Publications by Colleges and Departments (MSU - Bozeman)
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Item A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering(Institute of Electrical and Electronics Engineers, 2021-01) Qin, Yu; Fasy, Brittany Terese; Wenk, Carola; Summa, BrianPersistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances has been challenging due to the computational cost. In this paper, we propose a persistence diagram hashing framework that learns a binary code representation of persistence diagrams, which allows for fast computation of distances. This framework is built upon a generative adversarial network (GAN) with a diagram distance loss function to steer the learning process. Instead of using standard representations, we hash diagrams into binary codes, which have natural advantages in large-scale tasks. The training of this model is domain-oblivious in that it can be computed purely from synthetic, randomly created diagrams. As a consequence, our proposed method is directly applicable to various datasets without the need for retraining the model. These binary codes, when compared using fast Hamming distance, better maintain topological similarity properties between datasets than other vectorized representations. To evaluate this method, we apply our framework to the problem of diagram clustering and we compare the quality and performance of our approach to the state-of-the-art. In addition, we show the scalability of our approach on a dataset with 10k persistence diagrams, which is not possible with current techniques. Moreover, our experimental results demonstrate that our method is significantly faster with the potential of less memory usage, while retaining comparable or better quality comparisons.Item Comparison of silhouette‐based reallocation methods for vegetation classification(Wiley, 2021-01) Lengyel, Attila; Roberts, David W.; Botta-Dukát, ZoltánAims: Vegetation classification seeks to partition the variability of vegetation into relatively homogeneous but distinct types. There are many ways to evaluate, and potentially improve, such a partitioning. One effective approach involves calculating silhouette widths which measure the goodness-of-fit of plots to their cluster. We introduce a new iterative reallocation clustering method — Reallocation of Misclassified Objects based on Silhouette width (REMOS) — and compare its performance with an existing algorithm — OPTimizing SILhouette widths (OPTSIL). REMOS reallocates misclassified objects to their nearest-neighbour cluster iteratively. Of its two variants, REMOS1 reallocates only the object with the lowest silhouette width, while REMOS2 reallocates all objects with negative silhouette width in each iteration. We test how REMOS1, REMOS2 and OPTSIL perform in terms of: (a) cluster homogeneity and separation; (b) the number of diagnostic species; and (c) runtime. Methods: We classified simulated data with the flexible-beta algorithm for values of beta from −1 to 0. These classifications were subsequently optimized by REMOS1, REMOS2 and OPTSIL and compared for mean silhouette widths, misclassification rate, and runtime. We classified three vegetation data sets from two to ten clusters, optimized all outcomes with the three reallocation methods, and compared their mean silhouette widths, misclassification rate, and number of diagnostic species. Results: OPTSIL achieved the highest mean silhouette width across the majority of the data sets. REMOS achieved zero or negligible misclassifications, outperforming OPTSIL on this criterion. REMOS algorithms were typically more than an order of magnitude faster to calculate than OPTSIL. There was no clear difference between REMOS and OPTSIL in the number of diagnostic species. Conclusions:REMOS algorithms may be preferable to OPTSIL when: (a) the primary objective is to reduce the number of negative silhouette widths in a classification, as opposed to maximizing mean silhouette width; or (b) when the time efficiency of the algorithm is important.