The OGY method is one of control methods for a chaotic system. In the method, we have to calculate a target periodic orbit embedded in its chaotic attractor. Thus, we cannot use this method in the case where a precise mathematical model of the chaotic system cannot be identified. In this case, the delayed feedback control proposed by Pyragas is useful. However, even in the delayed feedback control, we need the mathematical model to determine a feedback gain that stabilizes the periodic orbit. Thus, we propose a reinforcement learning algorithm to the design of a controller for the chaotic system. Recently, reinforcement learning algorithms with deep neural networks have been paid much attention to. Those algorithms make it possible to control complex systems. We propose a controller design method consisting of two steps, where we determine a region including a target periodic point first, and make the controller learn an optimal control policy for its stabilization. The controller efficiently explores its control policy only in the region.

This letter proposes a gradient-enhanced softmax supervisor for face recognition (FR) based on a deep convolutional neural network (DCNN). The proposed supervisor conducts the constant-normalized cosine to obtain the score for each class using a combination of the intra-class score and the soft maximum of the inter-class scores as the objective function. This mitigates the vanishing gradient problem in the conventional softmax classifier. The experiments on the public Labeled Faces in the Wild (LFW) database denote that the proposed supervisor achieves better results when compared with those achieved using the current state-of-the-art softmax-based approaches for FR.

The natural gradient descent is an optimization method for real-valued neural networks that was proposed from the viewpoint of information geometry. Here, we present an extension of the natural gradient descent to complex-valued neural networks. Our idea is to use the Hermitian extension of the Fisher information matrix. Moreover, we generalize the projected natural gradient (PRONG), which is a fast natural gradient descent algorithm, to complex-valued neural networks. We also consider the advantage of complex-valued neural networks over real-valued neural networks. A useful property of complex numbers in the complex plane is that the rotation is simply expressed by the multiplication. By focusing on this property, we construct the output function of complex-valued neural networks, which is invariant even if the input is changed to its rotated value. Then, our complex-valued neural network can learn rotated data without data augmentation. Finally, through simulation of online character recognition, we demonstrate the effectiveness of the proposed approach.

This letter presents an objective quality index for benchmarking image inpainting algorithms. Under the guidance of the masks of damaged areas, the boundary region and the inpainting region are first located. Then, the statistical features are extracted from the boundary and inpainting regions respectively. For the boundary region, we utilize Weibull distribution to fit the gradient magnitude histograms of the exterior and interior regions around the boundary, and the Kullback-Leibler Divergence (KLD) is calculated to measure the boundary distortions caused by imperfect inpainting. Meanwhile, the quality of the inpainting region is measured by comparing the naturalness factors between the inpainted image and the reference image. Experimental results demonstrate that the proposed metric outperforms the relevant state-of-the-art quality metrics.

Estimation of the gradient of the logarithm of a probability density function is a versatile tool in statistical data analysis. A recent method for model-seeking clustering called the least-squares log-density gradient clustering (LSLDGC) [Sasaki et al., 2014] employs a sophisticated gradient estimator, which directly estimates the log-density gradients without going through density estimation. However, the typical implementation of LSLDGC is based on a spherical Gaussian function, which may not work well when the probability density function for data has highly correlated local structures. To cope with this problem, we propose a new gradient estimator for log-density gradients with Gaussian mixture models (GMMs). Covariance matrices in GMMs enable the new estimator to capture the highly correlated structures. Through the application of the new gradient estimator to mode-seeking clustering and hierarchical clustering, we experimentally demonstrate the usefulness of our clustering methods over existing methods.

It is known that policy gradient algorithm can not guarantee the convergence to a Nash equilibrium in mixed policies when it is applied in matrix games. To overcome this problem, we propose a novel multi-agent reinforcement learning (MARL) algorithm called a policy gradient lagging anchor (PGLA) algorithm. And we prove that the agents' policies can converge to a Nash equilibrium in mixed policies by using the PGLA algorithm in two-player two-action matrix games. By simulation, we confirm the convergence and also show that the PGLA algorithm has a better convergence than the LR-I lagging anchor algorithm.

This paper proposes a consensus-based subgradient method under a common constraint set with switching undirected graphs. In the proposed method, each agent has a state and an auxiliary variable as the estimates of an optimal solution and accumulated information of past gradients of neighbor agents. We show that the states of all agents asymptotically converge to one of the optimal solutions of the convex optimization problem. The simulation results show that the proposed consensus-based algorithm with accumulated subgradient information achieves faster convergence than the standard subgradient algorithm.

