Multiplicative Adaptive Algorithms for User Preference Retrieval

Abstract

In contrast to the adoption of linear additive query updating techniques in existing popular algorithms for user preference retrieval, in this paper we design two types of algorithms, the multiplicative adaptive query expansion algorithm MA and the multiplicative adaptive gradient search algorithm MG, both of which use multiplicative query expansion strategies to adaptively improve the query vector. We prove that algorithm MA has a substantially better mistake bound than the Rocchio’s and the Perceptron algorithms in learning a user preference relation determined by a linear classifier with a small number of non-zero coefficients over the real-valued vector space [0, 1]ⁿ.We also show that algorithm MG boosts the usefulness of an index term exponentially, while the gradient descent procedure does so linearly. Our work also generalize the algorithm Winnow in the following aspects: various updating functions may be used; multiplicative updating for a weight is dependent on the value of the corresponding index term, which is more realistic and applicable to real-valued vector space; and finally, a number of documents which may or may not be counterexamples to the algorithm’s current classification are allowed. Practical implementations of algorithms MA and MG have been underway in the next stage development of our intelligent web search tools.