Estimation of Minimum Measure Sets in Reproducing Kernel Hilbert Spaces and Applications.

Abstract

Minimum measure sets (MMSs) summarize the information of a (single-class) dataset. In many situations, they can be preferred to estimated probability density functions (pdfs): they are strongly related to pdf level sets while being much easier to estimate in large dimensions.The main contribution of this paper is a theoretical connection between MMSs and one class Support Vector Machines. This justifies the use of one-class SVMs in the following applications: novelty detection (we give explicit convergence rate) and change detection.

One-Class SVMs Challenges in Audio Detection and Classification Applications

“…such that most of the data in X belong to the set R X = {x ∈ R d with f X (x) ≥ 0} while the volume of R X is minimal. This problem is termed minimum volume set (MVS) estimation [31], and we see that membership of x to R X indicates whether this datum is overall similar to X, or not. Thus, by learning regions R Xi for each class of sound (i = 1, .…”

“…The 1-SVM approach proceeds in feature space by determining the hyperplane W that separates most of the data from the hypersphere origin, while being as far as possible from it. Since in H the image by φ of R X is included in the segment of hypersphere bounded by W , this indeed implements MVS estimation [31]. In practice, let…”

Improved One-class SVM Classifier for Sounds Classification

“…The aim of 1-SVMs is to use the training data so as to learn a function f X : R d → R such that most of the data in X belong to the set R X = {x ∈ R d with f X (x) ≥ 0} while the volume of R X is minimal. This problem is termed minimum volume set (MVS) estimation, see [11], and we see that membership of x to R X indicates whether this datum is overall similar to X , or not. Thus, by learning regions R Xi for each class of sound (i = 1, .…”

Kernel-Based Methods for Hypothesis Testing: A Unified View

“…Kernel-based test statistics related to the above information divergences were proposed, such as the KCD test statistic from [51]- [53]. The test statistic is in fact close to MMD and could be related to = learned by training oneclass SVMs on each sample independently; see [18] for more details.…”

“…The test statistic is in fact close to MMD and could be related to = learned by training oneclass SVMs on each sample independently; see [18] for more details. A statistical interpretation of one-class SVMs is given in [53] and [54].…”