Robust multi-modal Herder correlation space learning

In the traditional multiple canonical correlation analysis model, the sample mean is usually used to estimate the class mean vector. However, outlier samples can lead to the inability to effectively capture complex nonlinear failure modes among the data, making it difficult to reveal more significant correlations or differences among the data. To solve this problem, this paper propose the robust multi-model Herder correlation space learning. We handle the outliers of the samples through Herder vectors. Using the Herder vector, we constructed the Herder intra-class divergence matrix to solve the problem of class center deviation caused by intra-class outliers. To further capture the complex nonlinear data characteristics between classes, we constructed the Herder inter-class divergence matrix to better reflect the amplitude of the data between classes. Based on these, we constructed Robust multi-modal Herder correlation space learning model to reveal the greater influence of certain features or patterns in the data. The theoretical derivation of the model was carried out to obtain its analytical solution, and the direction of the spatial projection was further obtained. The Herder space features with good discrimination can be directly obtained through the projection direction. The experimental results show that the Robust multimodal Herder correlation space learning is more effective than the traditional multiple canonical correlation analysis.