Industrial processes often operate under diverse conditions to fulfill manufacturing strategies. A common approach involves segmenting data based on operational modes and developing tailored learning models for each. However, data from the same mode can still exhibit complex patterns due to non-Gaussian behaviors and fault occurrences. Merely analyzing coarse-grained correlations between modes may insufficiently partition modes. Addressing this, this chapter introduces a novel fault identification method for multi-mode industrial processes. Initially, a hierarchical clustering strategy captures the multi-grained information within process data, modeling correlations both across modes (different operation conditions) and within modes (patterns in each mode). Subsequently, a feature learning algorithm leveraging non-negative matrix factorization (NMF) is introduced to extract data features, enabling samples to be represented by the identified multi-grained structural information. A weighted metric is also designed to accurately measure the feature similarities obtained through the NMF. Notably, our framework employs an $$\ell _{p}$$ -norm $$(0