A fractional gradient descent algorithm robust to the initial weights of multilayer perceptron.

For multilayer perceptron (MLP), the initial weights will significantly influence its performance. Based on the enhanced fractional derivative extend from convex optimization, this paper proposes a fractional gradient descent (RFGD) algorithm robust to the initial weights of MLP. We analyze the effectiveness of the RFGD algorithm.

A global neural network learning machine: Coupled integer and fractional calculus operator with an adaptive learning scheme.

Find the global optimal solution of the model is one promising research topic in computational intelligent community. Dependent on analogies to natural processes, the evolutionary swarm intelligent algorithms are widely used for solving global optimization problems which directed by the fitness values. In this paper, we propose one efficient fractional global learning machine (Fragmachine) which includes two stages (descending and ascending) to determine the optimal search path.

A Fractional-Order Variational Framework for Retinex: Fractional-Order Partial Differential Equation-Based Formulation for Multi-Scale Nonlocal Contrast Enhancement with Texture Preserving.

This paper discusses a novel conceptual formulation of the fractional-order variational framework for retinex, which is a fractional-order partial differential equation (FPDE) formulation of retinex for the multi-scale nonlocal contrast enhancement with texture preserving. The well-known shortcomings of traditional integer-order computation-based contrast-enhancement algorithms, such as ringing artefacts and staircase effects, are still in great need of special research attention. Fractional calculus has potentially received prominence in applications in the domain of signal processing and image processing mainly because of its strengths like long-term memory, nonlocality, and weak singularity, and because of the ability of a fractional differential to enhance the complex textural details of an image in a nonlinear manner.

Defense Against Chip Cloning Attacks Based on Fractional Hopfield Neural Networks.

This paper presents a state-of-the-art application of fractional hopfield neural networks (FHNNs) to defend against chip cloning attacks, and provides insight into the reason that the proposed method is superior to physically unclonable functions (PUFs). In the past decade, PUFs have been evolving as one of the best types of hardware security. However, the development of the PUFs has been somewhat limited by its implementation cost, its temperature variation effect, its electromagnetic interference effect, the amount of entropy in it, etc.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks.

Fractional extreme value adaptive training method: fractional steepest descent approach.

The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed.

Efficient CT metal artifact reduction based on fractional-order curvature diffusion.

We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed.

A new CT metal artifacts reduction algorithm based on fractional-order sinogram inpainting.

In this paper, we propose a new metal artifacts reduction algorithm based on fractional-order total-variation sinogram inpainting model for X-ray computed tomography (CT). The numerical algorithm for our fractional-order framework is also analyzed. Simulations show that, both quantitatively and qualitatively, our method is superior to conditional interpolation methods and the classic integral-order total variation model.

Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement.

In this paper, we intend to implement a class of fractional differential masks with high-precision. Thanks to two commonly used definitions of fractional differential for what are known as GrUmwald-Letnikov and Riemann-Liouville, we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal. Moreover, by theoretical and experimental analyzing, we demonstrate the second is the best performance fractional differential mask of the proposed six ones.