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A New Dissimilarity Measure between FeatureVectors
"... Distance measures is very important in some clustering and machine learning techniques. At present there are many such measures for determining the dissimilarity between the featurevectors, but it is very important to make a choice that depends on the problem to be solved. This paper proposes a simp ..."
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Distance measures is very important in some clustering and machine learning techniques. At present there are many such measures for determining the dissimilarity between the featurevectors, but it is very important to make a choice that depends on the problem to be solved. This paper proposes a simple but robust distance measure called Reference Distance Weighted, for calculating distance between featurevectors with real values. The basic attribute that distinguishes it from other measures is that the distance is measured from one of the featurevector, considered as a reference system, to other featurevectors. In fact this reference vector belongs to a class of a classification system. A second distinctive attribute is that its value does not depend on the orders of magnitude of the different characteristics of vectors. In addition, through a parameter called factor of relevance, each feature receives a weight in terms of its influence, because different features have different influence on dissimilarity estimation depending on the final problem to be solved. An extension of the proposed distance allows working with hybrid vectors, ie real and logical values. Future research directions are also provided.
JOHNSONLINDENSTRAUSS DIMENSIONALITY REDUCTION ON THE SIMPLEX
"... Abstract. We propose an algorithm for dimensionality reduction on the simplex, mapping a set of highdimensional distributions to a space of lowerdimensional distributions, whilst approximately preserving pairwise Hellinger distance between distributions. By introducing a restriction on the input d ..."
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Abstract. We propose an algorithm for dimensionality reduction on the simplex, mapping a set of highdimensional distributions to a space of lowerdimensional distributions, whilst approximately preserving pairwise Hellinger distance between distributions. By introducing a restriction on the input data to distributions that are in some sense quite smooth, we can map n points on the dsimplex to the simplex of O(ε−2 log n) dimensions with εdistortion with high probability. The techniques used rely on a classical result by Johnson and Lindenstrauss on dimensionality reduction for Euclidean point sets and require the same number of random bits as nonsparse methods proposed by Achlioptas for databasefriendly dimensionality reduction. 1.