Semi-Supervised Deep Kernel Active Learning for Material Removal Rate Prediction in Chemical Mechanical Planarization.

The material removal rate (MRR) is an important variable but difficult to measure in the chemical-mechanical planarization (CMP) process. Most data-based virtual metrology (VM) methods ignore the large number of unlabeled samples, resulting in a waste of information. In this paper, the semi-supervised deep kernel active learning (SSDKAL) model is proposed. Clustering-based phase partition and phase-matching algorithms are used for the initial feature extraction, and a deep network is used to replace the kernel of Gaussian process regression so as to extract hidden deep features. Semi-supervised regression and active learning sample selection strategies are applied to make full use of information on the unlabeled samples. The experimental results of the CMP process dataset validate the effectiveness of the proposed method. Compared with supervised regression and co-training-based semi-supervised regression algorithms, the proposed model has a lower mean square error with different labeled sample proportions. Compared with other frameworks proposed in the literature, such as physics-based VM models, Gaussian-process-based regression models, and stacking models, the proposed method achieves better prediction results without using all the labeled samples.

Center-Aware Adversarial Autoencoder for Anomaly Detection.

Anomaly detection based on subspace learning has attracted much attention, in which the compactness of subspace is commonly considered as the core concern. Most related studies directly optimize the distance from the subspace representation to the fixed center, and the influence of the anomaly level of each normal sample is not considered to adjust the normal concentrated areas. In such cases, it is difficult to isolate the normal areas from the anomaly ones by making the subspace compact. To this end, we propose a center-aware adversarial autoencoder (CA-AAE) method, which detects anomaly samples by acquiring more compact and discriminative subspace representations. To fully exploit the subspace information to improve the compactness, anomaly-level description and feature learning are novelly integrated herein by dividing the output space of the encoder into presubspace and postsubspace. In presubspace, the toward-center prior distribution is imposed by the adversarial learning mechanism, and the anomaly level of normal samples can be described from a probabilistic perspective. In postsubspace, a novel center-aware strategy is established to enhance the compactness of the postsubspace, which achieves adaptive adjustment of the normal areas by constructing a weighted center based on the anomaly level. Then, a flexible anomaly score function is constructed in the testing stage, in which both the toward-center loss and the reconstruction loss are combined to balance the information in the learned subspace and the original space. Compared to other related methods, the proposed CA-AAE shows the effectiveness and advantages in numerical experiments.

Parameter selection of Gaussian kernel for one-class SVM.

One-class classification (OCC) builds models using only the samples from one class (the target class) so as to predict whether a new-coming sample belongs to the target class or not. OCC widely exists in many application fields, such as fault detection. As an effective tool for OCC, one-class SVM (OCSVM) with the Gaussian kernel has received much attention recently. However, its kernel parameter selection greatly affects its performance and is still an open problem. This paper proposes a novel method to solve this problem. First, an effective way is presented to measure the distances from the samples to the OCSVM enclosing surfaces. Then based on this measurement, an optimization objective function for the parameter selection is put forward. Extensive experiments are conducted on various data sets, and the results verify the effectiveness of the proposed method.

Hyperparameter Selection for Gaussian Process One-Class Classification.

Gaussian processes (GPs) provide predicted outputs with a full conditional statistical description, which can be used to establish confidence intervals and to set hyperparameters. This characteristic provides GPs with competitive or better performance in various applications. However, the specificity of one-class classification (OCC) makes GPs unable to select suitable hyperparameters in their traditional way. This brief proposes to select hyperparameters for GP OCC using the prediction difference between edge and interior positive training samples. Experiments on 2-D artificial and University of California benchmark data sets verify the effectiveness of this method.

Cutting plane method for continuously constrained kernel-based regression.

Incorporating constraints into the kernel-based regression is an effective means to improve regression performance. Nevertheless, in many applications, the constraints are continuous with respect to some parameters so that computational difficulties arise. Discretizing the constraints is a reasonable solution for these difficulties. However, in the context of kernel-based regression, most of existing works utilize the prior discretization strategy; this strategy suffers from a few inherent deficiencies: it cannot ensure that the regression result totally fulfills the original constraints and can hardly tackle high-dimensional problems. This paper proposes a cutting plane method (CPM) for constrained kernel-based regression problems and a relaxed CPM (R-CPM) for high-dimensional problems. The CPM discretizes the continuous constraints iteratively and ensures that the regression result strictly fulfills the original constraints. For high-dimensional problems, the R-CPM accepts a slight and controlled violation to attain a dimensional-independent computational complexity. The validity of the proposed methods is verified by numerical experiments.