We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

Measuring statistical dependence with Hilbert-Schmidt norms

Gearboxes are critical transmission components in the drivetrain of wind turbine, which have a dominant failure rate and the highest downtime loss in all wind turbine subsystems. However, load vari...

Performance degradation assessment of wind turbine gearbox based on maximum mean discrepancy and multi-sensor transfer learning:

Measuring similarity between sets of objects is a key step in a wide areas of machine learning. Popular examples include general classification framework and numerous applications in computer vision. In this paper, we propose a kernel-based similarity method which is inspired from an interesting biological behavior of trees and induced mathematically by formulating it as a quadratic optimization problem in a reproducing kernel Hilbert space (RKHS). The proposed method is compared to the maximum mean discrepancy, a recent and challenging kernel similarity method. We conduct and present several numerical experiments on synthetic data as well as real-word image data. The proposed method yields favorable performances in terms of classification performances in the context of supervised classification tasks on the challenging Caltech101 dataset and other datasets such as USPS and ETH80. Furthermore, the efficiency of the proposed method in the context of image segmentation through unsupervised clustering of superpixels has been also asserted.

Overlapping area hyperspheres for kernel-based similarity method

The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification problem. In the set classification problem the goal is to classify a set of data points that are assumed to have a common class. We prove that the average probability of error given a set is less than or equal to the Bayes error and decreases as a power of $n$ number of sample data points in the set. We use the positive definite Set Kernel for directly mapping sets of data to an associated Reproducing Kernel Hilbert Space, without the need to learn a probability distribution. We specifically solve the two-sample hypothesis testing problem using a one-class SVM in conjunction with the proposed Set Kernel. We compare the proposed method with the Maximum Mean Discrepancy, F-Test and T-Test methods on a number of challenging simulated high dimensional and small sample size data. We also perform two-sample hypothesis testing experiments on six cancer gene expression data sets and achieve zero type-I and type-II error results on all data sets.

Kernel Two-Sample Hypothesis Testing Using Kernel Set Classification

An Hmm-Based On-Line Fault Detection and Diagnosis Model for Underwater Gliders

The need to quantify distance between two groups of objects is prevalent throughout the signal processing world. The difference of group means computed using the Euclidean, or `2 distance, is one of the predominant distance measures used to compare feature vectors and groups of vectors, but many problems arise with it when high data dimensionality is present. Maximum mean discrepancy (MMD) is a recent unsupervised kernel-based pattern recognition method which may improve differentiation between two distinct populations over many commonly used methods such as the difference of means, when paired with the proper feature representations and kernels. MMD-based distance computation combines many powerful concepts from the machine learning literature, such as data distributionleveraging similarity measures and kernel methods for machine learning. Due to this heritage, we posit that dissimilarity-based classification and changepoint detection using MMD can lead to enhanced separation between different populations. To test this hypothesis, we conduct studies comparing MMD and the difference of means in two subareas of image analysis and understanding: first, to detect scene changes in video in an unsupervised manner, and secondly, in the biomedical imaging field, using clinical ultrasound to assess tumor response to treatment. We leverage effective computer vision data descriptors, such as the bag-of-visual-words and sparse combinations of SIFT descriptors, and choose from an assessment of several similarity kernels (e.g. Histogram Intersection, Radial Basis Function) in order to engineer useful systems using MMD. Promising improvements over the difference of means, measured primarily using precision/recall for scene change detection, and k-nearest neighbour classification accuracy for tumor response assessment, are obtained in both applications.

Image Analysis Applications of the Maximum Mean Discrepancy Distance Measure

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Image Analysis Applications of the Maximum Mean Discrepancy Distance Measure