Fisher's linear discriminant analysis (LDA) is a traditional dimensionality reduction method that has been proven to be successful for decades. Numerous variants, such as the kernel-based Fisher discriminant analysis (KFDA), have been proposed to enhance the LDA's power for nonlinear discriminants. Although effective, the KFDA is computationally expensive, since the complexity increases with the size of the data set. In this correspondence, we suggest a novel strategy to enhance the computation for an entire family of the KFDAs. Rather than invoke the KFDA for the entire data set, we advocate that the data be first reduced into a smaller representative subset using a prototype reduction scheme and that the dimensionality reduction be achieved by invoking a KFDA on this reduced data set. In this way, data points that are ineffective in the dimension reduction and classification can be eliminated to obtain a significantly reduced kernel matrix K without degrading the performance. Our experimental results demonstrate that the proposed mechanism dramatically reduces the computation time without sacrificing the classification accuracy for artificial and real-life data sets.

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data interpolation. However, they often underperform when the training and test missing patterns do not match. To alleviate this issue, here we propose a novel framework that is built upon the multi-modal adaptable diffusion models. In the training phase, following the common wisdom, we use the denoising diffusion probabilistic model with a cosine noise schedule. This cosine global noise configuration improves the use of seismic data by reducing the involvement of excessive noise stages. In the inference phase, we introduce the denoising diffusion implicit model to reduce the number of sampling steps. Different from the conventional unconditional generation, we incorporate the known trace information into each reverse sampling step for achieving conditional interpolation. To enhance the coherence and continuity between the revealed traces and the missing traces, we further propose two strategies, including successive coherence correction and resampling. Coherence correction penalizes the mismatches in the revealed traces, while resampling conducts cyclic interpolation between adjacent reverse steps. Extensive experiments on synthetic and field seismic data validate our model’s superiority and demonstrate its generalization capability to various missing patterns and different noise levels with just one training session. In addition, uncertainty quantification and ablation studies are also investigated.

This paper empirically evaluates two kinds of features, which are extracted, respectively, with traditional statistical methods and convolutional neural networks (CNNs), in order to improve the performance of seismic patch image classification. In the latter case, feature vectors, named “CNN-features”, were extracted from one trained CNN model, and were then used to learn existing classifiers, such as support vector machines. In this case, to learn the CNN model, a technique of transfer learning using synthetic seismic patch data in the source domain, and real-world patch data in the target domain, was applied. The experimental results show that CNN-features lead to some improvements in the classification performance. By analyzing the data complexity measures, the CNN-features are found to have the strongest discriminant capabilities. Furthermore, the transfer learning technique alleviates the problems of long processing times and the lack of learning data.

This paper presents an empirical study on selecting a small amount useful unlabeled data with which the classification accuracy of semi-supervised learning (SSL) algorithms can be improved. In particular, two selection strategies, named simply recycled selection and incrementally reinforced selection, are considered and empirically compared. The experimental results, obtained with well-known benchmark data sets, demonstrate that the latter works better than the former does in terms of classification accuracy.