Abstract:
Abstract. In this paper, we derive lower and upper bounds for the probability of error for a linear classifier, where the random vectors representing the underlying classes obey the multivariate normal distribution. The expression of the error is derived in the one-dimensional space, independently of the dimensionality of the original problem. Based on the two bounds, we propose an approximating expression for the error of a generic linear classifier. In particular, we derive the corresponding bounds and the expression for approximating the error of Fisher’s classifier. Our empirical results on synthetic data, including up to five-hundreddimensional featured samples, show that the computations for the error are extremely fast and quite accurate; the approximation differs from the actual error by at most ε = 0.0184340683. 1
Citations
|
1769
|
Introduction to Statistical Pattern Recognition
– Fukunaga
- 1990
|
|
1055
|
Pattern classification
– Duda, Hart, et al.
- 2001
|
|
148
|
Statistical pattern recognition
– Webb
- 1999
|
|
45
|
Kendall’s advanced theory of statistics, volume 1: Distribution theory
– Stuart, Ord
- 1994
|
|
27
|
A PAC-Bayesian margin bound for linear classifiers: Why SVMs work
– Herbrich, Graepel
- 2001
|
|
22
|
On expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix
– Raudys, Duin
- 1998
|
|
9
|
Numerically stable generation of correlation matrices and their factors
– Davies, Higham
- 2000
|
|
5
|
A linear classifier for gaussian class conditional distributions with unequal covariance matrices
– Vaswani
- 2002
|
|
3
|
SPECFUN: A portable FORTRAN package of special functions and test drivers
– Cody
- 1993
|
|
2
|
Bayes Error Evaluation of the Gaussian ML Classifier
– Lee, Choi
- 2000
|
|
2
|
An Efficient Approach to Compute the Threshold for Multi-dimensional Linear Classifiers
– Rueda
- 2004
|
|
2
|
A Novel Method for Fisher Discriminant Analysis
– Xu, Yang, et al.
- 2004
|
|
1
|
A One-dimensional Analysis for the Probability of Error of Linear Classifiers for Normally Distributed Classes. Submitted for Publication, 2004. Electronically available at http://davinci.newcs.uwindsor.ca/∼lrueda/papers/ErrorEstJnl.pdf
– Rueda
|
