Positive Definite Kernels in Machine Learning

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.Comment: draft. corrected a typo in figure

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Autoregressive Kernels For Time Series

We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_{\theta}(x) of different parameters \theta in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is integrated out w.r.t \theta using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel \kappa. In that case, the kernel between x and x' is a a function of the Gram matrices produced by \kappa on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines

A subpath kernel for learning hierarchical image representations

International audienceTree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discrimi-native role. While such kernels have been successfully applied to various domains such as nature language processing and bioinformatics, they mostly concentrate on ordered trees and whose nodes are described by symbolic data. Meanwhile, hierarchical representations have gained increasing interest to describe image content. This is particularly true in remote sensing, where such representations allow for revealing different objects of interest at various scales through a tree structure. However, the induced trees are unordered and the nodes are equipped with numerical features. In this paper, we propose a new structured kernel for hierarchical image representations which is built on the concept of subpath kernel. Experimental results on both artificial and remote sensing datasets show that the proposed kernel manages to deal with the hierarchical nature of the data, leading to better classification rates

Dynamically parallel CAMSHIFT: GPU accelerated object tracking in digital video

The CAMSHIFT algorithm is widely used for tracking dynamically sized and positioned objects in real-time applications. In spite of its extensive study on the platform of sequential CPU, its research on massively parallel Graphical Processing Unit (GPU) platform is quite limited. In this work, we designed and implemented two different parallel algorithms for CAMSHIFT using CUDA. The first design performs calculations on the GPU, but requires iterative data transfers back to the host CPU for condition checking, which bottlenecks the entire program. In the second design, we propose an enhanced parallel reduction-based CAMSHIFT using dynamic parallelism to reduce overhead of data transfers between the CPU and GPU. Test results for a 400 by 400 search window show that the second design is up to five times faster than the first design and nine times faster than a pure CPU implementation. We also investigate the deployment of dynamic parallelism for multiple object tracking using CAMSHIFT --Leaf iv

Spatial Pyramid Context-Aware Moving Object Detection and Tracking for Full Motion Video and Wide Aerial Motion Imagery

A robust and fast automatic moving object detection and tracking system is essential to characterize target object and extract spatial and temporal information for different functionalities including video surveillance systems, urban traffic monitoring and navigation, robotic. In this dissertation, I present a collaborative Spatial Pyramid Context-aware moving object detection and Tracking system. The proposed visual tracker is composed of one master tracker that usually relies on visual object features and two auxiliary trackers based on object temporal motion information that will be called dynamically to assist master tracker. SPCT utilizes image spatial context at different level to make the video tracking system resistant to occlusion, background noise and improve target localization accuracy and robustness. We chose a pre-selected seven-channel complementary features including RGB color, intensity and spatial pyramid of HoG to encode object color, shape and spatial layout information. We exploit integral histogram as building block to meet the demands of real-time performance. A novel fast algorithm is presented to accurately evaluate spatially weighted local histograms in constant time complexity using an extension of the integral histogram method. Different techniques are explored to efficiently compute integral histogram on GPU architecture and applied for fast spatio-temporal median computations and 3D face reconstruction texturing. We proposed a multi-component framework based on semantic fusion of motion information with projected building footprint map to significantly reduce the false alarm rate in urban scenes with many tall structures. The experiments on extensive VOTC2016 benchmark dataset and aerial video confirm that combining complementary tracking cues in an intelligent fusion framework enables persistent tracking for Full Motion Video and Wide Aerial Motion Imagery.Comment: PhD Dissertation (162 pages