Unbiased SVM Density Estimation with Application to Graphical Pattern Recognition

Classification of structured data (i.e., data that are represented as graphs) is a topic of interest in the machine learning community. This paper presents a different, simple approach to the problem of structured pattern recognition, relying on the description of graphs in terms of algebraic binary relations. Maximum-a-posteriori decision rules over relations require the estimation of class-conditional probability density functions (pdf) defined on graphs. A nonparametric technique for the estimation of the pdfs is introduced, on the basis of a factorization of joint probabilities into individual densities that are modeled, in an unsupervised fashion, via Support Vector Machine (SVM). The SVM training is accomplished applying support vector regression on an unbiased variant of the Parzen Window. The behavior of the estimation algorithm is first demonstrated on a synthetic distribution. Finally, experiments of graph-structured image recognition from the Caltech Benchmark dataset are reported, showing a dramatic improvement over the results (available in the literature) yielded by state-of-the-art connectionist models for graph processing, namely recursive neural nets and graph neural nets.