This letter proposes a new face sketch recognition method. Given a query sketch and face photos in a database, the proposed method first synthesizes pseudo sketches by computing the locality sensitive histogram and dense illumination invariant features from the resized face photos, then extracts discriminative features by computing histogram of averaged oriented gradients on the query sketch and pseudo sketches, and finally find a match with the shortest cosine distance in the feature space. It achieves accuracy comparable to the state-of-the-art while showing much more robustness than the existing face sketch recognition methods.

Dai-Yuan (DY) conjugate gradient method is an effective method for solving large-scale unconstrained optimization problems. In this paper, a new DY method, possessing a spectral conjugate parameter βk, is presented. An attractive property of the proposed method is that the search direction generated at each iteration is descent, which is independent of the line search. Global convergence of the proposed method is also established when strong Wolfe conditions are employed. Finally, comparison experiments on impulse noise removal are reported to demonstrate the effectiveness of the proposed method.

A significant portion of computational resources of embedded systems for visual detection is dedicated to feature extraction, and this severely affects the detection accuracy and processing performance of the system. To solve this problem, we propose a feature descriptor based on histograms of oriented gradients (HOG) consisting of simple linear algebra that can extract equivalent information to the conventional HOG feature descriptor at a low computational cost. In an evaluation, a leading-edge detection algorithm with this decomposed vector HOG (DV-HOG) achieved equivalent or better detection accuracy compared with conventional HOG feature descriptors. A hardware implementation of DV-HOG occupies approximately 14.2 times smaller cell area than that of a conventional HOG implementation.

The step size is a parameter of fundamental importance in learning algorithms, particularly for the natural policy gradient (NPG) methods. We derive an upper bound for the step size in an incremental NPG estimation, and propose an adaptive step size to implement the derived upper bound. The proposed adaptive step size guarantees that an updated parameter does not overshoot the target, which is achieved by weighting the learning samples according to their relative importances. We also provide tight upper and lower bounds for the step size, though they are not suitable for the incremental learning. We confirm the usefulness of the proposed step size using the classical benchmarks. To the best of our knowledge, this is the first adaptive step size method for NPG estimation.

We propose an efficient training method for memristor neural networks. The proposed method is suitable for the mini-batch-based training, which is a common technique for various neural networks. By integrating the two processes of gradient calculation in the backpropagation algorithm and weight update in the write operation to the memristors, the proposed method accelerates the training process and also eliminates the external computing resources required in the existing method, such as multipliers and memories. Through numerical experiments, we demonstrated that the proposed method achieves twice faster convergence of the training process than the existing method, while retaining the same level of the accuracy for the classification results.

Automatically recognizing pain and estimating pain intensity is an emerging research area that has promising applications in the medical and healthcare field, and this task possesses a crucial role in the diagnosis and treatment of patients who have limited ability to communicate verbally and remains a challenge in pattern recognition. Recently, deep learning has achieved impressive results in many domains. However, deep architectures require a significant amount of labeled data for training, and they may fail to outperform conventional handcrafted features due to insufficient data, which is also the problem faced by pain detection. Furthermore, the latest studies show that handcrafted features may provide complementary information to deep-learned features; hence, combining these features may result in improved performance. Motived by the above considerations, in this paper, we propose an innovative method based on the combination of deep spatiotemporal and handcrafted features for pain intensity estimation. We use C3D, a deep 3-dimensional convolutional network that takes a continuous sequence of video frames as input, to extract spatiotemporal facial features. C3D models the appearance and motion of videos simultaneously. For handcrafted features, we propose extracting the geometric information by computing the distance between normalized facial landmarks per frame and the ones of the mean face shape, and we extract the appearance information using the histogram of oriented gradients (HOG) features around normalized facial landmarks per frame. Two levels of SVRs are trained using spatiotemporal, geometric and appearance features to obtain estimation results. We tested our proposed method on the UNBC-McMaster shoulder pain expression archive database and obtained experimental results that outperform the current state-of-the-art.

A logo is a symbolic presentation that is designed not only to identify a product manufacturer but also to attract the attention of shoppers. Shoe logos are a challenging subject for automatic extraction and recognition using image analysis techniques because they have characteristics that distinguish them from those of other products; that is, there is much within-class variation in the appearance of shoe logos. In this paper, we propose an automatic extraction and recognition method for shoe logos with a wide variety of appearance using a limited number of training samples. The proposed method employs maximally stable extremal regions for the initial region extraction, an iterative algorithm for region grouping, and gradient features and a support vector machine for logo recognition. The results of performance evaluation experiments using a logo dataset that consists of a wide variety of appearances show that the proposed method achieves promising performance for both logo extraction and recognition.

