Unsupervised learning approaches have gained significant prominence in the field of statistics due to their ability to analyze and interpret complex, unstructured data without the need for labeled datasets. This paper primarily focuses on the areas of graphical models and clustering, highlighting both their theoretical foundations and practical applications. In the domain of graphical models, we introduce a novel method for constructing graphical models that effectively handle correlated replicates and unmeasured confounders. Specifically, we model the correlation among replicates within each independent subject using a one-lag vector autoregressive model and address latent effects induced by unmeasured confounders through a piecewise constant assumption. For clustering, we emphasize advanced techniques that account for overlapping clusters and explore the dynamics of these clusters over time. By applying a latent variable factor model, we estimate time-varying overlapping clusters, which can automatically match clusters across different time points. Furthermore, we extend the overlapping clustering method to non-Gaussian data by employing generalized factor models within the clustering structure.