Rival penalized competitive learning for clustering analysis, RBF net, and curve detection

Xu, Lei; Krzyżak, Adam; Oja, Erkki

doi:10.1109/72.238318

Cited by 551 publications

(252 citation statements)

References 22 publications

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“…Also, it will include the existing RPCL [9] and its Type A variant [8] as its special cases, but meanwhile providing a theoretical guidance to choose their awkward de-learning rate. We will go into the details elsewhere because of the space limitation.…”

Section: Rival Penalized Em Algorithmmentioning

confidence: 99%

A rival penalized EM algorithm towards maximizing weighted likelihood for density mixture clustering with automatic model selection

Cheung

2004

Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004.

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Section: Rival Penalized Em Algorithmmentioning

confidence: 99%

A rival penalized EM algorithm towards maximizing weighted likelihood for density mixture clustering with automatic model selection

Cheung

2004

Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004.

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“…Since both FSCL and FFSCL use non-Euclidean distance to determine the winner, they may lead to the problem of shared clusters in the sense that a number of prototypes may be updated into the same cluster during the learning process. This problem was considered by Xu et al in their rival penalized competitive learning (RPCL) algorithm [29]. The basic idea in RPCL is that for each input pattern, not only the weight of the frequency-sensitive winner is learned to shift toward the input pattern, but also the weight of its rival (the 2nd winner) is delearned by a smaller learning rate.…”

Section: Introductionmentioning

confidence: 99%

“…Although RPCL is applicable to some cases that the number of prototypes are larger than that of clusters, it is unable to deal with the situation that the number of prototypes is less than the actual number of clusters. To avoid this problem, Xu et al suggested to use a large number of prototypes initially [29]. However, it is difficult in most cases to choose a reasonably large number because of the lack of prior knowledge in the data set.…”

Section: Introductionmentioning

confidence: 99%

“…Kohonen's SOFM [8] is a learning process which takes WTM strategy at the early stages and becomes a WTA approach while its neighborhood size reduces to unity as a function of time in a predetermined manner. However, its main purpose is to form a topographic feature map which is a more complex task than just clustering analysis [29]. Several other algorithms, such as additive conscience competitive learning [38] and convex bridge [40], modulate the sensitivity of prototypes, so that less frequent winners increase their chances to win next time.…”

Section: Introductionmentioning

confidence: 99%

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Self-splitting competitive learning: a new on-line clustering paradigm

Zhang

Liu

2002

IEEE Trans. Neural Netw.

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Abstract-Clustering in the neural-network literature is generally based on the competitive learning paradigm. This paper addresses two major issues associated with conventional competitive learning, namely, sensitivity to initialization and difficulty in determining the number of prototypes. In general, selecting the appropriate number of prototypes is a difficult task, as we do not usually know the number of clusters in the input data a priori. It is therefore desirable to develop an algorithm that has no dependency on the initial prototype locations and is able to adaptively generate prototypes to fit the input data patterns. In this paper, we present a new, more powerful competitive learning algorithm, self-splitting competitive learning (SSCL), that is able to find the natural number of clusters based on the one-prototype-take-one-cluster (OPTOC) paradigm and a self-splitting validity measure. It starts with a single prototype randomly initialized in the feature space and splits adaptively during the learning process until all clusters are found; each cluster is associated with a prototype at its center. We have conducted extensive experiments to demonstrate the effectiveness of the SSCL algorithm. The results show that SSCL has the desired ability for a variety of applications, including unsupervised classification, curve detection, and image segmentation.

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“…(27) at D p (X) = D q (X), i.e., the following Bayesian Δπ(X, Y ), updating reverses the direction of the EM learning and actually becomes de-learning. In other words, the BYY harmony learning shares a mechanism similar to RPCL learning [64][65][66].…”

Section: Ying-yang Best Harmony Principlementioning

confidence: 99%

Bayesian Ying Yang System, Best Harmony Learning, and Gaussian Manifold Based Family

Lecture Notes in Computer Science

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Firstly proposed in 1995 and systematically developed in the past decade, Bayesian YingYang learning 1) is a statistical approach for a two pathway featured intelligent system via two complementary Bayesian representations of a joint distribution on the external observation X and its inner representation R, which can be understood from a perspective of the ancient Ying-Yang philosophy. We have q(X, R) = q(X|R)q(R) as Ying that is primary, with its structure designed according to tasks of the system, and p(X, R) = p(R|X)p(X) as Yang that is secondary, with p(X) given by samples of X while the structure of p(R|X) designed from Ying according to a Ying-Yang variety preservation principle, i.e., p(R|X) is designed as a functional with q(X|R), q(R) as its arguments. We call this pair Bayesian Ying-Yang (BYY) system. A YingYang best harmony principle is proposed for learning all the unknowns in the system, in help of an implementation featured by a five action circling under the name of A5 paradigm. Interestingly, it coincides with the famous ancient WuXing theory that provides a general guide to keep the A5 circling well balanced towards a Ying-Yang best harmony. This BYY learning provides not only a general framework that accommodates typical learning approaches from a unified perspective but also a new road that leads to improved model selection criteria, Ying-Yang alternative learning with automatic model selection, as well as coordinated implementation of Ying based model selection and Yang based learning regularization.This paper aims at an introduction of BYY learning in a twofold purpose. On one hand, we introduce fundamentals of BYY learning, including system design

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Rival penalized competitive learning for clustering analysis, RBF net, and curve detection

Cited by 551 publications

References 22 publications

A rival penalized EM algorithm towards maximizing weighted likelihood for density mixture clustering with automatic model selection

A rival penalized EM algorithm towards maximizing weighted likelihood for density mixture clustering with automatic model selection

Self-splitting competitive learning: a new on-line clustering paradigm

Bayesian Ying Yang System, Best Harmony Learning, and Gaussian Manifold Based Family

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