Enhancing Interpretability in UMAP.: A Methodological Approach to Understanding the Low-Dimensional Graph of UMAP.

Dimension reduction techniques are useful when working with large datasets to simplify data while preserving important information. One such technique is Uniform Manifold Approximation and Projection (UMAP), a nonlinear dimension reduction method. However, interpreting the low-dimensional embeddings produced by UMAP can be challenging, which limits its utility. This thesis addresses the interpretability challenge of UMAP by exploring the question: “How can the low-dimensional embedding of UMAP be interpreted?”. To answer this question, we developed an interpretation framework. After applying UMAP to the dataset (step 1), we apply an unsupervised clustering technique (step 2) to discretize the nonlinear structure and assign pseudo-labels to each data point. Next, we apply a supervised learning technique (step 3), where features serve as predictors and the pseudo-labels are the outcomes. By analyzing the goodness-of-fit metrics from this step, we can select features that provide...Show moreDimension reduction techniques are useful when working with large datasets to simplify data while preserving important information. One such technique is Uniform Manifold Approximation and Projection (UMAP), a nonlinear dimension reduction method. However, interpreting the low-dimensional embeddings produced by UMAP can be challenging, which limits its utility. This thesis addresses the interpretability challenge of UMAP by exploring the question: “How can the low-dimensional embedding of UMAP be interpreted?”. To answer this question, we developed an interpretation framework. After applying UMAP to the dataset (step 1), we apply an unsupervised clustering technique (step 2) to discretize the nonlinear structure and assign pseudo-labels to each data point. Next, we apply a supervised learning technique (step 3), where features serve as predictors and the pseudo-labels are the outcomes. By analyzing the goodness-of-fit metrics from this step, we can select features that provide insights into the global or local structure of the data (step 4), visualize their values, and provide interpretations (step 5). We applied this interpretation framework to two different datasets. The first dataset contains numeric and categorical features about houses and apartments, while the second is a larger dataset comprising numeric gene expression values from brain samples. Applying the framework to both datasets provided valuable insights into the embeddings. Specifically, it helped identify which features are important to better understand the overall distribution of data points (i.e., the global structure) and which ones explain the layout of data points within smaller clusters or areas of the graph (i.e., the the local structure). Identifying these features enhances our understanding of the UMAP outputs. Our interpretation framework is robust against changes in the fixed seed and demonstrates applicability across different datasets. This work enhances the practical utility of UMAP by making its embeddings more interpretable, thereby facilitating deeper data analysis. Future research could focus on developing alternative interpretation strategies or refining the proposed approach.Show less

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Enhancing Interpretability in UMAP. A Methodological Approach to Understanding the Low-Dimensional Graph of UMAP.