Conventional nonnegative matrix factorization and its variants cannot separate the noise data space into a clean space and learn an effective low-dimensional subspace from Salt and Pepper noise or Contiguous Occlusion. This paper proposes a weighted nonnegative matrix factorization (WNMF) to improve the robustness of existing nonnegative matrix factorization. In WNMF, a weighted graph is constructed to label the uncorrupted data as 1 and the corrupted data as 0, and an effective matrix factorization model is proposed to recover the noise data and achieve clustering from the recovered data. Extensive experiments on the image datasets corrupted by Salt and Pepper noise or Contiguous Occlusion are presented to demonstrate the effectiveness and robustness of the proposed method in image inpainting and clustering.

With the continuous advancement of the economy and technology, the number of cars continues to increase, and the traffic congestion problem on some key roads is becoming increasingly serious. This paper proposes a new vehicle information feature map (VIFM) method and a multi-branch convolutional neural network (MBCNN) model and applies it to the problem of traffic congestion detection based on camera image data. The aim of this study is to build a deep learning model with traffic images as input and congestion detection results as output. It aims to provide a new method for automatic detection of traffic congestion. The deep learning-based method in this article can effectively utilize the existing massive camera network in the transportation system without requiring too much investment in hardware. This study first uses an object detection model to identify vehicles in images. Then, a method for extracting a VIFM is proposed. Finally, a traffic congestion detection model based on MBCNN is constructed. This paper verifies the application effect of this method in the Chinese City Traffic Image Database (CCTRIB). Compared to other convolutional neural networks, other deep learning models, and baseline models, the method proposed in this paper yields superior results. The method in this article obtained an F1 score of 98.61% and an accuracy of 98.62%. Experimental results show that this method effectively solves the problem of traffic congestion detection and provides a powerful tool for traffic management.

Laser technology has made rapid progress in recent years and has been widely used in various fields such as medicine, biology, military, and materials science. However, the limitations of traditional Gaussian intensity distribution of the laser beams in applications have prompted the emergence and development of flat-top beam shaping technology, which has received widespread attention. Here, we introduce a new method for generating flat-top beams that combines the traditional Gerchberg-Saxton algorithm with convolutional neural networks, using spatial light modulators to achieve flat-top beam shaping. A comparative analysis was conducted by comparing the root mean square error and diffraction efficiency of the generated flat-top beam with the results obtained using only the traditional Gerchberg-Saxton algorithm. Compared with the traditional Gerchberg-Saxton algorithm, the method proposed in this paper can generate a flat-top beam with smaller differences from the target light intensity and higher energy utilization, providing new possibilities for the application of laser technology.

We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real‐world data illustrate the effectiveness and performance of the proposed method.