text: The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building robust classifier for the PU problem is very challenging, especially for complex data where the negative samples overwhelm and mislabeled samples or corrupted features exist. To address these three issues, we propose a robust learning framework that unifies AUC maximization (a robust metric for biased labels), outlier detection (for excluding wrong labels), and feature selection (for excluding corrupted features). The generalization error bounds are provided for the proposed model that give valuable insight into the theoretical performance of the method and lead to useful practical guidance, e.g., to train a model, we find that the included unlabeled samples are sufficient as long as the sample size is comparable to the number of positive samples in the training process. Empirical comparisons and two real-world applications on surgical site infection (SSI) and EEG seizure detection are also conducted to show the effectiveness of the proposed model.
  @cite_3: The outlier detection problem has important applications in the field of fraud detection, network robustness analysis, and intrusion detection. Most such applications are high dimensional domains in which the data can contain hundreds of dimensions. Many recent algorithms use concepts of proximity in order to find outliers based on their relationship to the rest of the data. However, in high dimensional space, the data is sparse and the notion of proximity fails to retain its meaningfulness. In fact, the sparsity of high dimensional data implies that every point is an almost equally good outlier from the perspective of proximity-based definitions. Consequently, for high dimensional data, the notion of finding meaningful outliers becomes substantially more complex and non-obvious. In this paper, we discuss new techniques for outlier detection which find the outliers by studying the behavior of projections from the data set.
summary: Outlier Detection To the best of our knowledge, the outlier issue has not been considered in PU classification. Thus, here we provide a brief overview of outlier detection methods in general settings. Existing outlier detection researches can be roughly categorized as variance-based approaches and model-based approaches. The variance-based approaches detect the outliers through a set of criterion used to measure the difference between the data and the rest of the dataset. These criterion can come from statistical analysis , distance metric and density ratio . They usually work well in low dimensional space when the data amount is not too huge. But they are difficult to be integrated into other models like PU learning. The model-based approaches detect outliers through certain models. Typical methods include the regularized principal component regression , regularized partial least square , SVM based algorithms and others. More detailed reviews can be found in @cite_3 . None of these works were integrated with PU learning models.