Low-rank tensor recovery in the presence of sparse but arbitrary errors is an important problem with many practical applications. In this work, we propose a general framework that recovers low-rank tensors, in which the data can be deformed by some unknown transformation and corrupted by arbitrary sparse errors. We present a unified presentation of the surrogate-based formulations that incorporate the feacture of rectification and alignment simultaneously, and establish worst-case error bounds of the recovered tensor. In this context, the state-of-the-art methods "RASL" and "TILT" can be viewed as two special cases of our work, and yet each only performs part of the function of our method. Subsequently, we study the optimization aspects of the problem in detail by deriving two algorithms, one based on ADMM and the other based on proximal gradient. We provide global optimality convergence guarantees for the latter algorithm, and demonstrate the performance of the former through in-depth simulations. Finally, we present extensive experimental results on public datasets to demonstrate the efficacy of our proposed framework and algorithms.
Complex Event Processing (CEP) has emerged as a technology for monitoring event streams in search of user specified event patterns. When a CEP system is deployed in sensitive environments the user may wish to mitigate leaks of private information while ensuring that useful nonsensitive patterns are still reported. In this paper we consider how to suppress events in a stream to reduce the disclosure of sensitive patterns while maximizing the detection of nonsensitive patterns. We first formally define the problem of utilitymaximizing event suppression with privacy preferences, and analyze its computational hardness. We then design a suite of real-time solutions to solve this problem. Our first solution optimally solves the problem at the event-type level. The second solution, at the event-instance level, further optimizes the event-type level solution by exploiting runtime event distributions using advanced pattern match cardinality estimation techniques. Our user study and experimental evaluation over both real-world and synthetic event streams show that our algorithms are effective in maximizing utility yet still efficient enough to offer near real-time system responsiveness.
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