Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Remove Cosine Window from Correlation Filter-based Visual Trackers: When and How

Correlation filters (CFs) have been continuously advancing the state-of-the-art tracking performance and have been extensively studied in the recent few years. Most of the existing CF trackers adopt a cosine window to spatially reweight base image to alleviate boundary discontinuity. However, cosine window emphasizes more on the central region of base image and has the risk of contaminating negative training samples during model learning. On the other hand, spatial regularization deployed in many recent CF trackers plays a similar role as cosine window by enforcing spatial penalty on CF coefficients. Therefore, we in this paper investigate the feasibility to remove cosine window from CF trackers with spatial regularization. When simply removing cosine window, CF with spatial regularization still suffers from small degree of boundary discontinuity. To tackle this issue, binary and Gaussian shaped mask functions are further introduced for eliminating boundary discontinuity while reweighting the estimation error of each training sample, and can be incorporated with multiple CF trackers with spatial regularization. In comparison to the counterparts with cosine window, our methods are effective in handling boundary discontinuity and sample contamination, thereby benefiting tracking performance. Extensive experiments on three benchmarks show that our methods perform favorably against the state-of-the-art trackers using either handcrafted or deep CNN features. The code is publicly available at https://github.com/lifeng9472/Removing_cosine_window_from_CF_trackers.Comment: 13 pages, 7 figures, submitted to IEEE Transactions on Image Processin