Kernel method

Kernel Methods (KM) are a class of algorithms for Pattern Analysis, whose best known element is the Support Vector Machine (SVM).

The general task of Pattern Analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in general types of data (such as: sequences, text documents, sets of points, vectors, images, etc).

KMs approach the problem by mapping the data into a high dimensional feature space, where each coordinate corresponds to one feature of the data items, transforming the data into a set of points in a euclidean space. In that space, a variety of methods can be used to find linear relations in the data. Since the mapping can be quite general (not necessarily linear, for example), the relations found in this way are accordingly very general.

KMs owe their name to the use of kernel functions, that enable them to operate in the feature space without ever computing the coordinates of the data in such space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often computationally cheaper than the explicit computation of the coordinates. Kernel functions have been introduced for sequence data, text, images, as well as vectors.

Algorithms capable of operating with kernels include: Support Vector Machines, Fisher Discriminant, Principal Components Analysis, Canonical Correlation Analysis, Ridge Regression, Spectral Clustering, and many others.

Since any kernel can be used with any kernel-algorithm, it is possible to construct exotic combinations such as: regression over biosequences; classification of documents; clustering of images; and so on.

Because of the particular culture of the research community that has been developing this approach since the mid 90s, most kernel-algorithms are based on convex optimization or eigenproblems, are computationally efficient and statistically well founded. Typically, their statistical properties are analyzed by means of Statistical Learning Theory.

At the moment, the main application areas are in bioinformatics, text categorization, handwriting recognition.