Decomposition in Transition: Adaptive Matrix Factorization - Realtime Data Mining - page 142

Chapter 8
Decomposition in Transition: Adaptive
Matrix Factorization
Abstract We introduce SVD/PCA-based matrix factorization frameworks and
present applications to prediction-based recommendation. Furthermore, we devise
incremental algorithms that enable to compute the considered factorizations adap-
tively in a realtime setting. Besides SVD and PCA-based frameworks, we discuss
more sophisticated approaches like non-negative matrix factorization and Lanczos-
based methods and assess their effectiveness by means of experiments on real-
world data. Moreover, we address a compressive sensing-based approach to
Netflix-like matrix completion problems and conclude the chapter by proposing a
remedy to complexity issues in computing large elements of the low-rank matrices,
which, as we shall see, is a recurring problem related to factorization-based
prediction methods.
In conventional modeling, the states correspond to the products being viewed. As
we saw in Chap. 5 , this assumption essentially complies with the Markov property
of most RE applications. It would of course be better, though, to gather more
information in each state. This applies mainly to previous transactions, but other
dimensions such as user, price, and channels with their various attributes may also
be useful. Thus, we will drop the considered Markov property and describe the
corresponding procedure in this chapter.
This is where the realtime approach described in this topic coincides with the
complex analysis models on which most RE researchers are currently working
(Chap. 2 ) . While we have so far concentrated only on the simplest analysis scenario,
namely, product rules in the form s ! s 0 , albeit in a modern realtime analytical
context, the latest analytical approaches can already achieve good predictions,
sometimes using multiple dimensions, but only in a static analysis context. So the
obvious solution is to combine the two approaches. In principle it makes no
difference which route is followed: expanding RL to include more extensive state
definitions or adding control functions to conventional approaches. Given the
general focus of this topic, we will concentrate on the first route: expanding the
definition of states in RL.