Local Tangent Distances for Classification Problems

Distance measure is quite important for pattern recognition. Utilizing invariance in image data, tangent distance is very powerful in classifying handwritten digits. For this measure a set of invariant transformations must be known a priori. But in many practical problems, it is very difficult to know these transformations. In this paper, an algorithm is proposed to approximate the invariant tangent distance exclusively from the data. By virtue of ideas arising from manifold learning, the algorithm needs no prior transformations and can be applied to more classification problems. k-nearest neighbor rule based on the new distance are implemented for classification problems. Experimental results on synthetic and real datasets illustrate its validity.