Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1

Locality Preserving Projections for Grassmann manifold

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in more wide areas. In this research, we propose an unsupervised dimensionality reduction algorithm on Grassmann manifold based on the Locality Preserving Projections (LPP) criterion. LPP is a commonly used dimensionality reduction algorithm for vector-valued data, aiming to preserve local structure of data in the dimension-reduced space. The strategy is to construct a mapping from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability. The proposed method can be optimized as a basic eigenvalue problem. The performance of our proposed method is assessed on several classification and clustering tasks and the experimental results show its clear advantages over other Grassmann based algorithms.Comment: Accepted by IJCAI 201

Tight Analysis of Decrypton Failure Probability of Kyber in Reality

Kyber is a candidate in the third round of the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) Standardization. However, because of the protocol\u27s independence assumption, the bound on the decapsulation failure probability resulting from the original analysis is not tight. In this work, we give a rigorous mathematical analysis of the actual failure probability calculation, and provides the Kyber security estimation in reality rather than only in a statistical sense. Our analysis does not make independency assumptions on errors, and is with respect to concrete public keys in reality. Through sample test and experiments, we also illustrate the difference between the actual failure probability and the result given in the proposal of Kyber. The experiments show that, for Kyber-512 and 768, the failure probability resulting from the original paper is relatively conservative, but for Kyber-1024, the failure probability of some public keys is worse than claimed. This failure probability calculation for concrete public keys can also guide the selection of public keys in the actual application scenarios. What\u27s more, we measure the gap between the upper bound of the failure probability and the actual failure probability, then give a tight estimate. Our work can also re-evaluate the traditional $1-\delta$ correctness in the literature, which will help re-evaluate some candidates\u27 security in NIST post-quantum cryptographic standardization

A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects

Temporal characteristics are prominently evident in a substantial volume of knowledge, which underscores the pivotal role of Temporal Knowledge Graphs (TKGs) in both academia and industry. However, TKGs often suffer from incompleteness for three main reasons: the continuous emergence of new knowledge, the weakness of the algorithm for extracting structured information from unstructured data, and the lack of information in the source dataset. Thus, the task of Temporal Knowledge Graph Completion (TKGC) has attracted increasing attention, aiming to predict missing items based on the available information. In this paper, we provide a comprehensive review of TKGC methods and their details. Specifically, this paper mainly consists of three components, namely, 1)Background, which covers the preliminaries of TKGC methods, loss functions required for training, as well as the dataset and evaluation protocol; 2)Interpolation, that estimates and predicts the missing elements or set of elements through the relevant available information. It further categorizes related TKGC methods based on how to process temporal information; 3)Extrapolation, which typically focuses on continuous TKGs and predicts future events, and then classifies all extrapolation methods based on the algorithms they utilize. We further pinpoint the challenges and discuss future research directions of TKGC