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Despite the popularity of principal component analysis (PCA) as an anomaly detection technique, the main shortage of PCA-based anomaly detection models is their interpretability. Constructing the abnormal subspace of PCA (i.e., the subspace spanned by the least significant principal components (PCs)), with sparse and orthogonal loading vectors provides a means of anomaly interpretation. However, solving all abnormal sparse PCs one by one through semi-definite programming is time consuming. In this paper, we derive an adapted projection deflation method for extracting least significant PCs and propose an alternating direction method of multipliers (ADMM) solution for constructing the sparse abnormal subspace. Our experiments on two real world datasets showed that the proposed ADMM solution achieved comparable detection accuracy and sparsity as the SDP solution and is 10 times more efficient, which makes it more suitable for application domains with higher dimensions.

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