Causal inference methods can be used to discover causal relationships on observation data. When making causal inferences on data having causal structure with confounder, wrong causal relationships may be obtained under the influence of confounders. To solve the problem, a causal inference method based on Confounder Hidden Compact Representation (CHCR) model was proposed. Firstly, the candidate models with intermediate hidden variables that compactly represented the cause variables were constructed based on CHCR model. Secondly, the Bayesian Information Criterion (BIC) was used to calculate the scores of the candidate models and obtain the best model with the highest score. Finally, the real causal relationship between the variables was judged according to the quality of compaction in the best model. Theoretical analysis shows that, the proposed method can identify the causal structures with confounders that cannot be correctly identified by the classical constraint-based methods. In some cases such as the small sample size, BIC scoring can also improve the performance of the proposed method. Experimental results show that, when the number of samples changes, the proposed method has a significant improvement in accuracy compared with the classical methods such as Really Fast Causal Inference algorithm (RFCI), and the proposed method is suitable for situations with different numbers of possible variable values. When mixing different types of causal structures, the accuracy of the proposed method is higher than those of the classical methods such as Max-Min Hill-Climbing algorithm (MMHC). Moreover, the proposed method can obtain the correct causal relationships on Abalone dataset.

In order to improve the visualization effect of the void evolution of materials, an adaptive color mapping method based on data characteristics was proposed. Firstly, a number of control points were selected in the CIELAB color space to form an initial color path. Then, based on the proportion of the data characteristic values, the positions of control points were optimized and the color path was adjusted according to the constraints such as uniformity of color difference and consistency of brightness, so as to meet the requirement of control points following the data adaptively. Finally, the distribution of the perceptual difference sum was remapped by the equalization algorithm, and the perceptual uniformity of the color mapping was optimized to form the final color map. The experimental results show that, compared with traditional color mapping methods which only consider the color space and ignore the diversity of data, the proposed adaptive color mapping method has better identifiability of the characteristics of visualization results by fully considering the color proportion, the number of control points and self-adaptation, and guarantees the perceptual uniformity of the visualization results of the void evolution, improving the accuracy of visualization results and reduces the time required to observe effective information.