Random Tensor Analysis: Outlier Detection and Sample-Size Determination

High-dimensional signal processing and data analysis have been appealing to researchers in recent decades. Outlier detection and sample-size determination are two essential pre-processing tasks for many signal processing applications. However, fast outlier detection for tensor data with arbitrary orders is still in high demand. Furthermore, sample-size determination for random tensor data has not been addressed in the literature. To fill this knowledge gap, we first derive new tensor Chernoff tail-bounds for random Hermitian tensors. According to our derived tail-bounds, we propose a novel approach for joint outlier detection and sample-size determination. The mathematical relationship among outlier-threshold (sample-size-threshold) probability, outlier-threshold spectrum, and critical sample-size along with the computational-complexity reduction brought by our proposed new analytic approach over the existing methods is also investigated through numerical evaluation over a variety of real tensor data.