Enhanced piecewise regression based on deterministic annealing

Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced plecewise regression algorithm by using ＂migration of prototypes＂ is proposed to eliminate ＂empty cell＂ in the annealing process. Numerical experiments on several benchmark datasets show that the new algorithm can remove redundancy and improve generalization of the piecewise regression model.

Real-Time Implementation of Quadrotor UAV Control System Based on a Deep Reinforcement Learning Approach

The popularity of quadrotor Unmanned Aerial Vehicles(UAVs)stems from their simple propulsion systems and structural design.However,their complex and nonlinear dynamic behavior presents a significant challenge for control,necessitating sophisticated algorithms to ensure stability and accuracy in flight.Various strategies have been explored by researchers and control engineers,with learning-based methods like reinforcement learning,deep learning,and neural networks showing promise in enhancing the robustness and adaptability of quadrotor control systems.This paper investigates a Reinforcement Learning(RL)approach for both high and low-level quadrotor control systems,focusing on attitude stabilization and position tracking tasks.A novel reward function and actor-critic network structures are designed to stimulate high-order observable states,improving the agent’s understanding of the quadrotor’s dynamics and environmental constraints.To address the challenge of RL hyper-parameter tuning,a new framework is introduced that combines Simulated Annealing(SA)with a reinforcement learning algorithm,specifically Simulated Annealing-Twin Delayed Deep Deterministic Policy Gradient(SA-TD3).This approach is evaluated for path-following and stabilization tasks through comparative assessments with two commonly used control methods:Backstepping and Sliding Mode Control(SMC).While the implementation of the well-trained agents exhibited unexpected behavior during real-world testing,a reduced neural network used for altitude control was successfully implemented on a Parrot Mambo mini drone.The results showcase the potential of the proposed SA-TD3 framework for real-world applications,demonstrating improved stability and precision across various test scenarios and highlighting its feasibility for practical deployment.

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging(MRI) reconstruction, termed gradient-based low rank MRI reconstruction(GLRMRI). In the proposed method,by incorporating the spatially adaptive iterative singular-value thresholding(SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure efficiently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both realvalued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio(PSNR) and lower high-frequency error norm(HFEN) values.