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Using Non-Zero Dimensions for the Cosine and Tanimoto Similarity Search Among Real Valued Vectors

Kryszkiewicz M.

Fundamenta Informaticae

2013

Vol. 127, nr 1-4

307--323

The cosine and Tanimoto similarity measures are typically applied in the area of chemical informatics, bio-informatics, information retrieval, text and web mining as well as in very large databases for searching sufficiently similar vectors. In the case of large sparse high dimensional data sets such as text or Web data sets, one typically applies inverted indices for identification of candidates for sufficiently similar vectors to a given vector. In this article, we offer new theoretical results on how the knowledge about non-zero dimensions of real valued vectors can be used to reduce the number of candidates for vectors sufficiently cosine and Tanimoto similar to a given one. We illustrate and discuss the usefulness of our findings on a sample collection of documents represented by a set of a few thousand real valued vectors with more than ten thousand dimensions.

Generalization of Sparse Two Spirals Set using Feedforward Learning Machines

Rataj A.

Archiwum Informatyki Teoretycznej i Stosowanej

2005

T. 17, z. 2

79-86

In this paper, generalization of data is discussed where are 'weakly' defined, that is the number of samples to define the patterns of a given complexity is relatively low. The generalization is tested using several feedforward learning machines. On the tested data, the feedforward neural networks with diffused nonlinear weight functions have shown a relatively good performance.

W artykule dyskutowane jest uogólnianie danych których cechy są zdefiniowane 'słabo', to znaczy liczba próbek do reprezentowania wzorców o danej złożoności jest względnie niska. W przypadku testowanych zbiorów jednokierunkowe sieci neuronowe z dyfundowanymi funkcjami wag wykazały się względnie dobrą wydajnością.