Rapid and brief communication: Improving support vector data description using local density degree
ABSTRACT We propose a new support vector data description (SVDD) incorporating the local density of a training data set by introducing a local density degree for each data point. By using a density-induced distance measure based on the degree, we reformulate a conventional SVDD. Experiments with various real data sets show that the proposed method more accurately describes training data sets than the conventional SVDD in all tested cases.
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ABSTRACT: One-class classification (OCC) has received a lot of attention because of its usefulness in the absence of statistically-representative non-target data. In this situation, the objective of OCC is to find the optimal description of the target data in order to better identify outlier or non-target data. An example of OCC, support vector data description (SVDD) is widely used for its flexible description boundaries without the need to make assumptions regarding data distribution. By mapping the target dataset into high-dimensional space, SVDD finds the spherical description boundary for the target data. In this process, SVDD considers only the kernel-based distance between each data point and the spherical description, not the density distribution of the data. Therefore, it may happen that data points in high-density regions are not included in the description, decreasing classification performance. To solve this problem, we propose a new SVDD introducing the notion of density weight, which is the relative density of each data point based on the density distribution of the target data using the k-nearest neighbor (k-NN) approach. Incorporating the new weight into the search for an optimal description using SVDD, this new method prioritizes data points in high-density regions, and eventually the optimal description shifts to these regions. We demonstrate the improved performance of the new SVDD by using various datasets from the UCI repository.Expert Systems with Applications 01/2014; 41(7):3343–3350. · 1.85 Impact Factor
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ABSTRACT: As we may know well, uniqueness of the Support Vector Machines (SVM) solution has been solved. However, whether Support Vector Data Description (SVDD), another best-known machine learning method, has a unique solution or not still remains unsolved. Due to the fact that the primal optimization of SVDD is not a convex programming problem, it is difficult for us to theoretically analyze the SVDD solution in an analogous way to SVM. In this paper, we concentrate on the theoretical analysis for the solution to the primal optimization problem of SVDD. We first reformulate equivalently the primal optimization problem of SVDD into a convex programming problem, and then prove that the optimal solution with respect to the sphere center is unique, derive the necessary and sufficient conditions of non-uniqueness of the optimal solution with respect to the sphere radius in the primal optimization problem of SVDD. Moreover, we also explore the property of the SVDD solution from the perspective of the SVDD dual form. Furthermore, according to the geometric interpretation of SVDD, a method of computing the sphere radius is proposed when the optimal solution with respect to the sphere radius in the primal optimization problem is non-unique. Finally, we have several examples to illustrate these findings.Neural networks: the official journal of the International Neural Network Society 05/2011; 24(4):360-9. · 1.88 Impact Factor
Conference Paper: Improved density-induced support vector data description.[Show abstract] [Hide abstract]
ABSTRACT: Support vector data description (SVDD) is a data description method which can give the target data set a spherically shaped description. A density-induced SVDD (D-SVDD) has been proposed to improve the SVDD. However, the dual optimization problem of the D-SVDD is not a simple optimization problem which makes the D-SVDD be not an easy data description method. This paper presents an improved density-induced SVDD. The hyper-spherically shaped boundary of our method resorts to a well-known quadratic programming problem, thus the proposed data description method improves the D-SVDD.International Conference on Machine Learning and Cybernetics, ICMLC 2011, Guilin, China, July 10-13, 2011, Proceedings; 01/2011