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Summary: 2003 Special issue
A network for recursive extraction of canonical coordinates
Ali Pezeshki*, Mahmood R. Azimi-Sadjadi, Louis L. Scharf
Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373, USA
Abstract
A network structure for canonical coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that
together extract the canonical coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient
descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections
perform a deflation process that subtracts the contributions of the already extracted coordinates from the input data subspace. This structure
allows for adding new nodes for extracting additional canonical coordinates without the need for retraining the previous nodes. The
performance of the network is evaluated on a synthesized data set.
q 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Canonical coordinates; Singular value decomposition; Deflation; Iterative learning
1. Introduction
Canonical correlation analysis (Hotelling, 1936; Ander-
son, 1958) provides a minimal description of the
correlation between two data channels by concentrating
the linear dependence of the channels into a small set of
canonical variables. Canonical correlations are maximal
invariants to uncoupled linear transformations of two-
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