradual enhancement. In this study, we amplify the geometric deep learning-based MI-EEG classifiers from the perspective of time-frequency analysis, introducing a new architecture called Graph-CSPNet. We refer to this category of classifiers as Geometric Classifiers, highlighting their foundation in differential geometry stemming from EEG spatial covariance matrices. Graph-CSPNet utilizes novel manifold-valued graph convolutional techniques to capture the EEG features in the time-frequency domain, offering heightened flexibility in signal segmentation for capturing localized fluctuations. To evaluate the effectiveness of Graph-CSPNet, we employ five commonly-used publicly available MI-EEG datasets, achieving near-optimal classification accuracies in nine out of eleven scenarios. The Python repository can be found at https://github.com/GeometricBCI/Tensor-CSPNet-and-Graph-CSPNet.

The domain adaption (DA) problem on symmetric positive definite (SPD) manifolds has raised interest in the machine learning community because of the growing potential for the SPD-matrix representations across many non-stationary applicable scenarios. This paper generalizes the joint distribution adaption (JDA) to align the source and target domains on SPD manifolds and proposes a deep network architecture, Deep Optimal Transport (DOT), using the generalized JDA and the existing deep network architectures on SPD manifolds. The specific architecture in DOT enables it to learn an approximate optimal transport (OT) solution to the DA problems on SPD manifolds. In the experiments, DOT exhibits a 2.32% and 2.92% increase on the average accuracy in two highly non-stationary cross-session scenarios in brain-computer interfaces (BCIs), respectively. The visualizational results of the source and target domains before and after the transformation also demonstrate the validity of DOT.

This paper proposes a novel ternary hash encoding for learning to hash methods, which provides a principled more efficient coding scheme with performances better than those of the state-of-the-art binary hashing counterparts. Two kinds of axiomatic ternary logic, Kleene logic and {\L}ukasiewicz logic are adopted to calculate the Ternary Hamming Distance (THD) for both the learning/encoding and testing/querying phases. Our work demonstrates that, with an efficient implementation of ternary logic on standard binary machines, the proposed ternary hashing is compared favorably to the binary hashing methods with consistent improvements of retrieval mean average precision (mAP) ranging from 1\% to 5.9\% as shown in CIFAR10, NUS-WIDE and ImageNet100 datasets.

The purpose of this paper is to write a complete survey of the (spectral) manifold learning methods and nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR methods in history were respectively published in Science in 2000 in which they solve the similar reduction problem of high-dimensional data endowed with the intrinsic nonlinear structure. The intrinsic nonlinear structure is always interpreted as a concept in manifolds from geometry and topology in theoretical mathematics by computer scientists and theoretical physicists. In 2001, the concept of Manifold Learning first appears as an NLDR method called Laplacian Eigenmaps purposed by Belkin and Niyogi. In the typical manifold learning setup, the data set, also called the observation set, is distributed on or near a low dimensional manifold $M$ embedded in $\mathbb{R}^D$, which yields that each observation has a $D$-dimensional representation. The goal of (spectral) manifold learning is to reduce these observations as a compact lower-dimensional representation based on the geometric information. The reduction procedure is called the (spectral) manifold learning method. In this paper, we derive each (spectral) manifold learning method with the matrix and operator representation, and we then discuss the convergence behavior of each method in a geometric uniform language. Hence, we name the survey Geometric Foundations of Data Reduction.

Matrix Factorization has been very successful in practical recommendation applications and e-commerce. Due to data shortage and stringent regulations, it can be hard to collect sufficient data to build performant recommender systems for a single company. Federated learning provides the possibility to bridge the data silos and build machine learning models without compromising privacy and security. Participants sharing common users or items collaboratively build a model over data from all the participants. There have been some works exploring the application of federated learning to recommender systems and the privacy issues in collaborative filtering systems. However, the privacy threats in federated matrix factorization are not studied. In this paper, we categorize federated matrix factorization into three types based on the partition of feature space and analyze privacy threats against each type of federated matrix factorization model. We also discuss privacy-preserving approaches. As far as we are aware, this is the first study of privacy threats of the matrix factorization method in the federated learning framework.

This paper investigates capabilities of Privacy-Preserving Deep Learning (PPDL) mechanisms against various forms of privacy attacks. First, we propose to quantitatively measure the trade-off between model accuracy and privacy losses incurred by reconstruction, tracing and membership attacks. Second, we formulate reconstruction attacks as solving a noisy system of linear equations, and prove that attacks are guaranteed to be defeated if condition (2) is unfulfilled. Third, based on theoretical analysis, a novel Secret Polarization Network (SPN) is proposed to thwart privacy attacks, which pose serious challenges to existing PPDL methods. Extensive experiments showed that model accuracies are improved on average by 5-20% compared with baseline mechanisms, in regimes where data privacy are satisfactorily protected.

Electroencephalography (EEG) classification techniques have been widely studied for human behavior and emotion recognition tasks. But it is still a challenging issue since the data may vary from subject to subject, may change over time for the same subject, and maybe heterogeneous. Recent years, increasing privacy-preserving demands poses new challenges to this task. The data heterogeneity, as well as the privacy constraint of the EEG data, is not concerned in previous studies. To fill this gap, in this paper, we propose a heterogeneous federated learning approach to train machine learning models over heterogeneous EEG data, while preserving the data privacy of each party. To verify the effectiveness of our approach, we conduct experiments on a real-world EEG dataset, consisting of heterogeneous data collected from diverse devices. Our approach achieves consistent performance improvement on every task.

Inverse reinforcement learning (IRL) is an ill-posed inverse problem since expert demonstrations may infer many solutions of reward functions which is hard to recover by local search methods such as a gradient method. In this paper, we generalize the original IRL problem to recover a probability distribution for reward functions. We call such a generalized problem stochastic inverse reinforcement learning (SIRL) which is first formulated as an expectation optimization problem. We adopt the Monte Carlo expectation-maximization (MCEM) method, a global search method, to estimate the parameter of the probability distribution as the first solution to SIRL. With our approach, it is possible to observe the deep intrinsic property in IRL from a global viewpoint, and the technique achieves a considerable robust recovery performance on the classic learning environment, objectworld.