The nature of statistical learning theory
The nature of statistical learning theory
Learning to extract symbolic knowledge from the World Wide Web
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Deterministic Annealing Approach for Parsimonious Design of Piecewise Regression Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Text Categorization Based on Regularized Linear Classification Methods
Information Retrieval
Pairwise Data Clustering by Deterministic Annealing
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Probabilistic Analysis of the Rocchio Algorithm with TFIDF for Text Categorization
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
Transforming classifier scores into accurate multiclass probability estimates
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robustness of regularized linear classification methods in text categorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Reducing multiclass to binary: a unifying approach for margin classifiers
The Journal of Machine Learning Research
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Convex Optimization
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
Deterministic annealing for semi-supervised kernel machines
ICML '06 Proceedings of the 23rd international conference on Machine learning
Solving multiclass learning problems via error-correcting output codes
Journal of Artificial Intelligence Research
A global optimization technique for statistical classifier design
IEEE Transactions on Signal Processing
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
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In this paper, we propose a general regularization framework for multiclass classification based on discriminant functions. Since the objective function in the primal optimization problem of this framework is always not differentiable, the optimal solution cannot be obtained directly. With the aid of the deterministic annealing approach, a differentiable objective function is derived subject to a constraint on the randomness of the solution. The problem can be approximated by solving a sequence of differentiable optimization problems, and such approximation converges to the original problem asymptotically. Based on this approach, class-conditional posterior probabilities can be calculated directly without assuming the underlying probabilistic model. We also notice that there is a connection between our approach and some existing statistical models, such as Fisher discriminant analysis and logistic regression.