As a crucial technique for identifying irregular samples or outlier patterns, anomaly detection has broad applications in many fields. Convex analysis (CA) is one of the fundamental methods used in anomaly detection, which contributes to the robust approximation of algebra and geometry, efficient computation to a unique global solution, and mathematical optimization for modeling. Despite the essential role and evergrowing research in CA-based anomaly detection algorithms, little work has realized a comprehensive survey of it. To fill this gap, we summarize the CA techniques used in anomaly detection and classify them into four categories of density estimation methods, matrix factorization methods, machine learning methods, and the others. The theoretical background, sub-categories of methods, typical applications as well as strengths and limitations for each category are introduced. This paper sheds light on a succinct and structured framework and provides researchers with new insights into both anomaly detection and CA. With the remarkable progress made in the techniques of big data and machine learning, CA-based anomaly detection holds great promise for more expeditious, accurate and intelligent detection capacities.

Image classification is vital and basic in many data analysis domains. Since real-world images generally contain multiple diverse semantic labels, it amounts to a typical multi-label classification problem. Traditional multi-label image classification relies on a large amount of training data with plenty of labels, which requires a lot of human and financial costs. By contrast, one can easily obtain a correlation matrix of concerned categories in current scene based on the historical image data in other application scenarios. How to perform image classification with only label correlation priors, without specific and costly annotated labels, is an important but rarely studied problem. In this paper, we propose a model to classify images with this kind of weak correlation prior. We use label correlation to recapitulate the sample similarity, employ the prior information to decompose the projection matrix when regressing the label indication matrix, and introduce the norm to select features for each image. Finally, experimental results on several image datasets demonstrate that the proposed model has distinct advantages over current state-of-the-art multilabel classification methods.

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