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Web page classification is one of the essential techniques for Web mining because classifying Web pages of an interesting class is often the first step of mining the Web. However, constructing a classifier for an interesting class requires laborious preprocessing such as collecting positive and negative training examples. For instance, in order to construct a "homepage" classifier, one needs to collect a sample of homepages (positive examples) and a sample of nonhomepages (negative examples). In particular, collecting negative training examples requires arduous work and caution to avoid bias. The paper presents a framework, called positive example based learning (PEBL), for Web page classification which eliminates the need for manually collecting negative training examples in preprocessing. The PEBL framework applies an algorithm, called mapping-convergence (M-C), to achieve high classification accuracy (with positive and unlabeled data) as high as that of a traditional SVM (with positive and negative data). M-C runs in two stages: the mapping stage and convergence stage. In the mapping stage, the algorithm uses a weak classifier that draws an initial approximation of "strong" negative data. Based on the initial approximation, the convergence stage iteratively runs an internal classifier (e.g., SVM) which maximizes margins to progressively improve the approximation of negative data. Thus, the class boundary eventually converges to the true boundary of the positive class in the feature space. We present the M-C algorithm with supporting theoretical and experimental justifications. Our experiments show that, given the same set of positive examples; the M-C algorithm outperforms one-class SVMs, and it is almost as accurate as the traditional SVMs.