異常検出におけるSimilarity Based ModelingとGaussian Processesの関連に関して

摘要

Anomaly detection can be applied to health monitoring of industrial plants, human medical conditions, vehicle conditions, and so on. A well-known anomaly detection method "Similarity Based Modeling" (SBM) proposed by Stephan W. Wegerich is acknowledged as an effective and essential method in this field. This report first shows that SBM is naturally derived as a special case of "Gaussian Processes" (GP) by regarding the similarity function in SBM as the kernel function in GP, where GP was proposed before the SBM patent. This fact provides us a new interpretation that GP is an example based nonlinear regression method. Based on this interpretation, next we proposed a method for relaxing the scalability problem of GP, that is, a method for reducing the size of gram matrix consisting of pairwise similarities on training samples. This method picks up the reference data for explaining the input data from the training dataset and dynamically construct "reduced" gram matrix. By using this matrix, we can estimate the output without losing the accuracy. The anomaly detection algorithm is applied to practical health monitoring problem of an electric plant with human operation and we confirmed that our algorithm successfully detect the pre-fault events before the actual fault.%プラントや生体，乗り物などのシステムに取り付けた複数のセンサ出力をもとにして，システムの異常を検出する手法として，Stephan W.Wegerichらが提案したSimilarity Based Modeling（SBM）がある。この手法は，高感度な異常検出器を構築するために必要な本質的技術であり，その特許も成立している.本報告では，まず，この手法以前に存在していた非線形回帰アルゴリズムの-つであるGaussian Processes（GP）を用いて異常検出アルゴリズムを構成した場合，カーネル関数を類似度とみなせば，SBMがOPを使った異常検出の特殊ケースとなることを示す.この解釈から，GPは事例ベースの非線形回帰計算法であることが分かり，その解釈に基づいて，動的にグラム行列を構築ながら出力値の分布を推定できる異常検出手法を提案する.この手法を実際のプラントに適用し，異常の予兆現象を捉えることに成功した.