Mixture modeling and inference for recognition of multiple recurring unknown patterns

We consider the problem of finding unknown patterns that are recurring across multiple sets. For example, finding multiple objects that are present in multiple images or a short DNA code that is repeated across multiple DNA sequences. Earlier work on the topic includes a statistical modeling approach in which the same template is placed at a random position in multiple independent sets. Using mixture modeling, we propose an extension to the approach that allows the detection of multiple templates placed across multiple sets. Moreover, we present an expectation-maximization algorithm for jointly estimating multiple templates based on a mixture of non-Gaussian distributions. To address the non-convexity of the problem, a robust initialization method is presented and theoretical guarantees are provided. We evaluate the performance of the algorithm on both synthetic data and real-world data consisting of electrical voltage recordings of home appliance activations. Our results indicate that the proposed algorithm significantly improves the detection accuracy relative to the single pattern model.