scholarly journals Behavior of Limited Memory BFGS When Applied to Nonsmooth Functions and Their Nesterov Smoothings

2021 ◽  
pp. 25-55
Author(s):  
Azam Asl ◽  
Michael L. Overton
Keyword(s):  
Limited Memory ◽  
Nonsmooth Functions

scholarly journals Attitude and Heading Estimation for Indoor Positioning Based on the Adaptive Cubature Kalman Filter

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 79
Author(s):  
Jijun Geng ◽  
Linyuan Xia ◽  
Dongjin Wu
Keyword(s):  
Kalman Filter ◽  
Angular Rate ◽  
Indoor Positioning ◽  
Location Based Services ◽  
Statistical Characteristics ◽  
Fading Memory ◽  
Limited Memory ◽  
Cubature Kalman Filter ◽  
The Mean ◽  
Heading Estimation

The demands for indoor positioning in location-based services (LBS) and applications grow rapidly. It is beneficial for indoor positioning to combine attitude and heading information. Accurate attitude and heading estimation based on magnetic, angular rate, and gravity (MARG) sensors of micro-electro-mechanical systems (MEMS) has received increasing attention due to its high availability and independence. This paper proposes a quaternion-based adaptive cubature Kalman filter (ACKF) algorithm to estimate the attitude and heading based on smart phone-embedded MARG sensors. In this algorithm, the fading memory weighted method and the limited memory weighted method are used to adaptively correct the statistical characteristics of the nonlinear system and reduce the estimation bias of the filter. The latest step data is used as the memory window data of the limited memory weighted method. Moreover, for restraining the divergence, the filter innovation sequence is used to rectify the noise covariance measurements and system. Besides, an adaptive factor based on prediction residual construction is used to overcome the filter model error and the influence of abnormal disturbance. In the static test, compared with the Sage-Husa cubature Kalman filter (SHCKF), cubature Kalman filter (CKF), and extended Kalman filter (EKF), the mean absolute errors (MAE) of the heading pitch and roll calculated by the proposed algorithm decreased by 4–18%, 14–29%, and 61–77% respectively. In the dynamic test, compared with the above three filters, the MAE of the heading reduced by 1–8%, 2–18%, and 2–21%, and the mean of location errors decreased by 9–22%, 19–31%, and 32–54% respectively by using the proposed algorithm for three participants. Generally, the proposed algorithm can effectively improve the accuracy of heading. Moreover, it can also improve the accuracy of attitude under quasistatic conditions.

scholarly journals On-Shelf Utility Mining of Sequence Data

2021 ◽  
Vol 16 (2) ◽  
pp. 1-31
Author(s):  
Chunkai Zhang ◽  
Zilin Du ◽  
Yuting Yang ◽  
Wensheng Gan ◽  
Philip S. Yu
Keyword(s):  
High Efficiency ◽  
Sequence Data ◽  
Real Life ◽  
Search Space ◽  
Upper Bounds ◽  
Utility Mining ◽  
Limited Memory ◽  
Time Periods ◽  
High Utility ◽  
Synthetic Datasets

Utility mining has emerged as an important and interesting topic owing to its wide application and considerable popularity. However, conventional utility mining methods have a bias toward items that have longer on-shelf time as they have a greater chance to generate a high utility. To eliminate the bias, the problem of on-shelf utility mining (OSUM) is introduced. In this article, we focus on the task of OSUM of sequence data, where the sequential database is divided into several partitions according to time periods and items are associated with utilities and several on-shelf time periods. To address the problem, we propose two methods, OSUM of sequence data (OSUMS) and OSUMS + , to extract on-shelf high-utility sequential patterns. For further efficiency, we also design several strategies to reduce the search space and avoid redundant calculation with two upper bounds time prefix extension utility ( TPEU ) and time reduced sequence utility ( TRSU ). In addition, two novel data structures are developed for facilitating the calculation of upper bounds and utilities. Substantial experimental results on certain real and synthetic datasets show that the two methods outperform the state-of-the-art algorithm. In conclusion, OSUMS may consume a large amount of memory and is unsuitable for cases with limited memory, while OSUMS + has wider real-life applications owing to its high efficiency.

scholarly journals Analysis and Prediction of COVID-19 Using SIR, SEIQR, and Machine Learning Models: Australia, Italy, and UK Cases

Information ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 109 ◽  
Author(s):  
Iman Rahimi ◽  
Amir H. Gandomi ◽  
Panagiotis G. Asteris ◽  
Fang Chen
Keyword(s):  
Machine Learning ◽  
Logistic Function ◽  
Prediction Performance ◽  
Machine Learning Algorithms ◽  
Model Parameters ◽  
The Novel ◽  
Chinese City ◽  
Limited Memory ◽  
Increasing Trend ◽  
Novel Coronavirus

The novel coronavirus disease, also known as COVID-19, is a disease outbreak that was first identified in Wuhan, a Central Chinese city. In this report, a short analysis focusing on Australia, Italy, and UK is conducted. The analysis includes confirmed and recovered cases and deaths, the growth rate in Australia compared with that in Italy and UK, and the trend of the disease in different Australian regions. Mathematical approaches based on susceptible, infected, and recovered (SIR) cases and susceptible, exposed, infected, quarantined, and recovered (SEIQR) cases models are proposed to predict epidemiology in the above-mentioned countries. Since the performance of the classic forms of SIR and SEIQR depends on parameter settings, some optimization algorithms, namely Broyden–Fletcher–Goldfarb–Shanno (BFGS), conjugate gradients (CG), limited memory bound constrained BFGS (L-BFGS-B), and Nelder–Mead, are proposed to optimize the parameters and the predictive capabilities of the SIR and SEIQR models. The results of the optimized SIR and SEIQR models were compared with those of two well-known machine learning algorithms, i.e., the Prophet algorithm and logistic function. The results demonstrate the different behaviors of these algorithms in different countries as well as the better performance of the improved SIR and SEIQR models. Moreover, the Prophet algorithm was found to provide better prediction performance than the logistic function, as well as better prediction performance for Italy and UK cases than for Australian cases. Therefore, it seems that the Prophet algorithm is suitable for data with an increasing trend in the context of a pandemic. Optimization of SIR and SEIQR model parameters yielded a significant improvement in the prediction accuracy of the models. Despite the availability of several algorithms for trend predictions in this pandemic, there is no single algorithm that would be optimal for all cases.

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