Co-clustering structural temporal data with applications to semiconductor manufacturing

Recent years have witnessed data explosion in semiconductor manufacturing due to advances in instrumentation and storage techniques. The large amount of data associated with process variables monitored over time form a rich reservoir of information, which can be used for a variety of purposes, such as anomaly detection, quality control, and fault diagnostics. In particular, following the same recipe for a certain Integrated Circuit device, multiple tools and chambers can be deployed for the production of this device, during which multiple time series can be collected, such as temperature, impedance, gas flow, electric bias, etc. These time series naturally fit into a two-dimensional array (matrix), i.e., each element in this array corresponds to a time series for one process variable from one chamber. To leverage the rich structural information in such temporal data, in this article, we propose a novel framework named C-Struts to simultaneously cluster on the two dimensions of this array. In this framework, we interpret the structural information as a set of constraints on the cluster membership, introduce an auxiliary probability distribution accordingly, and design an iterative algorithm to assign each time series to a certain cluster on each dimension. Furthermore, we establish the equivalence between C-Struts and a generic optimization problem, which is able to accommodate various distance functions. Extensive experiments on synthetic, benchmark, as well as manufacturing datasets demonstrate the effectiveness of the proposed method.