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Fractional-Step Dimensionality Reduction
June 2000 (vol. 22 no. 6)
pp. 623-627

Abstract—Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA.

[1] I.T. Jolliffe, Principal Component Analysis. New York: Springer-Verlag, 1986.
[2] J.W. Sammon, “A Non-Linear Mapping Algorithm for Data Structure Analysis,” IEEE Trans. Computers, vol. 19, pp. 401-409, 1969.
[3] T. Kohonen, Self-Organizing Maps. Berlin: Springer-Verlag, 1995.
[4] P. Demartines and J. Herault, “Curvilinear Component Analysis: A Self-Organizing Neural Network for Nonlinear Mapping of Data Sets,” IEEE Trans. Neural Networks, vol. 8, pp. 1,197-1,206, 1997.
[5] L.J. Buturovic, Toward Bayes-Optimal Linear Dimension Reduction IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, pp. 420-424, 1994.
[6] R. Lotlikar and R. Kothari, “Bayes-Optimality Motivated Linear and Multi-Layered Perceptron Based Dimensionality Reduction,” IEEE Trans. Neural Networks, vol. 11, no. 2, pp. 452-463, 2000.
[7] K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. Academic Press, 1990.
[8] C.J. Merz and P.M. Murphy, UCI Repository of Machine Learning Databases, Irvine, Calif: Univ. of California, Department of Information and Computer Science, 1996. http://www.ics.uci.edu/~mlearnMLRepository.html .
[9] B.D. Ripley, “Ftp Archive,” Department of Statistics, Univ. of Oxford, http://www.stats.ox.ac.uk/pub/PRNN.

Index Terms:
Dimensionality reduction, classification, Fisher's Linear Discriminant.
Citation:
Rohit Lotlikar, Ravi Kothari, "Fractional-Step Dimensionality Reduction," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 6, pp. 623-627, June 2000, doi:10.1109/34.862200
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