Augmented Embedding of Dissimilarity Data into (Pseudo-)Euclidean Spaces
Pairwise proximities describe the properties of objects in terms of their similarities. By using different distance-based functions one may encode different characteristics of a given problem. However, to use the framework of statistical pattern recognition some vector representation should be constructed. One of the simplest ways to do that is to define an isometric embedding to some vector space. In this work, we will focus on a linear embedding into a (pseudo-)Euclidean space.
This is usually well defined for training data. Some inadequacy, however, appears when projecting new or test objects due to the resulting projection errors. In this paper we propose an augmented embedding algorithm that enlarges the dimensionality of the space such that the resulting projection error vanishes. Our preliminary results show that it may lead to a better classification accuracy, especially for data with high intrinsic dimensionality.
KeywordsIsometric Embedding Projection Error Linear Embedding Statistical Pattern Recognition Radar Return
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