An Efficient Recursive Partitioning Algorithm for Classification, Using Wavelets

We describe and analyze a new dyadic recursive partitioning algorithm for efficient classification of large two-dimensional data sets, called progressive classification. It uses generic (parametric or nonparametric) classifiers on a low-resolution representation of the data obtained using the discrete wavelet transform. In this representation, each point corresponds to a block of samples from the original data. At each step of the classification process, the algorithm either decides to classify the whole block as belonging to a certain class, or to re-examine the data at a higher-resolution level. We present simple theoretical results showing that, compared to sample-by-sample algorithms, progressive classification is computationally more efficient and also (under certain conditions) more accurate. We outline how progressive classification deals with data in one dimension and in dimensions higher than three, and we briefly discuss the complexity/accuracy tradeoff.