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We have a variety of linear methods for data analysis and machine learning that are familiar & intuitive, but our data are often nonlinear in complicated ways, or come in a form where the idea of "linear" doesn't have an obvious meaning, such as DNA sequences or graphs based on protein interactions.

Kernel methods allow us to apply some of our familiar linear tools to nonlinear and structured data, using similarities between data points as the basis for classification, regression, and other analyses like PCA. I'll explain the "kernel trick" as a principled way to extend linear methods to work with similarities, talk about algorithms based on kernels (support vector machines, support vector regression, & kernelized PCA), introduce example kernels for a variety of data types (e.g., vectors, graphs, strings), and discuss approximations that allow kernels to be applied to very large datasets.