37 research outputs found
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 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