Publication

Tangent Vector Kernels for Invariant Image Classification with SVMs

2003
Reports

Abstract

This paper presents an application of the general sample-to-object approach to the problem of invariant image classification. The approach results in defining new SVM kernels based on tangent vectors that take into account prior information on known invariances. Real data of face images are used for experiments. The presented approach integrates virtual sample and tangent distance methods. We observe a significant increase in performance with respect to standard approaches. The experiments also illustrate (as expected) that prior knowledge becomes more important as the amount of training data decreases.

Official source

https://infoscience.epfl.ch/entities/publication/02b2ca39-b5cb-4ea6-bceb-6dfa8b47dc57

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2003
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/02b2ca39-b5cb-4ea6-bceb-6dfa8b47dc57

About this result

Related concepts (32)

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c if the line passes through the point (c, f(c)) on the curve and has slope f(c), where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

Kernel method

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets.

Tangent lines to circles

In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonal circles. A tangent line t to a circle C intersects the circle at a single point T.

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