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With the development of convolutional neural networks (CNNs) in recent years, the network structure has become more and more complex and varied, and has achieved very good results in pattern recognition, image classification, object detection and tracking. For CNNs used for image classification, in addition to the network structure, more and more research is now focusing on the improvement of the loss function, so as to enlarge the inter-class feature differences, and reduce the intra-class feature variations as soon as possible. Besides the traditional Softmax, typical loss functions include L-Softmax, AM-Softmax, ArcFace, and Center loss, etc.Based on the concept of predefined evenly-distributed class centroids (PEDCC) in CSAE network, this paper proposes a PEDCC-based loss function called PEDCC-Loss, which can make the inter-class distance maximal and intra-class distance small enough in hidden feature space. Multiple experiments on image classification and face recognition have proved that our method achieve the best recognition accuracy, and network training is stable and easy to converge. Code is available in https://github.com/ZLeopard/PEDCC-Loss

In this paper, we propose an end-to-end image clustering auto-encoder algorithm: ICAE. The algorithm uses PEDCC (Predefined Evenly-Distributed Class Centroids) as the clustering centers of the images, which ensures the inter-class distance of latent features is maximal, and adds data distribution constraint, data augmentation constraint, autoencoder reconstruction loss constraint and latent features plus noise constraint to improve clustering performance. Specifically, we perform one-to-one data augmentation such as rotation, shear, and shift before data is input to the encoder to learn the more effective features. The data and the enhanced data are simultaneously input into the auto-encoder to obtain latent features and augmented latent features whose similarity are constrained by an augmentation loss. Then, making use of the MMD distance, we combine the latent features and augmented latent features to make their distribution close to the PEDCC distribution (uniform distribution between classes, Dirac distribution within the class) to further learn the features used for clustering. At the same time, the MSE of the original input image and reconstructed image is used as reconstruction constraint, and the noise is added to the latent features to build generalization constraint to improve the generalization ability. Finally, extensive experiments on three common datasets MNIST, Fashion-MNIST, COIL20 are conducted. The experimental results show that the algorithm has achieved the best clustering results so far, and also has good generalization ability. In addition, we can use the pre-defined PEDCC class centers, and the decoding module of the auto-encoder to clearly generate the samples of each class. The code can be downloaded at xxx!

Reconstructing a three-dimensional (3D) structure from a single two-dimensional training image (TI) is a challenging issue. Multiple-point statistics (MPS) is an effective method to solve this problem. However, in the traditional MPS method, errors occur while statistical features of reconstruction, such as porosity, connectivity, and structural properties, deviate from those of TI. Due to the MPS reconstruction mechanism that the voxel being reconstructed is dependent on the reconstructed voxel, it may cause error accumulation during simulations, which can easily lead to a significant difference between the real 3D structure and the reconstructed result. To reduce error accumulation and improve morphological similarity, an improved MPS method based on porosity matching is proposed. In the reconstruction, we search the matching pattern in the TI directly. Meanwhile, a multigrid approach is also applied to capture the large-scale structures of the TI. To demonstrate its superiority over the traditional MPS method, our method is tested on different sandstone samples from many aspects, including accuracy, stability, generalization, and flow characteristics. Experimental results show that the reconstruction results by the improved MPS method effectively match the CT sandstone samples in correlation functions, local porosity distribution, morphological parameters, and permeability.

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