Time series are often irregularly sampled with uneven time intervals. In multivariate cases, such irregularities may lead to misaligned observations across variables and varying observation counts, making it difficult to extract intrinsic patterns and degrading the classification performance of deep learning models. In this study, we propose an adaptive time encoding approach to address the challenge of irregular sampling in multivariate time-series classification. Our approach generates latent representations at learnable reference points that capture missingness patterns in irregular sequences, enhancing classification performance. We also introduce consistency regularization techniques to incorporate intricate temporal and intervariable information into the learned representations. Extensive experiments demonstrate that our method achieves state-of-the-art performance with high computational efficiency in irregular multivariate time-series classification tasks.

In semiconductor manufacturing, virtual metrology (VM) is a method of predicting physical measurements of wafer qualities using in-process information from sensors on production equipment. The relevance vector machine (RVM) is a sparse Bayesian kernel machine that has been widely used for VM modeling in semiconductor manufacturing. Missing values from equipment sensors, however, preclude training an RVM model due to missing kernels from incomplete instances. Moreover, imputation for such kernels can lead to a loss of model sparsity. In this work, we propose a restricted RVM (RRVM) that selects its basis functions from only complete instances to handle incomplete data for VM. We conduct the experiments using toy data and real-life data from an etching process for wafer fabrication. The results indicate the model’s competitive prediction accuracy with massive missing data while maintaining model sparsity. Note to Practitioners—In recent decades, virtual metrology (VM) has focused on wafer fabrication in semiconductor manufacturing due to its advantages for process monitoring and automation. Typically, signals from production process equipment can predict wafer qualities in VM, which often leads to high data dimensionality. The relevance vector machine (RVM) is an algorithm that can provide a sparse solution to a Bayesian kernel method for a prediction model. Missing components in incomplete data due to sensor failures in wafer fabrication processes, however, hinder model training, and the existing approaches to handling missing data using imputation may lead to a loss of model sparsity. This article proposes a new method for RVM with incomplete data to train a model built on fully available instances by incorporating the available components of incomplete instances into model training. Using the proposed method, one can predict wafer qualities building a model trained to maintain its sparsity. Experiments indicate that the proposed model achieves competitive prediction performance and maintains model sparsity when incomplete instances are used.

Support-based clustering using kernels suffers from serious computational limitations inherent in many kernel methods when applied to very large-scale problems despite its ability to identify clusters with complex shapes. In this paper, we propose a novel clustering algorithm called Voronoi cell-based clustering to expedite support-based clustering using kernels. In contrast to previous studies, including the basin cell-based method, the proposed method achieves computational efficiency in both the training phase to construct a support estimate using sampled data to reduce the evaluation of kernels and the labeling phase to assign a cluster label on each data point nearest its representative point. The performance superiority of the proposed method over the other basin cell-based methods in terms of computational time and storage efficiency is verified by various experiments using benchmark sets and in real applications to image segmentation.