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Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems. 

Unaltered biological matter (biomatter) can be harnessed to fabricate cohesive, sustainable bioplastics. However, controlling the material properties of these bioplastics is challenging, as the contributions of different macromolecular building blocks to processability and performance are unknown. To deconvolute the roles of different classes of biomolecules, we developed experimental and computational methods to construct and analyze biomatter analogs composed of carbohydrates, proteins, and lipids. These analogs are intended to improve fundamental understanding of biomatter plastics. Spectroscopic analyses of biomatter analogs suggest that cohesion depends on protein aggregation during thermomechanical processing. Molecular dynamics simulations confirm that alterations to protein conformation and hydrogen bonding are likely the primary mechanisms underlying the formation of a cohesive, proteinaceous matrix. Simulations also corroborate experimental measurements highlighting the importance of hydrogen bonding and self-assembly between specific, small-molecule constituents. These conclusions may enable the engineering of next-generation biomatter plastics with improved performance. 

Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision-making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value(SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models.