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With the proliferation of Web services as a business solution to enterprise application integration, ranking and selecting the best Web services among the providers become an important factor in the success of the business solution. Quality of service (QoS) determines the quality and usability of a service including its price, performance, reliability, integrity, accessibility, availability, interoperability, and security. Given a set of QoS attributes from a variety of sources, it is a challenge to sort through all of them and be able to get the best services that meet QoS requirement. In this paper, we describe a novel method by which Web services can be ranked and selected automatically based on a number of observed QoS parameters and feedback responses learned from prior knowledge. This new approach treats the observed Web services QoS attributes and target Web services relationship, represented by a matrix, as a statistical problem. Using singular value decomposition (SVD) technique, and an user assisted weighting system, implicit higher order correlations among Web services and their associated QoS attributes are extracted and used to estimate the selection of recommended Web services.