HiMuV: Hierarchical Framework for Modeling Multi-Modality Multi-Resolution Data

Many real-world applications are characterized by temporal data collected from multiple modalities, each sampled with a different resolution. Examples include manufacturing processes and financial market prediction. In these applications, an interesting observation is that within the same modality, we often have data from multiple views, thus naturally forming a 2 level hierarchy: with the multiple modalities on the top, and the multiple views at the bottom. For example, in aluminum smelting processes, the multiple modalities include power, noise, alumina feed, etc; and within the same modality such as power, the different views correspond to various voltage, current and resistance control signals and measured responses. For such applications, we aim to address the following challenge, i.e., how can we integrate such multi-modality multi-resolution data to effectively predict the targets of interest, such as bath temperature in aluminum smelting cell and the volatility in financial market. In this paper, for the first time, we simultaneously model the hierarchical data structure and the multi-resolution property via a novel framework named HiMuV. Different from existing work based on multiple views on a single level or a single resolution, the proposed framework is based on the key assumption that the information from different modalities is complementary, whereas the information within the same modality (across different views) is redundant in terms of predicting the targets of interest. Therefore, we introduce an optimization framework where the objective function contains both the prediction loss and a novel regularizer enforcing the consistency among different views within the same modality. To solve this optimization framework, we propose an iterative algorithm based on randomized block coordinate descent. Experimental results on synthetic data, benchmark data, and various real data sets from aluminum smelting processes, and stock market prediction demonstrate the effectiveness and efficiency of the proposed algorithm.