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Register a new userA novel perspective to gradient method: the fractional order approach
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Added by
Yiheng Wei
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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In this paper, we give some new thoughts about the classical gradient method (GM) and recall the proposed fractional order gradient method (FOGM). It is proven that the proposed FOGM holds a super convergence capacity and a faster convergence rate around the extreme point than the conventional GM. The property of asymptotic convergence of conventional GM and FOGM is also discussed. To achieve both a super convergence capability and an even faster convergence rate, a novel switching FOGM is proposed. Moreover, we extend the obtained conclusion to a more general case by introducing the concept of p-order Lipschitz continuous gradient and p-order strong convex. Numerous simulation examples are provided to validate the effectiveness of proposed methods.
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This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified fractional order gradient method is designed based on Caputos definition. The parameters within layers are updated by the designed gradient method, but the propagations between layers still use integer order gradients, and thus the complicated derivatives of composite functions are avoided and the chain rule will be kept. By connecting every layers in series and adding loss functions, the proposed convolutional neural networks can be trained smoothly according to various tasks. Some practical experiments are carried out in order to demonstrate fast convergence, high accuracy and ability to escape local optimal point at last.
Safety and automatic control are extremely important when operating manipulators. For large engineering manipulators, the main challenge is to accurately recognize the posture of all arm segments. In classical sensing methods, the accuracy of an inclinometer is easily affected by the elastic deformation in the manipulators arms. This results in big error accumulations when sensing the angle of joints between arms one by one. In addition, the sensing method based on machine vision is not suitable for such kind of outdoor working situation yet. In this paper, we propose a novel posture positioning method for multi-joint manipulators based on wireless sensor network localization. The posture sensing problem is formulated as a Nearest-Euclidean-Distance-Matrix (NEDM) model. The resulting approach is referred to as EDM-based posture positioning approach (EPP) and it satisfies the following guiding principles: (i) The posture of each arm segment on a multi-joint manipulator must be estimated as accurately as possible; (ii) The approach must be computationally fast; (iii) The designed approach should not be susceptible to obstructions. To further improve accuracy, we explore the inherent structure of manipulators, i.e., fixed-arm length. This is naturally presented as linear constraints in the NEDM model. For concrete pumps, a typical multi-joint manipulator, the mechanical property that all arm segments always lie in a 2D plane is used for dimension-reduction operation. Simulation and experimental results show that the proposed method provides efficient solutions for posture sensing problem and can obtain preferable localization performance with faster speed than applying the existing localization methods.
In this paper, we propose a new approach, based on the so-called modulating functions to estimate the average velocity, the dispersion coefficient and the differentiation order in a space fractional advection dispersion equation. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with Newtons method is applied to estimate all three parameters simultaneously. Numerical results are presented with noisy measurements to show the effectiveness and the robustness of the proposed method.
This paper focuses on the convergence problem of the emerging fractional order gradient descent method, and proposes three solutions to overcome the problem. In fact, the general fractional gradient method cannot converge to the real extreme point of the target function, which critically hampers the application of this method. Because of the long memory characteristics of fractional derivative, fixed memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The one is the truncation of the infinite series, and the other is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods.
Nonuniformities in the imaging characteristics of modern image sensors are a primary factor in the push to develop a pixel-level generalization of the photon transfer characterization method. In this paper, we seek to develop a body of theoretical results leading toward a comprehensive approach for tackling the biggest obstacle in the way of this goal: a means of pixel-level conversion gain estimation. This is accomplished by developing an estimator for the reciprocal-difference of normal variances and then using this to construct a novel estimator of the conversion gain. The first two moments of this estimator are derived and used to construct exact and approximate confidence intervals for its absolute relative bias and absolute coefficient of variation, respectively. A means of approximating and computing optimal sample sizes are also discussed and used to demonstrate the process of pixel-level conversion gain estimation for a real image sensor.
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