Kernels and Regularization on Graphs
نویسندگان
چکیده
We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.
منابع مشابه
Co-regularized Spectral Clustering with Multiple Kernels
We propose a co-regularization based multiview spectral clustering algorithm which enforces the clusterings across multiple views to agree with each-other. Since each view can be used to define a similarity graph over the data, our algorithm can also be considered as learning with multiple similarity graphs, or equivalently with multiple kernels. We propose an objective function that implicitly...
متن کاملCombining Graph Laplacians for Semi-Supervised Learning
A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs. For each of these graphs we associate a basic graph kernel. We then compute an optimal combined kernel. This kernel solves an extended regularization problem which requires a joint minimization over...
متن کاملFrom Regularization Operators to Support Vector Kernels
We derive the correspondence between regularization operators used in Regularization Networks and Hilbert Schmidt Kernels appearing in Support VectorMachines. More specifically, we prove that the Green’s Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. As a by–product we show that a large number of Radial Basis Fun...
متن کاملThe connection between regularization operators and support vector kernels
In this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green's Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, the paper provides an analysis of currently used support vector kernels in the view of regulariz...
متن کاملL2 Regularization for Learning Kernels
The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of non-negative linear combinations of p base kernels, constrained by a trace or L1 regularization. This paper studies the problem of learning kernels with the same fam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003