An Eecient Recursive Partitioning Algorithm for Classiication, Using Wavelets

We describe and analyze a new dyadic recursive partitioning algorithm for eecient classiication of large two-dimensional data sets, called progressive classiication. It uses generic (parametric or nonparametric) classiiers 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 classiication process, the algorithm either decides to classify the whole block as belonging to a certain class, or to reexamine the data at a higher-resolution level. We present simple theoretical results showing that, compared to sample-by-sample algorithms, progressive classiication is computationally more eecient and also (under certain conditions) more accurate. We outline how progressive classiication deals with data in one dimension and in dimensions higher than three, and we brieey discuss the complexity/accuracy tradeoo.