Classification with nonmetric distances: image retrieval and class representation

Abstract

ÐOne of the key problems in appearance-based vision is understanding how to use a set of labeled images to classify new images. Classification systems that can model human performance, or that use robust image matching methods, often make use of similarity judgments that are nonmetric; but when the triangle inequality is not obeyed, most existing pattern recognition techniques are not applicable. We note that exemplar-based (or nearest-neighbor) methods can be applied naturally when using a wide class of nonmetric similarity functions. The key issue, however, is to find methods for choosing good representatives of a class that accurately characterize it. We show that existing condensing techniques for finding class representatives are ill-suited to deal with nonmetric dataspaces. We then focus on developing techniques for solving this problem, emphasizing two points: First, we show that the distance between two images is not a good measure of how well one image can represent another in nonmetric spaces. Instead, we use the vector correlation between the distances from each image to other previously seen images. Second, we show that in nonmetric spaces, boundary points are less significant for capturing the structure of a class than they are in Euclidean spaces. We suggest that atypical points may be more important in describing classes. We demonstrate the importance of these ideas to learning that generalizes from experience by improving performance using both synthetic and real images. In addition, we suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions, showing in particular how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces.

Dissimilarity-based representation for local parts

“…To run experiments, we used the original C++ implementation of PMK 3 and extended it to implement the new proposed kernels based on the dissimilarity representations.…”

“…In recent years, the dissimilarity-based representation paradigm [1], [2], [3], [4], [5], [6], [7] has aroused a lively interest in the pattern recognition community. This paradigm differs from typical pattern recognition approaches where objects to be classified are represented by feature vectors.…”

Grouping with Asymmetric Affinities: A Game-Theoretic Perspective

“…However, recently there has been a strong interest in relaxing these requirements [9,4,16]. This is due to the fact that in many applications non-metric similarities arise naturally [15,2].…”

“…This is due to the fact that in many applications non-metric similarities arise naturally [15,2]. More fundamentally, some researches argue that human perception does not satisfy metric properties [4]. While the literature presents many approaches that lift the assumption of non-negativity and triangle inequality [9,4], little progress has been made in relaxing the symmetry constraint.…”

“…More fundamentally, some researches argue that human perception does not satisfy metric properties [4]. While the literature presents many approaches that lift the assumption of non-negativity and triangle inequality [9,4], little progress has been made in relaxing the symmetry constraint. Note, however, that the limited progress in grouping with asymmetric affinities is not due to the lack of interest.…”