Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations

By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations AX+YB=C and DX+YE=F in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation AXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm

Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle

This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm

Understanding Hidden Memories of Recurrent Neural Networks

Recurrent neural networks (RNNs) have been successfully applied to various natural language processing (NLP) tasks and achieved better results than conventional methods. However, the lack of understanding of the mechanisms behind their effectiveness limits further improvements on their architectures. In this paper, we present a visual analytics method for understanding and comparing RNN models for NLP tasks. We propose a technique to explain the function of individual hidden state units based on their expected response to input texts. We then co-cluster hidden state units and words based on the expected response and visualize co-clustering results as memory chips and word clouds to provide more structured knowledge on RNNs' hidden states. We also propose a glyph-based sequence visualization based on aggregate information to analyze the behavior of an RNN's hidden state at the sentence-level. The usability and effectiveness of our method are demonstrated through case studies and reviews from domain experts.Comment: Published at IEEE Conference on Visual Analytics Science and Technology (IEEE VAST 2017

AdaVis: Adaptive and Explainable Visualization Recommendation for Tabular Data

Automated visualization recommendation facilitates the rapid creation of effective visualizations, which is especially beneficial for users with limited time and limited knowledge of data visualization. There is an increasing trend in leveraging machine learning (ML) techniques to achieve an end-to-end visualization recommendation. However, existing ML-based approaches implicitly assume that there is only one appropriate visualization for a specific dataset, which is often not true for real applications. Also, they often work like a black box, and are difficult for users to understand the reasons for recommending specific visualizations. To fill the research gap, we propose AdaVis, an adaptive and explainable approach to recommend one or multiple appropriate visualizations for a tabular dataset. It leverages a box embedding-based knowledge graph to well model the possible one-to-many mapping relations among different entities (i.e., data features, dataset columns, datasets, and visualization choices). The embeddings of the entities and relations can be learned from dataset-visualization pairs. Also, AdaVis incorporates the attention mechanism into the inference framework. Attention can indicate the relative importance of data features for a dataset and provide fine-grained explainability. Our extensive evaluations through quantitative metric evaluations, case studies, and user interviews demonstrate the effectiveness of AdaVis

Reversible Watermarking in Deep Convolutional Neural Networks for Integrity Authentication

Deep convolutional neural networks have made outstanding contributions in many fields such as computer vision in the past few years and many researchers published well-trained network for downloading. But recent studies have shown serious concerns about integrity due to model-reuse attacks and backdoor attacks. In order to protect these open-source networks, many algorithms have been proposed such as watermarking. However, these existing algorithms modify the contents of the network permanently and are not suitable for integrity authentication. In this paper, we propose a reversible watermarking algorithm for integrity authentication. Specifically, we present the reversible watermarking problem of deep convolutional neural networks and utilize the pruning theory of model compression technology to construct a host sequence used for embedding watermarking information by histogram shift. As shown in the experiments, the influence of embedding reversible watermarking on the classification performance is less than 0.5% and the parameters of the model can be fully recovered after extracting the watermarking. At the same time, the integrity of the model can be verified by applying the reversible watermarking: if the model is modified illegally, the authentication information generated by original model will be absolutely different from the extracted watermarking information.Comment: Accepted to ACM MM 202

Robust model of fresh jujube soluble solids content with near-infrared (NIR) spectroscopy

A robust partial least square (PLS) calibration model with high accuracy and stability was established for the measurement of soluble solids content (SSC) of fresh jujube using near-infrared (NIR) spectroscopytechnique. Fresh jujube samples were collected in different areas of Taigu and Taiyuan cities, central China in 2008 and 2009. A partial least squares (PLS) calibration model was established based on the NIR spectra of 70 fresh jujube samples collected in 2008. A good calibration result was obtained with correlation coefficient (Rc) of 0.9530 and the root mean square error of calibration (RMSEC) of 0.3951 °Brix. Another PLS calibration model was established based on the NIR spectral of 180 samples collected in 2009; it resulted in the Rc of 0.8536 and the RMSEC of 1.1410 °Brix. It could be seen that the accuracy of established PLS models were different when samples harvested in different years were used for the model calibration. In order to improve the accuracy and robustness of model, different numbers (5, 10, 15, 20, 30 and 40) of samples harvested in 2008 were added to the calibration sample set of the model with samples harvested in 2009, respectively. The established PLS models obtained Rc with the range of 0.8846 to 0.8893 and RMSEC with the range of 1.0248 to 0.9645 °Brix. The obtained results werebetter than the result of the model which was established only with samples harvested in 2009. Moreover, the models established using different numbers of added samples had similar results. Therefore, it was concluded that adding samples from another harvest year could improve the accuracy and robustness of the model for SSC prediction of fresh jujube. The overall results proved that the consideration of samples from different harvest places and years would be useful for establishing an accuracy and robustness spectral model.Keywords: Near-infrared (NIR) spectroscopy, Huping jujube, soluble solids content (SSC), partial least squares (PLS), accuracy, stabilit