A novel tensor algebraic approach for high-dimensional outlier detection under data misalignment

In this paper, we present a novel unsupervised method for detecting outliers in image databases, when the images are misaligned by action of transformations forming a group. The main idea is that when the aligned data lie in a low dimensional subspace, the misaligned data, assuming that the group size is small, will lie in a low dimensional group-invariant subspace. We then explicitly exploit this additional algebraic property and propose an algorithm for detecting outliers that is robust to data misalignment. We perform extensive comparison with current state of the art methods and show the superior performance of our algorithm.