An Effective Region Force for Some Variational Models for Learning and Clustering

Yin, Ke; Tai, Xue–Cheng

doi:10.1007/s10915-017-0429-4

Cited by 35 publications

(71 citation statements)

References 29 publications

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“…• Classical SSL methods are taken as the baselines for several benchmark datasets, including the K-NN classifier (K-NN), spectral graph transduction (SGT) [16], Laplacian regularized least squares (LapRLS) [1], P SQ solved using SQ-Loss-1 [27], and measure propagation (MP) [27]. • TVRF [31]. TV-based multi-class graph partitioning with a region force is an approach to combine the graph cut in the spectral clustering method and a region force is inspired by the Chan-Vese model [4].…”

Section: Experimental Settingsmentioning

confidence: 99%

Probabilistic Semi-Supervised Learning via Sparse Graph Structure Learning

Wang

Chan

Zeng

2021

IEEE Trans. Neural Netw. Learning Syst.

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We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance because of an improper graph or the high computational complexity of the large-scale optimization problem. In this paper, we propose to address both challenging problems by constructing a proper graph for graph-based SSL methods. Different from existing approaches, we simultaneously learn a small set of vertexes to characterize the high-dense regions of the input data and a graph to depict the relationships among these vertexes. A novel approach is then proposed to construct the graph of the input data from the learned graph of a small number of vertexes with some preferred properties. Without explicitly calculating the constructed graph of inputs, two transductive graph-based SSL approaches are presented with the computational complexity in linear with the number of input data. Extensive experiments on synthetic data and real datasets of varied sizes demonstrate that the proposed method is not only scalable for large-scale data, but also achieve good classification performance, especially for extremely small number of labels.Zitong Wang is with the

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Section: Experimental Settingsmentioning

confidence: 99%

Probabilistic Semi-Supervised Learning via Sparse Graph Structure Learning

Wang

Chan

Zeng

2021

IEEE Trans. Neural Netw. Learning Syst.

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“…Three Moons. This data set is as described in [YT18] and elsewhere. It has three clusters, generated by sampling points uniformly at random from the upper semi-circle of radius 1 centered at (0, 0), the lower semi-circle of radius 1.5 centered at (1.5, 0.4) and the upper semi-circle of radius 1 centered at (3, 0).…”

Section: The Data Setsmentioning

confidence: 99%

Power weighted shortest paths for clustering Euclidean data

McKenzie¹,

Damelin²

2019

Foundations of Data Science

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We study the use of power weighted shortest path metrics for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also present a fast algorithm for computing these distances.1. We prove that p-wspm's behave as expected for data satisfying the manifold hypothesis.That is, we show that the maximum distance between points in the same cluster is small with high probability, and tends to zero as the number of data points tends to infinity. On the other hand, the maximum distance between points in different clusters remains bounded away from zero.2. We show how p-wspm's can be thought of as interpolants between the Euclidean metric and the longest leg path distance (defined in §2.3), which we shall abbreviate to LLPD.3. We introduce a novel modified version of Dijkstra's algorithm that computes the k nearest neighbors, with respect to any p-wspm or the LLPD, of any x α in X in O(k 2 T Enn ) time, where T Enn is the cost of a Euclidean nearest-neighbor query. Hence one can construct a p-wspm k-NN graph in O(nk 2 T Enn ). As we typically have k n, i.e. k = O(log(n)) or even k = O(1), this means that constructing a p-wspm k-NN graph requires only marginally more time than constructing a Euclidean k-NN graph (which requires O(nkT Enn )).4. We verify experimentally that using a p-wspm in lieu of the Euclidean metric results in an appreciable increase in clustering accuracy, at the cost of a small increase in run time, for a wide range of real and synthetic data sets.After establishing notation and surveying the literature in §2, we prove our main results in §3 and §4. In §5 we present our algorithm for computing k nearest neighbors in any p-wspm, while in §6 we report the results of our numerical experiments.

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“…In this work, five real-world networks are used to validate the proposed TSOS method, which includes three classical networks of Dolphin network [50], Football network [13] and Political book network [51], and two data clustering sets of MINST [34] and COIL [52]. The three classical social networks are widely used in many community detection studies; the COIL-100 (Columbia object image library-100) data set [53] contains many color images of 100 different objects, its related graph network used in this paper includes 24 randomly selected objects (1500 images) from the dataset and the edge weights of the built-up 5-NN graph are calculated through the Euclidean distance between two images; the MINST data [54] totally consists of 70000 size-normalized and centered images of handwritten digits 0 − 9, the images are naturally partitioned to 10 roughly balanced clusters, a 10-NN graph is constructed from the original MINST data set and its edge weights are computed from the Euclidean distance between two images as 784-dim vectors [34]. These networks are considered as undirected and their network parameters are shown in Tab.…”

Section: Experiments On Real-world Networkmentioning

confidence: 99%

Variational community partition with novel network structure centrality prior

Bai

Yuan

Liu

et al. 2019

Applied Mathematical Modelling

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In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of both links and vertices to construct the key affinity description of the given network, where the direct similarities between graph nodes or nodal features are not available to obtain the classical affinity matrix. Indeed, such calculated network centrality information presents the essential structure of network, hence, the proper measure for detecting network communities, which also introduces a 'confidence' criterion for referencing new labeled benchmark nodes. For the resulted challenging combinatorial optimization problem of graph clustering, the proposed optimization method iteratively employs an efficient convex optimization algorithm which is developed based under a new variational perspective of primal and dual. Experiments over both artificial and real-world network datasets demonstrate that the proposed optimization strategy of community detection significantly improves result accuracy and outperforms the state-of-the-art algorithms in terms of accuracy and reliability.

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An Effective Region Force for Some Variational Models for Learning and Clustering

Cited by 35 publications

References 29 publications

Probabilistic Semi-Supervised Learning via Sparse Graph Structure Learning

Probabilistic Semi-Supervised Learning via Sparse Graph Structure Learning

Power weighted shortest paths for clustering Euclidean data

Variational community partition with novel network structure centrality prior

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