SemanticallyAware Statistical Metrics via Weighting Kernels Distance metrics between statistical distributions are widely used as an efficient mean to aggregatesimplify the underlying probabilities, thus enabling highlevel analyses. In this paper we investigate the collisions that can arise with such metrics, and a mitigation technique rooted on kernels. In detail, we first show that the existence of colliding functions (socalled isocurves) is widespread across metrics and families of functions (e.g., gaussians, heavytailed). Later, we propose a solution based on kernels for augmenting distance metrics and summary statistics, thus avoiding collisions and highlighting semanticallyrelevant phenomena. This study is supported by a thorough theoretical evaluation of our solution against a large number of functions and metrics, complemented by a realworld evaluation carried out by applying our solution to an existing problem. Some further research venues are also discussed. The theoretical construction and the achieved results show the soundness, viability, and quality of our proposal that, other being interesting on its own, also paves the way for further research in the highlighted directions.

SpaceEfficient Feature Maps for String Alignment Kernels String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits largescale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call spaceefficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs). The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors. Thus, we present novel spaceefficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for largescale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.