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This work presents a novel method called dense projection for unsupervised anomaly detection (DPAD). The main idea is maximizing the local density of (normal) training data and then determining whether a test data is anomalous or not by evaluating its density. Specifically, DPAD uses a deep neural network to learn locally dense representations of normal data. Since density estimation is computationally expensive, we minimize the local distances of the representations in an iteratively reweighting manner, where the weights are updated adaptively and the parameters are regularized to avoid model collapse (all representations collapse to a single point). Compared with many state-of-the-art methods of anomaly detection, our DPAD does not rely on any assumption about the distribution or spatial structure of the normal data and representations. Moreover, we provide theoretical guarantees for the effectiveness of DPAD. The experiments show that our method DPAD is effective not only in traditional one-class classification problems but also in scenarios with complex normal data composed of multiple classes.