Massive data discrimination via linear support vector machines

• Published in: Optimization methods & software Vol. 13; no. 1; pp. 1 - 10
• Main Authors: Bradley, P.S., Mangasarian, O.L.
• Format: Journal Article
• Language: English
• Published: Gordon and Breach Science Publishers 01.01.2000
• Subjects: Linear Programming Chunking; Support Vector Machines
• ISSN: 1055-6788; 1029-4937
• DOI: 10.1080/10556780008805771

A linear support vector machine formulation is used to generate a fast, finitely-terminating linear-programming algorithm for discriminating between two massive sets in n-dimen-sional space, where the number of points can be orders of magnitude larger than n. The algorithm creates a succession of sufficiently small linear programs that separate chunks of the data at a time. The key idea is that a small number of support vectors, corresponding to linear programming constraints with positive dual variables, are carried over between the successive small linear programs, each of which containing a chunk of the data. We prove that this procedure is monotonic and terminates in a finite number of steps at an exact solution that leads to an optimal separating plane for the entire dataset. Numerical results on fully dense publicly available datasets, numbering 20,000 to 1 million points in 32-dimensional space, confirm the theoretical results and demonstrate the ability to handle very large problems