One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream $k$-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the mis-clustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used $k$-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods.
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theoretical framework for multilayer spectral graph clustering of the nodes via convex layer aggregation. Under a novel multilayer signal plus noise model, we provide a phase transition analysis that establishes the existence of a critical value on the noise level that permits reliab…
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal plus noise model, we provide a phase transition analysis of clustering reliability. Moreover, we use the phase transition criterion to propose a multilayer i…
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes 2012) in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show how the LB divergences have a number of properties akin to many permutation based metrics, and in fact have as special cases forms very similar to the Kendall-tau metric. We also show how the LB divergences subsume a number of commonly used ranking measures in information retrieval…
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show how the LB divergences have a number of properties akin to many permutation based metrics, and in fact have as special cases forms very similar to the Kendall-$τ$ metric. We also show how the LB divergences subsume a number of commonly used ranking measures in information retrieva…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Nanjing University of Science and Technology（南京理工大学）
Cluster analysis, which focuses on the grouping and categorization of similar elements, is widely used in various fields of research. A novel and fast clustering algorithm, fission clustering algorithm, is proposed in recent year. In this article, we propose a robust fission clustering (RFC) algorithm and a self-adaptive noise identification method. The RFC and the self-adaptive noise identification method are combine to propose a self-adaptive robust fission clustering (SARFC) algorithm. Several frequently-used datasets were applied to test the performance of the proposed clustering approach …
Renmin University of China（中国人民大学）；University of Surrey（萨里大学）
Existing few-shot learning (FSL) methods assume that there exist sufficient training samples from source classes for knowledge transfer to target classes with few training samples. However, this assumption is often invalid, especially when it comes to fine-grained recognition. In this work, we define a new FSL setting termed few-shot fewshot learning (FSFSL), under which both the source and target classes have limited training samples. To overcome the source class data scarcity problem, a natural option is to crawl images from the web with class names as search keywords. However, the crawled i…
A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic representation. We show that the reconstruction error of this representation can be modelled as a random walk with pinned start and end points, a so-called Brownian bridge. This insight allows us to make ABBA essentially parameter-free, except for the approximation tolerance which must be chosen. Extensive comparisons with the SAX and 1d-SAX representations are …
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being robust to short-term variations. Several evolutionary clustering algorithms have recently been proposed, often by adding a temporal smoothness penalty to the cost function of a static clustering method. In this paper, we introduce a different approach to evolutionary clustering by …
Multiple kernel methods based on k-means aims to integrate a group of kernels to improve the performance of kernel k-means clustering. However, we observe that most existing multiple kernel k-means methods exploit the nonlinear relationship within kernels, whereas the local manifold structure among multiple kernel space is not sufficiently considered. In this paper, we adopt the manifold adaptive kernel, instead of the original kernel, to integrate the local manifold structure of kernels. Thus, the induced multiple manifold adaptive kernels not only reflect the nonlinear relationship but also …
In this paper we are going to introduce a new nearest neighbours based approach to clustering, and compare it with previous solutions; the resulting algorithm, which takes inspiration from both DBscan and minimum spanning tree approaches, is deterministic but proves simpler, faster and doesnt require to set in advance a value for k, the number of clusters.
Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the data cannot be represented well enough and may lose the accuracy. This paper proposes a novel approach to enhance the data-adaptive capability for OMP-based sparse subspace clustering. In our method a parameter selection process is developed to adjust the parameters based on the data distribution for information representation. Our theoretical analysis indicates th…
University of Costa Rica（哥斯达黎加大学）；Costa Rica Institute of Technology（哥斯达黎加理工学院）
We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization metaheuristics: first ones are simulated annealing, threshold accepting and tabu search, and the others are a genetic algorithm and ant colony optimization. The methods are implemented, performing the proper calibration of parameters in the case of heuristics, to ensure good results. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Singapore Management University（新加坡管理大学）
Class-Incremental Learning (CIL) aims to learn a classification model with the number of classes increasing phase-by-phase. An inherent problem in CIL is the stability-plasticity dilemma between the learning of old and new classes, i.e., high-plasticity models easily forget old classes, but high-stability models are weak to learn new classes. We alleviate this issue by proposing a novel network architecture called Adaptive Aggregation Networks (AANets), in which we explicitly build two types of residual blocks at each residual level (taking ResNet as the baseline architecture): a stable block …
Adaptive Graph Auto-Encoder for General Data Clustering
School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University（西北工业大学人工智能、光学与电子学院（iOPEN））；Key Laboratory of Intelligent Interaction and Applications (Northwestern Polytechnical University), Ministry of Industry and Information Technology（工业和信息化部智能交互与应用重点实验室（西北工业大学））
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution o…
Mississippi State University（密西西比州立大学）；International University of Business Agriculture and Technology（国际商业农业与技术大学）；Rajshahi University of Engineering and Technology（拉杰沙希工程技术大学）
Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm which has the high-performance rate for dataset where clusters have the constant density of data points. One of the significant attributes of this algorithm is noise cancellation. However, DBSCAN demonstrates reduced performances for clusters with different densities. Therefore, in this paper, an adaptive DBSCAN is proposed which can work significantly well for identifying clusters with varying densities.
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as Hölder continuity, but only require intuitive geometric assumptions…
This paper presents a new approach to non-parametric cluster analysis called Adaptive Weights Clustering (AWC). The idea is to identify the clustering structure by checking at different points and for different scales on departure from local homogeneity. The proposed procedure describes the clustering structure in terms of weights \( w_{ij} \) each of them measures the degree of local inhomogeneity for two neighbor local clusters using statistical tests of "no gap" between them. % The procedure starts from very local scale, then the parameter of locality grows by some factor at each step. The …
This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states is characterized by the nonnegative rank of the Markov transition matrix. Motivated by the success of the nuclear norm relaxation in low rank minimization problems, we propose an atomic regularizer as a convex surrogate for the nonnegative rank and formulate a convex optimization problem. Because the atomic regularizer itself is not computationall…
