** High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However, in many cases, data sets have underlying structures, such as in advanced manufacturing systems. If extracted correctly, efficient methods for process control can be developed. This paper proposes a robust sparse dimensionality reduction approach for correlated high-dimensional process monitoring to address the aforementioned issues. The developed monitoring technique uses robust sparse probabilistic PCA to reduce the dimensionality of the data stream while retaining interpretability. The proposed methodology utilizes Bayesian variational inference to obtain the estimates of a probabilistic representation of PCA. Simulation studies were conducted to verify the efficacy of the proposed methodology. Furthermore, we conducted a case study for change detection for in-line Raman spectroscopy to validate the efficiency of our proposed method in a practical scenario. **

** Artificial neural networks (ANNs) have become the driving force behind recent artificial intelligence (AI) research. An important problem with implementing a neural network is the design of its architecture. Typically, such an architecture is obtained manually by exploring its hyperparameter space and kept fixed during training. This approach is both time-consuming and inefficient. Furthermore, modern neural networks often contain millions of parameters, whereas many applications require small inference models. Also, while ANNs have found great success in big-data applications, there is also significant interest in using ANNs for medium- and small-data applications that can be run on energy-constrained edge devices. To address these challenges, we propose a neural network synthesis methodology (SCANN) that can generate very compact neural networks without loss in accuracy for small and medium-size datasets. We also use dimensionality reduction methods to reduce the feature size of the datasets, so as to alleviate the curse of dimensionality. Our final synthesis methodology consists of three steps: dataset dimensionality reduction, neural network compression in each layer, and neural network compression with SCANN. We evaluate SCANN on the medium-size MNIST dataset by comparing our synthesized neural networks to the well-known LeNet-5 baseline. Without any loss in accuracy, SCANN generates a $46.3\times$ smaller network than the LeNet-5 Caffe model. We also evaluate the efficiency of using dimensionality reduction alongside SCANN on nine small to medium-size datasets. Using this methodology enables us to reduce the number of connections in the network by up to $5078.7\times$ (geometric mean: $82.1\times$), with little to no drop in accuracy. We also show that our synthesis methodology yields neural networks that are much better at navigating the accuracy vs. energy efficiency space. **

** In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a generic EM problem to considerably reduce the dimensionality of the problem and thus, the computational complexity, without imposing considerable errors. By employing the dimensionality reduction concept using the more recently demonstrated autoencoder technique, we redefine the conventional many-to-one design problem in EM nanostructures into a one-to-one problem plus a much simpler many-to-one problem, which can be simply solved using an analytic formulation. This approach reduces the computational complexity in solving both the forward problem (i.e., analysis) and the inverse problem (i.e., design) by orders of magnitude compared to conventional approaches. In addition, it provides analytic formulations that, despite their complexity, can be used to obtain intuitive understanding of the physics and dynamics of EM wave interaction with nanostructures with minimal computation requirements. As a proof-of-concept, we applied such an efficacious method to design a new class of on-demand reconfigurable optical metasurfaces based on phase-change materials (PCM). We envision that the integration of such a DL-based technique with full-wave commercial software packages offers a powerful toolkit to facilitate the analysis, design, and optimization of the EM nanostructures as well as explaining, understanding, and predicting the observed responses in such structures. **

** In recent years, there has been an exponential growth in the number of complex documents and texts that require a deeper understanding of machine learning methods to be able to accurately classify texts in many applications. Many machine learning approaches have achieved surpassing results in natural language processing. The success of these learning algorithms relies on their capacity to understand complex models and non-linear relationships within data. However, finding suitable structures, architectures, and techniques for text classification is a challenge for researchers. In this paper, a brief overview of text classification algorithms is discussed. This overview covers different text feature extractions, dimensionality reduction methods, existing algorithms and techniques, and evaluations methods. Finally, the limitations of each technique and their application in the real-world problem are discussed. **

** We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that coherent sets of particle trajectories can be computed by applying kernel CCA to Lagrangian data. We demonstrate the efficiency of this approach with several examples, namely the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Furthermore, we propose a straightforward generalization of dynamic mode decomposition (DMD) called coherent mode decomposition (CMD). **

** Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not robust, as they are sensitive to outliers. To alleviate this problem, this paper introduces the Self-Paced Learning mechanism into PPCA, and proposes a novel method called Self-Paced Probabilistic Principal Component Analysis (SP-PPCA). Furthermore, we design the corresponding optimization algorithm based on the alternative search strategy and the expectation-maximization algorithm. SP-PPCA looks for optimal projection vectors and filters out outliers iteratively. Experiments on both synthetic problems and real-world datasets clearly demonstrate that SP-PPCA is able to reduce or eliminate the impact of outliers. **

** Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a newly developed metric on the space of SPDMs to quantify differences across FC observations and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with classification rates that match or outperform state-of-the-art techniques. **

** We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude. **

** Is all of machine learning supervised to some degree? The field of machine learning has traditionally been categorized pedagogically into $supervised~vs~unsupervised~learning$; where supervised learning has typically referred to learning from labeled data, while unsupervised learning has typically referred to learning from unlabeled data. In this paper, we assert that all machine learning is in fact supervised to some degree, and that the scope of supervision is necessarily commensurate to the scope of learning potential. In particular, we argue that clustering algorithms such as k-means, and dimensionality reduction algorithms such as principal component analysis, variational autoencoders, and deep belief networks are each internally supervised by the data itself to learn their respective representations of its features. Furthermore, these algorithms are not capable of external inference until their respective outputs (clusters, principal components, or representation codes) have been identified and externally labeled in effect. As such, they do not suffice as examples of unsupervised learning. We propose that the categorization `supervised vs unsupervised learning' be dispensed with, and instead, learning algorithms be categorized as either $internally~or~externally~supervised$ (or both). We believe this change in perspective will yield new fundamental insights into the structure and character of data and of learning algorithms. **

** Objective: A variety of pattern analysis techniques for model training in brain interfaces exploit neural feature dimensionality reduction based on feature ranking and selection heuristics. In the light of broad evidence demonstrating the potential sub-optimality of ranking based feature selection by any criterion, we propose to extend this focus with an information theoretic learning driven feature transformation concept. Methods: We present a maximum mutual information linear transformation (MMI-LinT), and a nonlinear transformation (MMI-NonLinT) framework derived by a general definition of the feature transformation learning problem. Empirical assessments are performed based on electroencephalographic (EEG) data recorded during a four class motor imagery brain-computer interface (BCI) task. Exploiting state-of-the-art methods for initial feature vector construction, we compare the proposed approaches with conventional feature selection based dimensionality reduction techniques which are widely used in brain interfaces. Furthermore, for the multi-class problem, we present and exploit a hierarchical graphical model based BCI decoding system. Results: Both binary and multi-class decoding analyses demonstrate significantly better performances with the proposed methods. Conclusion: Information theoretic feature transformations are capable of tackling potential confounders of conventional approaches in various settings. Significance: We argue that this concept provides significant insights to extend the focus on feature selection heuristics to a broader definition of feature transformation learning in brain interfaces. **

** In this paper, we propose a novel Convolutional Neural Network (CNN) structure for general-purpose multi-task learning (MTL), which enables automatic feature fusing at every layer from different tasks. This is in contrast with the most widely used MTL CNN structures which empirically or heuristically share features on some specific layers (e.g., share all the features except the last convolutional layer). The proposed layerwise feature fusing scheme is formulated by combining existing CNN components in a novel way, with clear mathematical interpretability as discriminative dimensionality reduction, which is referred to as Neural Discriminative Dimensionality Reduction (NDDR). Specifically, we first concatenate features with the same spatial resolution from different tasks according to their channel dimension. Then, we show that the discriminative dimensionality reduction can be fulfilled by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN. The use of existing CNN components ensures the end-to-end training and the extensibility of the proposed NDDR layer to various state-of-the-art CNN architectures in a "plug-and-play" manner. The detailed ablation analysis shows that the proposed NDDR layer is easy to train and also robust to different hyperparameters. Experiments on different task sets with various base network architectures demonstrate the promising performance and desirable generalizability of our proposed method. The code of our paper is available at https://github.com/ethanygao/NDDR-CNN. **

** In this paper, we present a novel approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the \textit{kernel trick} can be adapted to be applicable. Some dimensionality reductions and variable fixing strategies are also developed for these models. An extensive battery of experiments has been run which reveal the powerfulness of our proposal as compared with other previously proposed methodologies. **