Title：Nonlinear Smooth Support Vector Machines I, II
Nonlinear Smooth Support Vector Machines,
Time：6/27, 14:00-16:00)
Abstract：
(1) Review of optimization problems with constraints
----Primal form, dual form, Karush-Kuhn-Tuker (KKT) conditions.
----Tangent vectors to feasible set and linearized feasible directions.
(2) Binary classification problems/Supervised learning problems
----Linearly separable case: Maximizing the margin between boundary planes, primal and dualforms.
----Nonseparable case: primal/dual maximization problems for 1-norm/2-norm soft margin SVM.
(3) Nonlinear support vector machine
----Two spiral data set.
----Learning linear machine in feature space.
----Kernel: represent inner product in feature space.
----Kernel Techniques: monomials of degree d, polynomial kernel, Guassian (radial basis function) kernel.
----Dual representation of SVM classifier.
(4) Smooth support vector machine
----SVM as an unconstrained minimization problem.
----Smooth with plus function.
----Newton-Armijo Algorithm.
(5) Nonlinear smooth support vector machine
----Nonlinear SSVM motivation.
----Kernel trick: Gaussian kernel, monomials, polynomials.
----Nonlinear classifier.
(6) Reduced support vector machine
----Reduced SVM: A compressed model.
----A nonlinear kernel application: checkerboard training set.
----Using 50 randomly selected points out of 1000 points.
----Compressed model vs full model.
Title：Clustering and Expectation/Maximization Algorithms I, II
(Time：6/28, 14:00-16:00)
Abstract：
(1) Searching the optimal combination of the regularization parameter and the width parameter in the Gaussian kernel
----Grid search, Nested uniform design method (UDM).
----Experimental results: grid search vs UDM (13/9) vs UDM(9/5).
(2) Three fundamental algorithms
----Naive Bayes classifier.
----K-nearest neighbors algorithm.
----Online perception algorithm.
(3) Unsupervised learning problems
----K-Means clustering problem formulation.
----K-Means Algorithm.
----K-Means ++ Algorithm.
(4) Expectation/Maximization Algorithm
----E-step: Compute the probability, the point n is generated by distribution k.
----M-step: update mean, variance and probability distribution k.
