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Feature space reduction by the criterion of contingency with null-space

V.A. Shustov1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 239 kB

Pages: 66-68.

Full text of article: Russian language.

Abstract:
Often, when forming a feature space, an excessive number of features is defined deliberately, and then, uninformative features are excluded. This technique is known as the feature space reduction [1]. It raises a problem of choosing an informativeness indicator and a threshold value of the selected indicator.
The works [2, 3] investigated the possibility that an indicator of contingency of a vector corresponding to a particular feature with null-space of the transposed matrix, composed of the remaining feature vectors, can be used as a criterion of informativeness of this feature. This technique involves setting a certain threshold for the contingency indicator and excluding the features if their contingency is less than specified. However, the issue of a reasonable choice of a threshold for obtaining an optimal set of features from the original set remains open.
This paper proposes and investigates a method for assigning a quantitative value to the threshold based on calculating the criterion of contingency of a feature space component, which is introduced to allow for the displacement of the separating hyperplane.

Keywords:
null-space, feature space, feature space reduction, indicator of contingency of a vector, transposed matrix, hyperplane.

Citation:
Shustov VA. Feature space reduction by the criterion of contingency with null-space. Computer Optics 2002; 23: 66-68.

References:
  1. Fu KS. Sequential methods in pattern recognition and machine learning. New York, London: Academic Press; 1968.
  2. Fursov VA, Shustov VA. Formation of feature space by the criterion of conjugacy of measurement vectors [In Russian]. Computer Optics 2000; 20: 140-142.
  3. Fursov VA, Shustov VA. Algorithms of feature space formation by the criterion of conjugacy of measurement vectors [In Russian]. Computer Optics 2001; 21: 176-178.
  4. Duda RO, Hart PE. Pattern classification and scene analysis. New York: John Wiley and Sons; 1973.

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