Data Analysis with Kernels: [an introduction]

I am going to take an intuitive, CS-style approach to a discussion about the use of kernels in modern data analysis. This approach often lends us efficient ways to consider a dataset under various choices of inner product, which is roughly comparable to a measure of "similarity". Many new tools in AI arise from kernel methods, such as the infamous Support Vector Machines for classification, and kernel-PCA for nonlinear dimensionality reduction. I will attempt to highlight, and provide visualization for some of the math involved in these methods while keeping the material at an accessible, undergraduate level.