The New Privacy Preserving Algorithms For Linear Programming And SVMS

When solving a linear program, the coefficient of objective function, the equality constraint matrix and the relevant vector may be possessed by different entities who do not want to make them public, this phenomenon cause privacy problems. How to dealing with the linear program without revealing the privacy data is an urgent problem.Support Vector Machines is a new method in the field of data mining, which have more advantages than traditional learning theory. Furthermore, the method can overcome many problems such as overfitting, dimension disaster, local extremum and so on. Distributed support vector machines which allocate training samples to each node, could overcome the complexity of data exchange, variability and privacy issues.Firstly, we introduce a privacy-preserving linear programming in this paper. Based on the privacy-preserving algorithm for a linear program on vertical distribution data and horizontal distribution data, Mangasarian propose an random matrix which make the original linear programming problem into a secure linear programming problem. However, when the random matrix is irreversible, the original linear programming problem and the secure linear programming problem are not equivalent. Here, a reversible random matrix is used to make sure the original linear program could be transformed into an equivalent secure linear program. The numerical experiments show that the results obtained by the algorithm in this paper coincide with that by original linear program ifλis large enough.Secondly, we introduce the basic theories of support vector machines and consensus based distributed support vector machines. Using the basic theories, we design an algorithm for horizontal distribution data which regard a entity as a node. Moreover, this algorithm can guarantee the privacy of data.