A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs. Complex notions of similar(cid:173) ity appear necessary for cognitive models and applications, while simple notions of similarity form a tractable basis for current computational ap(cid:173) proaches to classification. We explore the nature of this dichotomy and why it calls for new approaches to well-studied problems in learning. We begin this process by demonstrating new computational methods for supervised learning that can handle complex notions of similarity.

Non-metric distances are often more reasonable compared with metric ones in terms of consistency with human perceptions. However, existing locality-sensitive hashing (LSH) algorithms can only support data which are gauged with metrics. In this paper we propose a novel locality-sensitive hashing algorithm targeting such non-metric data. Data in original feature space are embedded into an implicit reproducing kernel Krein space and then hashed to obtain binary bits. Here we utilize the norm-keeping property of p-stable functions to ensure that two data's collision probability reflects their non-metric distance in original feature space. We investigate various concrete examples to validate the proposed algorithm. Extensive empirical evaluations well illustrate its effectiveness in terms of accuracy and retrieval speedup.

In many applications non-metric distances are better than metric distances in reflecting the perceptual distances of human beings. Previous studies on non-metric distances mainly focused on supervised setting and did not consider the usefulness of unlabeled data. In this paper, we present probably the first study of label propagation on graphs induced from non-metric distances. The challenge here lies in the fact that the triangular inequality does not hold for non-metric distances and therefore, a direct application of existing label propagation methods will lead to inconsistency and conflict. We show that by applying spectrum transformation, non-metric distances can be converted into metric ones, and thus label propagation can be executed. Such methods, however, suffer from the change of original semantic relations. As a main result of this paper, we prove that any non-metric distance matrix can be decomposed into two metric distance matrices containing different information of the data. Based on this recognition, our proposed NMLP method derives two graphs from the original non-metric distance and performs a joint label propagation on the joint graph. Experiments validate the effectiveness of the proposed NMLP method.

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.

A key question in vision is how to represent our knowledge of previously encountered objects to classify new ones. The answer depends on how we determine the similarity of two objects. Similarity tells us how relevant each previously seen object is in determining the category to which a new object belongs.