Object detection is an essential and expensive process in many computer vision systems. Standard off-the-shelf embedded processors are hard to achieve performance-power balance for implementation of object detection applications. In this work, we explore an Application Specific Instruction set Processor (ASIP) for object detection using Histogram of Oriented Gradients (HOG) feature. Algorithm simplifications are adopted to reduce memory bandwidth requirements and mathematical complexity without losing reliability. Also, parallel histogram generation and on-the-fly Support Vector Machine (SVM) calculation architecture are employed to reduce the necessary cycle counts. The HOG algorithm on the proposed ASIP was accelerated by a factor of 63x compared to the pure software implementation. The ASIP was synthesized for a standard 90nm CMOS library, with a silicon area of 1.31mm2 and 47.8mW power consumption at a 200MHz frequency. Our object detection processor can achieve 42 frames-per-second (fps) on VGA video. The evaluation and implementation results show that the proposed ASIP is both area-efficient and power-efficient while being competitive with commercial CPUs/DSPs. Furthermore, our ASIP exhibits comparable performance even with hard-wire designs.

In this work, two new proposed NMF models are developed for facial expression recognition. They are called maximum volume constrained nonnegative matrix factorization (MV_NMF) and maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). They achieve sparseness from a larger simplicial cone constraint and the extracted features preserve the topological structure of the original images.

In this paper, the concept of gradient order is introduced and a novel gradient order curve descriptor (GOCD) for curve matching is proposed. The GOCD is constructed in the following main steps: firstly, curve support region independent of the dominant orientation is determined and then divided into several sub-regions based on gradient magnitude order; then gradient order feature (GOF) of each feature point is generated by encoding the local gradient information of the sample points; the descriptor is finally achieved by turning to the description matrix of GOF. Since both the local and the global gradient information are captured by GOCD, it is more distinctive and robust compared with the existing curve matching methods. Experiments under various changes, such as illumination, viewpoint, image rotation, JPEG compression and noise, show the great performance of GOCD. Furthermore, the application of image mosaic proves GOCD can be used successfully in actual field.

This work presents a new approach which derives a learned data representation method through matrix factorization on the complex domain. In particular, we introduce an encoding matrix-a new representation of data-that satisfies the simplicial constraint of the projective basis matrix on the field of complex numbers. A complex optimization framework is provided. It employs the gradient descent method and computes the derivative of the cost function based on Wirtinger's calculus.

Establishing local visual correspondences between images taken under different conditions is an important and challenging task in computer vision. A common solution for this task is detecting keypoints in images and then matching the keypoints with a feature descriptor. This paper proposes a robust and low-dimensional local feature descriptor named Adaptively Integrated Gradient and Intensity Feature (AIGIF). The proposed AIGIF descriptor partitions the support region surrounding each keypoint into sub-regions, and classifies the sub-regions into two categories: edge-dominated ones and smoothness-dominated ones. For edge-dominated sub-regions, gradient magnitude and orientation features are extracted; for smoothness-dominated sub-regions, intensity feature is extracted. The gradient and intensity features are integrated to generate the descriptor. Experiments on image matching were conducted to evaluate performances of the proposed AIGIF. Compared with SIFT, the proposed AIGIF achieves 75% reduction of feature dimension (from 128 bytes to 32 bytes); compared with SURF, the proposed AIGIF achieves 87.5% reduction of feature dimension (from 256 bytes to 32 bytes); compared with the state-of-the-art ORB descriptor which has the same feature dimension with AIGIF, AIGIF achieves higher accuracy and robustness. In summary, the AIGIF combines the advantages of gradient feature and intensity feature, and achieves relatively high accuracy and robustness with low feature dimension.

In the field of adaptive notch filtering, Monotonically Increasing Gradient (MIG) algorithm has recently been proposed by Sugiura and Shimamura [1], where it is claimed that the MIG algorithm shows monotonically increasing gradient characteristics. However, our analysis has found that the underlying theory in [1] includes crucial errors. This letter shows that the formulation of the gradient characteristics in [1] is incorrect, and reveals that the MIG algorithm fails to realize monotonically increasing gradient characteristics when the input signal includes white noise.