Related papers: Higher-Order Neighborhood Truss Decomposition
We present $k^{O(k^2)} m$ time algorithms for various problems about decomposing a given undirected graph by edge cuts or vertex separators of size $<k$ into parts that are ``well-connected'' with respect to cuts or separators of size $<k$;…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…
Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations,…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…
Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
Previously in 2014, we proposed the Nearest Descent (ND) method, capable of generating an efficient Graph, called the in-tree (IT). Due to some beautiful and effective features, this IT structure proves well suited for data clustering.…
Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking…
The traditional k nearest neighbor (kNN) approach uses a distance formula within a spherical region to determine the k closest training observations to a test sample point. However, this approach may not work well when test point is located…
In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the metrics of all neighboring vectors are computed to determine the best one to move to. This strategy requires high computational…
Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to compute the truncated Tucker decomposition of higher-order tensors with a given error tolerance, and prove that the method is locally optimal and…
The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
The k-core of a graph is its maximal subgraph with minimum degree at least k, and the core value of a vertex u is the largest k for which u is contained in the k-core of the graph. Among cohesive subgraphs, k-core and its variants have…