Matrix methods for perfect signal recovery underlying range space of operators

The purpose of this work is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by a new matrix method. To this end, first we obtain more structures of the canonical $K$-dual. % and survey optimal $K$-dual problem under probabilistic erasures. Then, we survey the problem of recovering and robustness of signals when the erasure set satisfies the minimal redundancy condition or the $K$-frame is maximal robust. Furthermore, we show that the error rate is reduced under erasures if the $K$-frame is of uniform excess. Toward the protection of encoding frame (K-dual) against erasures, we introduce a new concept so called $(r,k)$-matrix to recover lost data and solve the perfect recovery problem via matrix equations. Moreover, we discuss the existence of such matrices by using minimal redundancy condition on decoding frames for operators. We exhibit several examples that illustrate the advantage of using the new matrix method with respect to the previous approaches in existence construction. And finally, we provide the numerical results to confirm the main results in the case noise-free and test sensitivity of the method with respect to noise.

Data-Driven Quality Prediction of Batch Processes Based on Minimal-Redundancy-Maximal-Relevance Integrated Convolutional Neural Network

For batch processes that are extensively applied in modern industry and characterized by nonlinearity and dynamics, quality prediction is significant to obtain high-quality products and maintain production safety. However, some quality variables and key performance indicators are difficult to measure online. In addition, the mechanism-based model for batch processes is usually tough to acquire due to the strong nonlinearity and dynamics, which makes quality prediction a challenge. With the accumulation of historical process data, data-driven methods for quality prediction gain increasing attention, among which convolutional neural network (CNN) is quite successful for its automatic feature extraction of nonlinear features from raw data. Considering that most CNN-based methods mainly take the variety of extracted features into account and ignore the redundancy between them, this paper introduces the minimal-redundancy-maximal-relevance algorithm to select features obtained by original CNN and further improves it with a feature selection layer to form the proposed method referred as mRMR-CNN. Then, a quality prediction model is established based on mRMR-CNN and the effectiveness of it is verified on the penicillin fermentation process, where the proposed method shows remarkable performance.

Study of Auditory Brain Cognition Laws-Based Recognition Method of Automobile Sound Quality

The research shows that subjective feelings of people, such as emotions and fatigue, can be objectively reflected by electroencephalography (EEG) physiological signals Thus, an evaluation method based on EEG, which is used to explore auditory brain cognition laws, is introduced in this study. The brain cognition laws are summarized by analyzing the EEG power topographic map under the stimulation of three kinds of automobile sound, namely, quality of comfort, powerfulness, and acceleration. Then, the EEG features of the subjects are classified through a machine learning algorithm, by which the recognition of diversified automobile sound is realized. In addition, the Kalman smoothing and minimal redundancy maximal relevance (mRMR) algorithm is used to improve the recognition accuracy. The results show that there are differences in the neural characteristics of diversified automobile sound quality, with a positive correlation between EEG energy and sound intensity. Furthermore, by using the Kalman smoothing and mRMR algorithm, recognition accuracy is improved, and the amount of calculation is reduced. The novel idea and method to explore the cognitive laws of automobile sound quality from the field of brain-computer interface technology are provided in this study.

Minimal Redundancy Linear Array and Uniform Linear Arrays Beamforming Applications in 5G Smart Devices

Minimum Redundancy Linear Arrays (MRLAs) and Uniform Linear Arrays (ULAs) investigation conducted with the possibility of using them in future 5G smart devices. MRLAs are designed to minimize the number of sensor pairs with the same spatially correlated delay. It eliminates selected antennas from the entire composite antenna array and preserves all possible antenna spacing. MRLAs have attractive features for linear sparse arrays, even if the built-in surface is deformed, it works without problems. To our knowledge, MRLAs have not been applied to smart devices so far. In this work, a 7-element ULAs and 4-element MRLAs (same aperture) were used for the simulation. The Half Power Beamwidth (HPBW) is 0.666 and the Null-to-Null Beamwidth ( ) is 1.385 in ψ-space. In comparison, the standard 4-element arrays are 1.429 and 3.1416, while the standard 7-element linear arrays are 0.801 and 1.795 respectively. Experimental results show that 4-element MLRAs have a narrower mean beam, much higher sidelobes and shallow nulls. Therefore, in terms of main lobe features, 4- elements MRLAs have an improvement over the standard 7-element ULAs. Doi: 10.28991/esj-2021-SP1-05 Full Text: PDF

Performance Evaluation of Epileptic Seizure Prediction Using Time, Frequency, and Time–Frequency Domain Measures

The prediction of epileptic seizures is crucial to aid patients in gaining early warning and taking effective intervention. Several features have been explored to predict the onset via electroencephalography signals, which are typically non-stationary, dynamic, and varying from person-to-person. In the former literature, features applied in the classification have shared similar contributions to all patients. Therefore, in this paper, we analyze the impact of the specific combination of feature and channel from time, frequency, and time–frequency domains on prediction performance of disparate patients. Based on the minimal-redundancy-maximal-relevance criterion, the proposed framework uses a sequential forward selection approach to individually find the optimal features and channels. Trained models could discriminate the pre-ictal and inter-ictal electroencephalography with a sensitivity of 90.2% and a false prediction rate of 0.096/h. We also present the comparison between the classification accuracy obtained by the optimal features, several features summarized from optimal features, and the complete set of features from three domains. The results indicate that various patient interpretations have a certain specificity in the selection of feature-channel. Furthermore, the detailed list of optimal features and summarized features are proffered for reference to those who research the corresponding database.

Raincloud plots: a multi-platform tool for robust data visualization

Across scientific disciplines, there is a rapidly growing recognition of the need for more statistically robust, transparent approaches to data visualization. Complementary to this, many scientists have called for plotting tools that accurately and transparently convey key aspects of statistical effects and raw data with minimal distortion. Previously common approaches, such as plotting conditional mean or median barplots together with error-bars have been criticized for distorting effect size, hiding underlying patterns in the raw data, and obscuring the assumptions upon which the most commonly used statistical tests are based. Here we describe a data visualization approach which overcomes these issues, providing maximal statistical information while preserving the desired ‘inference at a glance’ nature of barplots and other similar visualization devices. These “raincloud plots” can visualize raw data, probability density, and key summary statistics such as median, mean, and relevant confidence intervals in an appealing and flexible format with minimal redundancy. In this tutorial paper, we provide basic demonstrations of the strength of raincloud plots and similar approaches, outline potential modifications for their optimal use, and provide open-source code for their streamlined implementation in R, Python and Matlab (https://github.com/RainCloudPlots/RainCloudPlots). Readers can investigate the R and Python tutorials interactively in the browser using Binder by Project Jupyter.

Feature Selections Using Minimal Redundancy Maximal Relevance Algorithm for Human Activity Recognition in Smart Home Environments

In this paper, maximal relevance measure and minimal redundancy maximal relevance (mRMR) algorithm (under D-R and D/R criteria) have been applied to select features and to compose different features subsets based on observed motion sensor events for human activity recognition in smart home environments. And then, the selected features subsets have been evaluated and the activity recognition accuracy rates have been compared with two probabilistic algorithms: naïve Bayes (NB) classifier and hidden Markov model (HMM). The experimental results show that not all features are beneficial to human activity recognition and different features subsets yield different human activity recognition accuracy rates. Furthermore, even the same features subset has different effect on human activity recognition accuracy rate for different activity classifiers. It is significant for researchers performing human activity recognition to consider both relevance between features and activities and redundancy among features. Generally, both maximal relevance measure and mRMR algorithm are feasible for feature selection and positive to activity recognition.