Auto-association by multilayer perceptrons and singular value decomposition
- 874 Downloads
The multilayer perceptron, when working in auto-association mode, is sometimes considered as an interesting candidate to perform data compression or dimensionality reduction of the feature space in information processing applications. The present paper shows that, for auto-association, the nonlinearities of the hidden units are useless and that the optimal parameter values can be derived directly by purely linear techniques relying on singular value decomposition and low rank matrix approximation, similar in spirit to the well-known Karhunen-Loève transform. This approach appears thus as an efficient alternative to the general error back-propagation algorithm commonly used for training multilayer perceptrons. Moreover, it also gives a clear interpretation of the rôle of the different parameters.
KeywordsFeature Space Dimensionality Reduction Processing Application Data Compression Multilayer Perceptrons
Unable to display preview. Download preview PDF.
- Bourlard H, Kamp Y, Wellekens CJ (1985) Speaker dependent connected speech recognition via phonemic Markov models. Proc ICASSP, pp 1213–1216Google Scholar
- Cottrell GW, Munro PW, Zipser D (1988) Image compression by back propagation: a demonstration of extensional programming. In: Sharkey NE (ed) Advances in cognitive science, vol 2. Abbex, Norwood, (NJ) (in press)Google Scholar
- Delsarte P, Kamp Y (1988) Low rank matrices with a given sign pattern Philips Research Laboratory, Brussels SIAM J: (to be published)Google Scholar
- Golub GH (1968) Least squares, singular values and matrix approximations. Applikace Matematiky 13:44–51Google Scholar
- Golub GH, Van Loan CF (1983) Matrix computations. North Oxford Academic, OxfordGoogle Scholar
- Harrison TD (1987) A Connectionist framework for continuous speech recognition. Cambridge University Ph. D. dissertationGoogle Scholar
- Lippmann RP (1987) An introduction to computing with neural nets. IEEE ASSP Magazine, pp 4–22Google Scholar
- Minsky M, Papert S (1969) Perceptrons. MIT Press, CambridgeGoogle Scholar
- Rumelhart DE, McClellarnd JL, and the PDP Research Group (1986) Parallel distributed processing. Exploration in the microstructure of cognition. vol 1–2. MIT Press, CambridgeGoogle Scholar
- Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Rumelhart DE, McClellan JL (eds) Parallel distributed processing. Exploration in the microstructure of cognition, vol 1. Foundations. MIT Press, CambridgeGoogle Scholar
- Stewart GW (1973) Introduction to matrix computations. Academic Press, New YorkGoogle Scholar