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2012

Confusion Matrix Stability Bounds for Multiclass Classification

Machart, Pierre, Ralaivola, Liva

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In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems.

The originality of our work is that we propose to use the confusion matrix of a classifier as a measure of its quality; our contribution is in the line of work which attempts to set up and study the statistical properties of new evaluation measures such as, e.g.
ROC curves.
In the confusion-based learning framework we propose, we claim that a targetted objective is to minimize the size of the confusion matrix C, measured through its operator norm ||C||.

Confusion Matrix Stability Bounds for Multiclass Classification · Around

Built on

Solutions of Ill-Posed Problems
Tikhonov, A.N., Arsenin, V.Y.: · 1977
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Estimation of Dependences Based on Empirical Data
Vapnik, V.N.: · 1982
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On the method of bounded differences
McDiarmid, C.: · 1989
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Multi-class support vector machines
Original
Weston, J., Watkins, C.: · 1998
Earlier work this paper cites.
An Introduction to Support Vector Machines
Cristianini, N., Shawe-Taylor, J.: · 2000
Earlier work this paper cites.

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