Robust data clustering by learning multi-metric Lq-norm distances

Zhang, Junying; Peng, Liuqing; Zhao, Xiaoxue; Kuruoğlu, Erçan E.

doi:10.1016/j.eswa.2011.07.023

Cited by 12 publications

(5 citation statements)

References 37 publications

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“…In some applications clustering algorithms with the 1 -norm produce A DC Optimization Algorithm for Clustering Problems with 1 -norm 3 easy interpreting results than those with the squared 2 -norm. The former algorithms are more preferred in high dimensional data mining applications [1] and they are also more robust to outliers [34].…”

Section: Introductionmentioning

confidence: 99%

A DC Optimization Algorithm for Clustering Problems with $𝑳_𝟏$-norm

Bagirov

Taheri

2017

IJOR

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Clustering problems with the similarity measure defined by the 1-norm are studied. Characterizations of different stationary points of these problems are given using their difference of convex representations. An algorithm for finding the Clarke stationary points of the clustering problems is designed and a clustering algorithm is developed based on it. The clustering algorithm finds a center of a data set at the first iteration and gradually adds one cluster center at each consecutive iteration. The proposed algorithm is tested using large real world data sets and compared with other clustering algorithms.

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Section: Introductionmentioning

confidence: 99%

A DC Optimization Algorithm for Clustering Problems with $𝑳_𝟏$-norm

Bagirov

Taheri

2017

IJOR

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“…Utilizing existing regularization methods [21,22] is another method to avoid overfitting. With this approach, optimal parameters can be obtained to simplify models by adjusting either the L1 norm or the L2 norm of the weight coefficients [23]. Also, adjusting algorithm parameters, dimensionality reduction, and cross validation experiments [24] are effective means to avoid the overfitting problem.…”

Section: Introductionmentioning

confidence: 99%

A Study on the Generalized Approximation Modeling Method Based on Fitting Sensitivity for Prediction of Engine Performance

Lin

Wang

Zhong

2017

Discrete Dynamics in Nature and Society

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Prediction technology for aeroengine performance is significantly important in operational maintenance and safety engineering. In the prediction of engine performance, to address overfitting and underfitting problems with the approximation modeling technique, we derived a generalized approximation model that could be used to adjust fitting precision. Approximation precision was combined with fitting sensitivity to allow the model to obtain excellent fitting accuracy and generalization performance. Taking the Grey model (GM) as an example, we discussed the modeling approach of the novel GM based on fitting sensitivity, analyzed the setting methods and optimization range of model parameters, and solved the model by using a genetic algorithm. By investigating the effect of every model parameter on the prediction precision in experiments, we summarized the change regularities of the root-mean-square errors (RMSEs) varying with the model parameters in novel GM. Also, by analyzing the novel ANN and ANN with Bayesian regularization, it is concluded that the generalized approximation model based on fitting sensitivity can achieve a reasonable fitting degree and generalization ability.

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“…In this framework, the data matrix and the output vector are not exactly known, however, estimates for both of them as well as uncertainty bounds on the estimates are given [2,8,[15][16][17][18][19]]. Since the model parameters are not known exactly, the performances of the classical LS estimators may significantly degrade, especially when the perturbations on the data matrix and the output vector are relatively high [9,15,16,[20][21][22]. Hence, robust estimation algorithms are needed to obtain a satisfactory performance under such perturbations.…”

Section: Introductionmentioning

confidence: 99%

Robust least squares methods under bounded data uncertainties

Vanli

Donmez

Kozat

2015

Digital Signal Processing

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We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations. © 2014 Elsevier Inc. All rights reserved

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Robust data clustering by learning multi-metric Lq-norm distances

Cited by 12 publications

References 37 publications

A DC Optimization Algorithm for Clustering Problems with $𝑳_𝟏$-norm

A DC Optimization Algorithm for Clustering Problems with $𝑳_𝟏$-norm

A Study on the Generalized Approximation Modeling Method Based on Fitting Sensitivity for Prediction of Engine Performance

Robust least squares methods under bounded data uncertainties

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