Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net

We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied. We also propose an algorithm called MU-QP-RR-W-$l_1$ to efficiently solve ARGEN. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. Finally an application of S&P 500 index tracking with constraints on the stock allocations is performed to provide general guidance for adapting ARGEN to solve real-world problems.

Accelerometer-Based Gait Segmentation: Simultaneously User and Adversary Identification

In this paper, we introduce a new gait segmentation method based on accelerometer data and develop a new distance function between two time series, showing novel and effectiveness in simultaneously identifying user and adversary. Comparing with the normally used Neural Network methods, our approaches use geometric features to extract walking cycles more precisely and employ a new similarity metric to conduct user-adversary identification. This new technology for simultaneously identify user and adversary contributes to cybersecurity beyond user-only identification. In particular, the new technology is being applied to cell phone recorded walking data and performs an accuracy of $98.79\%$ for 6 classes classification (user-adversary identification) and $99.06\%$ for binary classification (user only identification). In addition to walking signal, our approach works on walking up, walking down and mixed walking signals. This technology is feasible for both large and small data set, overcoming the current challenges facing to Neural Networks such as tuning large number of hyper-parameters for large data sets and lacking of training data for small data sets. In addition, the new distance function developed here can be applied in any signal analysis.