Multi-prototype Support Vector Machine

We extend multiclass SVM to multiple prototypes per class. For this framework, we give a compact constrained quadratic problem and we suggest an efficient algorithm for its optimization that guarantees a local minimum of the objective function. An annealed process is also proposed that helps to escape from local minima. Finally, we report experiments where the performance obtained using linear models is almost comparable to that obtained by state-of-art kernel-based methods but with a significant reduction (of one or two orders) in response time.

[1]  Nathan S. Netanyahu,et al.  PHA*: Finding the Shortest Path with A* in An Unknown Physical Environment , 2011, J. Artif. Intell. Res..

[2]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[3]  Mihalis Yannakakis,et al.  Shortest Paths Without a Map , 1989, Theor. Comput. Sci..

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Koby Crammer,et al.  On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines , 2002, J. Mach. Learn. Res..

[6]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[7]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[8]  Sven Koenig,et al.  Performance bounds for planning in unknown terrain , 2003, Artif. Intell..

[9]  Alessandro Sperduti,et al.  A re-weighting strategy for improving margins , 2002, Artif. Intell..

[10]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[11]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[12]  Maxim Likhachev,et al.  D*lite , 2002, AAAI/IAAI.

[13]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[14]  Baruch Schieber,et al.  The Canadian Traveller Problem , 1991, SODA '91.

[15]  Alessandro Sperduti,et al.  An efficient SMO-like algorithm for multiclass SVM , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[16]  Jorma Laaksonen,et al.  LVQ_PAK: The Learning Vector Quantization Program Package , 1996 .

[17]  Koby Crammer,et al.  On the Learnability and Design of Output Codes for Multiclass Problems , 2002, Machine Learning.

[18]  Alessandro Sperduti,et al.  Discriminant Pattern Recognition Using Transformation-Invariant Neurons , 2000, Neural Computation.