Fuzzy least squares twin support vector clustering

Khemchandani, Reshma; Pal, Aman; Chandra, Suresh

doi:10.1007/s00521-016-2468-4

Cited by 31 publications

(10 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…al. [30] present a fuzzy version of TWSVC (FLSTWSVC) with the soft assignments of clusters. Subsequently, to deal with noisy clustering cases, Ye et.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

MPMSVC: Multiple Parametric-Margin Support Vector Clustering

et al. 2021

View full text Add to dashboard Cite

Under the nonparallel plane-based clustering paradigm, in this work, we propose an unsupervised multiple parametric-margin support vector clustering (MPMSVC) for noisy clustering tasks. The main idea of MPMSVC is to find a parametric-margin center hyperplane for each cluster in a manner that gathers the within-cluster instances around the corresponding center hyperplane, and keeps the betweencluster instances far away. Specifically, our MPMSVC owns the following attractive merits: i) The primal of MPMSVC is enhanced in the least squares sense, which enjoys an effective learning procedure. ii) The utilization of the linear L 1-norm loss makes MPMSVC be more robust to noisy clustering tasks. iii) An efficient iterative algorithm is presented to optimize the non-smooth problem of MPMSVC, which only involves a set of linear equations. Also, the convergence of the proposed algorithm is guaranteed theoretically. iv) The nonlinear extension is further derived via kernel technique to deal with more complex clustering tasks. Finally, the feasibility and effectiveness of MPMSVC are validated by extensive experiments on both synthetic and real-world datasets. INDEX TERMS Plane-based clustering, Nonparallel support vector clustering, L 1-norm, Robustness.

show abstract

“…al. [30] present a fuzzy version of TWSVC (FLSTWSVC) with the soft assignments of clusters. Subsequently, to deal with noisy clustering cases, Ye et.…”

Section: Introductionmentioning

confidence: 99%

“…into(30), then achieve(29). Algorithm 2 monotonically non-increases the objective function of problem(17) in each iteration.…”

mentioning

confidence: 99%

MPMSVC: Multiple Parametric-Margin Support Vector Clustering

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Hence, its k fitting/clustering planes are solved by k quadratic programming (QP) problems. To speed training TWSVC, Fuzzy Least Squares TWSVC (F-LS-TWSVC) [23] relaxes the inequality constrains with equalities, and introduces fuzzy membership into the objective, thus it is analytically solved by linear equations.…”

Section: Introductionmentioning

confidence: 99%

Robust Plane Clustering Based on L1-Norm Minimization

Yang

Zhang

et al. 2020

IEEE Access

View full text Add to dashboard Cite

Plane clustering methods, typically, k plane clustering (kPC), play conclusive roles in the family of data clustering. Instead of point-prototype, they aim to seek multiple plane-prototype fitting planes as centers to group the given data into their corresponding clusters based on L2 norm metric. However, they are usually sensitive to outliers because of square operation on the L2 norm. In this paper, we focus on robust plane clustering and propose a L1 norm plane clustering method, termed as L1kPC. The leading problem is optimized on the L1 ball hull, a non-convex feasible domain. To handle the problem, we provide a new strategy and its related mathematical proofs for L1 norm optimization. Compared to state-of-the-art methods, the advantages of our proposed lie in 4 folds: 1) similar to kPC, it has clear geometrical interpretation; 2) it is more capable of resisting to outlier; 3) theoretically, it is proved that the leading non-convex problem is equivalent to several convex sub-problems. To our best knowledge, this opens up a new way for L1 norm optimization; 4) the k fitting planes are solved by k individual linear programming problems, rather than higher time-consuming eigenvalue equations or quadratic programming problems used in the conventional plane clustering methods. Experiments on some artificial, benchmark UCI and human face datasets show its superiorities in robustness, training time, and clustering accuracy. INDEX TERMS L1 norm, plane clustering, eigenvalue problem, linear programming.

show abstract

“…This model is called support vector clustering model, which has recently absorbed plenty of attention because of its applications in solving the difficult and diverse clustering or outlier detection problem. Faster version of support vector clustering model is based on twin support vector machines, which uses two small models instead of one big model for data clustering (Forgy, ; Khemchandani, Pal, & Chandra, ).…”

Section: Introductionmentioning

confidence: 99%

Alternating optimization to solve penalized regression‐based clustering model

2019

View full text Add to dashboard Cite

Two previously proposed heuristic algorithms for solving penalized regression‐based clustering model (PRClust) are (a) an algorithm that combines the difference‐of‐convex programming with a coordinate‐wise descent (DC‐CD) algorithm and (b) an algorithm that combines DC with the alternating direction method of multipliers (DC‐ADMM). In this paper, a faster method is proposed for solving PRClust. DC‐CD uses p × n × (n − 1)/2 slack variables to solve PRClust, where n is the number of data and p is the number of their features. In each iteration of DC‐CD, these slack variable and cluster centres are updated using a second‐order cone programming (SOCP). DC‐ADMM uses p × n × (n − 1) slack variables. In each iteration of DC‐ADMM, these slack variables and cluster centres are updated using ADMM. In this paper, PRClust is reformulated into an equivalent model to be solved using alternating optimization. Our proposed algorithm needs only n × (n − 1)/2 slack variables, which is much less than that of DC‐CD and DC‐ADMM and updates them analytically using a simple equation in each iteration of the algorithm. Our proposed algorithm updates only cluster centres using an SOCP. Therefore, our proposed SOCP is much smaller than that of DC‐CD, which is used to update both cluster centres and slack variables. Experimental results on real datasets confirm that our proposed method is faster and much faster than DC‐ADMM and DC‐CD, respectively.

show abstract

Fuzzy least squares twin support vector clustering

Cited by 31 publications

References 23 publications

MPMSVC: Multiple Parametric-Margin Support Vector Clustering

MPMSVC: Multiple Parametric-Margin Support Vector Clustering

Robust Plane Clustering Based on L1-Norm Minimization

Alternating optimization to solve penalized regression‐based clustering model

Contact Info

Product

Resources

About