Browsing by Author "Wenk, Carola"

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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, Brian
Persistence 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.
Persistent Homology for the Quantitative Evaluation of Architectural Features in Prostate Cancer Histology
(2019-02) Lawson, Peter; Sholl, Andrew B.; Brown, J. Quincy; Fasy, Brittany T.; Wenk, Carola
The current system for evaluating prostate cancer architecture is the Gleason grading system which divides the morphology of cancer into five distinct architectural patterns, labeled 1 to 5 in increasing levels of cancer aggressiveness, and generates a score by summing the labels of the two most dominant patterns. The Gleason score is currently the most powerful prognostic predictor of patient outcomes; however, it suffers from problems in reproducibility and consistency due to the high intra-observer and inter-observer variability amongst pathologists. In addition, the Gleason system lacks the granularity to address potentially prognostic architectural features beyond Gleason patterns. We evaluate prostate cancer for architectural subtypes using techniques from topological data analysis applied to prostate cancer glandular architecture. In this work we demonstrate the use of persistent homology to capture architectural features independently of Gleason patterns. Specifically, using persistent homology, we compute topological representations of purely graded prostate cancer histopathology images of Gleason patterns 3,4 and 5, and show that persistent homology is capable of clustering prostate cancer histology into architectural groups through a ranked persistence vector. Our results indicate the ability of persistent homology to cluster prostate cancer histopathology images into unique groups with dominant architectural patterns consistent with the continuum of Gleason patterns. In addition, of particular interest, is the sensitivity of persistent homology to identify specific sub-architectural groups within single Gleason patterns, suggesting that persistent homology could represent a robust quantification method for prostate cancer architecture with higher granularity than the existing semi-quantitative measures. The capability of these topological representations to segregate prostate cancer by architecture makes them an ideal candidate for use as inputs to future machine learning approaches with the intent of augmenting traditional approaches with topological features for improved diagnosis and prognosis.