matterhacker

Given a kernel, want to construct a feature space (aka space obtained by map from data to feature space) . Feature spaces that can be constructed from a given kernel are not unique (they can even have different dimensions) but vice versa is not true… see below. Want to show that this constructed feature space is a dot product Hilbert space (aka pre-Hilbert space). Can construct a reproducing kernel map and show that it has the properties of a dot product space. Also can use mercer thm to construct a mercer map and show that it’s a dot product space. Although a mercer map is a rkm (is a mm a subspace of a rkm??). Other notes:

• A reproducing kernel hilbert space uniquely determines a kernel.
• Think of the map to feature space as a function at a particular data point . that relates it to the other data points x: Phi(x)(.) = k(.,x)

PDF is here

Another SVMs applied to DNA microarray data project.  Looks like it’s from a collaboration called MLExAI between the University of Hartford and Central Connecticut State University that is an information exchange on teaching machine learning and AI material.

A really good (but basic) intro on Support Vector Machines from Nature Biotechnology written by William Noble. Explains the basics of SVMs using DNA Microarray data analysis. From the article:

“…to understand the essence of SVM classification, one needs only to grasp four basic concepts: (i) the separating hyperplane, (ii) the maximum-margin hyperplane, (iii) the soft margin and (iv) the kernel function.”

Good read for a conceptual understanding… but no math.

A paper published in PNAS on using SVMs to analyze DNA microarray data:

“We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge of gene function to identify unknown genes of similar function from expression data. SVMs avoid several problems associated with unsupervised clustering methods, such as hierarchical clustering and self-organizing maps. SVMs have many mathematical features that make them attractive for gene expression analysis, including their flexibility in choosing a similarity function, sparseness of solution when dealing with large data sets, the ability to handle large feature spaces, and the ability to identify outliers. We test several SVMs that use different similarity metrics, as well as some other supervised learning methods, and find that the SVMs best identify sets of genes with a common function using expression data. Finally, we use SVMs to predict functional roles for uncharacterized yeast ORFs based on their expression data.”