Learning an invariant distance metric

The requirement for suitable ways to measure the distance or similarity between data is omnipresent in machine learning, pattern recognition and data mining, but extracting such good metrics for particular problems is in general challenging.

This has led to the emergence of metric learning ideas, which intend to automatically learn a distance function tuned to a specific task. In many tasks and data types, there are natural transformations to which the classification result should be invariant or insensitive. This demand and its implications are essential in many machine learning applications, and insensitivity to image transformations was in the first place achieved by using invariant feature vectors.

Aim of this project is to learn a metric which is invariant to the different transformations such as horizontal translation, vertical translation, global scale, rotation, line thickness, and shear and also illumination changes that might be applied on data. To do so, the first idea is taking the advantage of the Projection metric on the Grassmann manifolds.

Stichworte

• Metric learning, Mahalanobis Metric, Grassmann manifolds