Factorization Machines (FMs) are a widely used method for efficiently using high-order feature interactions in classification and regression tasks. Unfortunately, despite increasing interests in FMs, existing work only considers high order information of the input features which limits their capacities in non-linear problems and fails to capture the underlying structures of more complex data. In this work, we present a novel Locally Linear Factorization Machines (LLFM) which overcomes this limitation by exploring local coding technique. Unlike existing local coding classifiers that involve a phase of unsupervised anchor point learning and predefined local coding scheme which is suboptimal as the class label information is not exploited in discovering the encoding and thus can result in a suboptimal encoding for prediction, we formulate a joint optimization over the anchor points, local coding coordinates and FMs variables to minimize classification or regression risk. Empirically, we demonstrate that our approach achieves much better predictive accuracy than other competitive methods which employ LLFM with unsupervised anchor point learning and predefined local coding scheme.
Linear factorization of hypercyclic functions for differential operators
