Sign constrained rectifier networks with applications to pattern decompositions
MetadataShow full item record
© Springer International Publishing Switzerland 2015. In this paper we introduce sign constrained rectifier networks (SCRN), demonstrate their universal classification power and illustrate their applications to pattern decompositions.We prove that the proposed two-hidden-layer SCRN, with sign constraints on the weights of the output layer and on those of the top hidden layer, are capable of separating any two disjoint pattern sets. Furthermore, a two-hidden-layer SCRN of a pair of disjoint pattern sets can be used to decompose one of the pattern sets into several subsets so that each subset is convexly separable from the entire other pattern set; and a single-hidden-layer SCRN of a pair of convexly separable pattern sets can be used to decompose one of the pattern sets into several subsets so that each subset is linearly separable from the entire other pattern set. SCRN can thus be used to learn the pattern structures from the decomposed subsets of patterns and to analyse the discriminant factors of different patterns from the linear classifiers of the linearly separable subsets in the decompositions. With such pattern decompositions exhibiting convex separability or linear separability, users can also analyse the complexity of the classification problem, remove the outliers and the non-crucial points to improve the training of the traditional unconstrained rectifier networks in terms of both performance and efficiency.
Showing items related by title, author, creator and subject.
Duong, Thi V. T. (2008)Modeling patterns in temporal data has arisen as an important problem in engineering and science. This has led to the popularity of several dynamic models, in particular the renowned hidden Markov model (HMM) [Rabiner, ...
An, Senjian; Boussaid, F.; Bennamoun, M. (2015)This paper investigates how hidden layers of deep rectifier networks are capable of transforming two or more pattern sets to be linearly separable while preserving the distances with a guaranteed degree, and proves the ...
An, Senjian; Boussaid, F.; Bennamoun, M.; Sohel, F. (2018)© 2018 Elsevier Ltd By introducing sign constraints on the weights, this paper proposes sign constrained rectifier networks (SCRNs), whose training can be solved efficiently by the well known majorization–minimization ...