The idea of Innovation Search, which was initially proposed for data clustering, was recently used for outlier detection. In the application of Innovation Search for outlier detection, the directions of innovation were utilized to measure the innovation of the data points. We study the Innovation Values computed by the Innovation Search algorithm under a quadratic cost function and it is proved that Innovation Values with the new cost function are equivalent to Leverage Scores. This interesting connection is utilized to establish several theoretical guarantees for a Leverage Score based robust PCA method and to design a new robust PCA method. The theoretical results include performance guarantees with different models for the distribution of outliers and the distribution of inliers. In addition, we demonstrate the robustness of the algorithms against the presence of noise. The numerical and theoretical studies indicate that while the presented approach is fast and closed-form, it can outperform most of the existing algorithms.

中文翻译：

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通过利用统计和创新搜索的封闭形式、可证明和稳健的 PCA

最初提出用于数据聚类的创新搜索的想法最近被用于异常值检测。在创新搜索异常值检测的应用中，创新的方向被用来衡量数据点的创新。我们研究了创新搜索算法在二次成本函数下计算的创新价值，证明了具有新成本函数的创新价值相当于杠杆分数。这个有趣的联系被用来为基于杠杆分数的稳健 PCA 方法建立几个理论保证，并设计一种新的稳健 PCA 方法。理论结果包括对异常值分布和内部值分布的不同模型的性能保证。此外，我们证明了算法对噪声存在的鲁棒性。数值和理论研究表明，虽然所提出的方法是快速和封闭形式的，但它可以胜过大多数现有算法。