In this paper, a novel approach is presented to mitigate the issue of domain shift observed in big-data classification. Since little information is available about the shift, we introduce a "distortion model", and obtain additional data-samples to represent the shift. Next, a deep neural network (DNN), referred as "classifier," is used to compensate for the shift by learning through these additional samples while maintaining performance on training samples. As the exact magnitude of domain shift is uncertain, we compensate for the optimal expected shift by formulating a zero-sum game. In the proposed game, the distortion model is viewed as the maximizing player which increases the domain shift while the classifier becomes the minimizing player that reduces the impact of domain shift on learning. The Nash solution of the game, which is demonstrated mathematically, provides the domain shift and its optimal adaptation through the classifier. To solve the proposed game for the Nash solution, a direct error-driven learning scheme is introduced where a cost function is derived and solved for each layer in the DNN and the distortion model. Comprehensive mathematical and simulation study is presented to demonstrate the efficacy of the approach.

In this article, a novel learning methodology is introduced for the problem of classification in the context of high-dimensional data. In particular, the challenges introduced by high-dimensional data sets are addressed by formulating a$L_{1}$regularized zero-sum game where optimal sparsity is estimated through a two-player game between the penalty coefficients/sparsity parameters and the deep neural network weights. In order to solve this game, a distributed learning methodology is proposed where additional variables are utilized to derive layerwise cost functions. Finally, an alternating minimization approach developed to solve the problem where the Nash solution provides optimal sparsity and compensation through the classifier. The proposed learning approach is implemented in a parallel and distributed environment through a novel computational algorithm. The efficiency of the approach is demonstrated both theoretically and empirically with nine data sets.

In this brief, heterogeneity and noise in big data are shown to increase the generalization error for a traditional learning regime utilized for deep neural networks (deep NNs). To reduce this error, while overcoming the issue of vanishing gradients, a direct error-driven learning (EDL) scheme is proposed. First, to reduce the impact of heterogeneity and data noise, the concept of a neighborhood is introduced. Using this neighborhood, an approximation of generalization error is obtained and an overall error, comprised of learning and the approximate generalization errors, is defined. A novel NN weight-tuning law is obtained through a layer-wise performance measure enabling the direct use of overall error for learning. Additional constraints are introduced into the layer-wise performance measure to guide and improve the learning process in the presence of noisy dimensions. The proposed direct EDL scheme effectively addresses the issue of heterogeneity and noise while mitigating vanishing gradients and noisy dimensions. A comprehensive simulation study is presented where the proposed approach is shown to mitigate the vanishing gradient problem while improving generalization by 6%.

In this paper, a novel dimension-reduction approach is presented to overcome challenges such as nonlinear relationships, heterogeneity, and noisy dimensions. Initially, the p attributes in the data are first organized into random groups. Next, to systematically remove redundant and noisy dimensions from the data, each group is independently mapped into a low dimensional space via a parametric mapping. The group-wise transformation parameters are estimated using a low-rank approximation of distance covariance. The transformed attributes are reorganized into groups based on the magnitude of their respective eigenvalues. The group-wise organization and reduction process is performed until a user-defined criterion on eigenvalues is satisfied. In addition, novel procedures are introduced to aggregate the transformation parameters when the data is available in batches. Overall performance is demonstrated with extensive simulation analysis on classification by employing 10 data-sets.

While analyzing high dimensional data-sets using deep neural network (NN), increased sparsity is desirable but requires careful selection of "sparsity parameters." In this paper, a novel distributed learning methodology is proposed to optimize the NN while addressing this challenge. To address this challenge, the optimal sparsity in the NN is estimated via a two player zero-sum game in the paper. In the proposed game, sparsity parameter is the first player with the aim of increasing sparsity in the NN while NN weights is the second player with the goal of improving its performance in the presence of increased sparsity. To solve the game, additional variables are introduced into the optimization problem such that the output at every layer in the NN depends on this variable instead of the previous layer. Using these additional variables, layer wise cost-functions are derived that are then independently optimized to learn the additional variables, NN weights and the sparsity parameters. To implement the proposed learning procedure in a parallelized and distributed environment, a novel computational algorithm is also proposed. The efficiency of the proposed approach is demonstrated using a total of six data-sets.

In this paper, a novel methodology to reduce the generalization errors occurring due to domain shift in big data classification is presented. This reduction is achieved by introducing a suitably selected domain shift to the training data via what is referred to as "distortion model". These distortions are introduced through an affine transformation and additional data-samples are obtained. Next, a deep neural network (NN), referred as "classifier", is used to classify both the original and the additional data samples. By learning from both the original and additional data-samples, the classifier compensates for the domain shift while maintaining its performance on original data. However, as the exact magnitude of the shift one would encounter in real applications is unknown a priori and difficult to predict. The objective is to compensate for the optimal shift that can be introduced by the distortion model without significantly degrading the performance of the model. A two-player zero-sum game is thus designed where the first player is the distortion model with the aim of increasing the domain shift. The classifier then becomes the second player whose aim is to minimize the impact of domain shift. Finally, a direct error-driven learning scheme is utilized to minimize the impact of the classifier while maximizing the domain shift. A comprehensive simulation study is presented where a 12% improvement in the presence of domain shift is demonstrated. The proposed approach is also shown to improve generalization by 6%.

Traffic volume forecasts are used by many transportation analysis and management systems to better characterize and react to fluctuating traffic patterns. Most current forecasting methods do not take advantage of the underlying functional characteristics of the time series to make predictions. This paper presents a methodology that uses functional principal components analysis to create high-quality online traffic volume forecasts. The methodology is validated with a data set of 1755 days of 15 min aggregated traffic volume time series. Compared with 365 randomly selected days, the functional forecasts are found to outperform traditional seasonal autoregressive integrated moving average-based methods in both count deviation and root mean squared error. In addition, through the functional data analysis approach the full exploitation of the continuous nature of the data can be achieved.

In this paper, the relevance of deep neural network (DNN) is studied in big data scenarios, specifically for prognostics applications. It is observed that fault predictions can be performed more efficiently when DNN is used with a pre-processing step. A novel hierarchical dimension reduction (HDR) approach is therefore proposed as a pre-processing step to DNN. This two-step approach is shown to be effective in extracting value from complex and uncertain big data. It is shown that use of HDR prior to DNN improves convergence and allows for the possibility of reduction in model size without any drop in accuracy. A comprehensive methodology is developed to facilitate prognostics using DNN. Simulation results are included to demonstrate the overall methodology using big data-sets.