Semblance: An empirical similarity kernel on probability spaces

In data science, determining proximity between observations is critical to many downstream analyses such as clustering, classification, and prediction. However, when the data’s underlying probability distribution is unclear, the function used to compute similarity between data points is often arbitrarily chosen. Here, we present a novel definition of proximity, Semblance, that uses the empirical distribution of a feature to inform the pair-wise similarity between observations. The advantage of Semblance lies in its distribution-free formulation and its ability to place greater emphasis on proximity between observation pairs that fall at the outskirts of the data distribution, as opposed to those toward the center. Semblance is a valid Mercer kernel, allowing its principled use in kernel-based learning algorithms, and for any data modality. We demonstrate its consistently improved performance against conventional methods through simulations and real case studies from diverse applications in single-cell transcriptomics, image reconstruction, and financial forecasting.

Combining Entropy Measures for Anomaly Detection

The combination of different sources of information is a problem that arises in several situations, for instance, when data are analysed using different similarity measures. Often, each source of information is given as a similarity, distance, or a kernel matrix. In this paper, we propose a new class of methods which consists of producing, for anomaly detection purposes, a single Mercer kernel (that acts as a similarity measure) from a set of local entropy kernels and, at the same time, avoids the task of model selection. This kernel is used to build an embedding of data in a variety that will allow the use of a (modified) one-class Support Vector Machine to detect outliers. We study several information combination schemes and their limiting behaviour when the data sample size increases within an Information Geometry context. In particular, we study the variety of the given positive definite kernel matrices to obtain the desired kernel combination as belonging to that variety. The proposed methodology has been evaluated on several real and artificial problems.

Novel Method of MRI Medical Image Segmentation Combining Watershed Algorithm and WKFCM Algorithm

Aimed at the disadvantage of over-segmentation that traditional watershed algorithm segmented MRI images, a new method of MRI image segmentation was presented. First, through traditional watershed segmentation algorithm, the image was segmented into different areas, and then based on the improved kernel-clustering algorithm, we used Mercer-kernel to map average gray value of each area to high-dimensional feature space, making originally not displayed features manifested. In this way, we can achieve a more accurate clustering, and solve over-segmentation problem of watershed algorithm segmenting MRI images efficiently, thereby get better segmentation result. Experimental results show that the method of this paper can segment brain MRI images satisfactorily, and obtain clearer segmentation images.