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Register a new userScalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications
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Added by
Shusen Liu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications.
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A first line of attack in exploratory data analysis is data visualization, i.e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable. Standard Johnson-Lindenstrauss dimensionality reduction does not produce data visualizations. The t-SNE heuristic of van der Maaten and Hinton, which is based on non-convex optimization, has become the de facto standard for visualization in a wide range of applications. This work gives a formal framework for the problem of data visualization - finding a 2-dimensional embedding of clusterable data that correctly separates individual clusters to make them visually identifiable. We then give a rigorous analysis of the performance of t-SNE under a natural, deterministic condition on the ground-truth clusters (similar to conditions assumed in earlier analyses of clustering) in the underlying data. These are the first provable guarantees on t-SNE for constructing good data visualizations. We show that our deterministic condition is satisfied by considerably general probabilistic generative models for clusterable data such as mixtures of well-separated log-concave distributions. Finally, we give theoretical evidence that t-SNE provably succeeds in partially recovering cluster structure even when the above deterministic condition is not met.
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A large number of sensors deployed in recent years in various setups and their data is readily available in dedicated databases or in the cloud. Of particular interest is real-time data processing and 3D visualization in web-based user interfaces that facilitate spatial information understanding and sharing, hence helping the decision making process for all the parties involved. In this research, we provide a prototype system for near real-time, continuous X3D-based visualization of processed sensor data for two significant applications: thermal monitoring for residential/commercial buildings and nitrogen cycle monitoring in water beds for aquaponics systems. As sensors are sparsely placed, in each application, where they collect data for large periods (of up to one year), we employ a Finite Differences Method and a Neural Networks model to approximate data distribution in the entire volume.
Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not trivial and may require redevelopment from scratch. Machine Learning (ML) techniques have the potential to automate and significantly speed up the development of compact models. In addition, ML provides a range of modeling options that can be used to develop hierarchies of compact models tailored to specific circuit design stages. In this paper, we explore three such options: (1) table-based interpolation, (2)Generalized Moving Least-Squares, and (3) feed-forward Deep Neural Networks, to develop compact models for a p-n junction diode. We evaluate the performance of these data-driven compact models by (1) comparing their voltage-current characteristics against laboratory data, and (2) building a bridge rectifier circuit using these devices, predicting the circuits behavior using SPICE-like circuit simulations, and then comparing these predictions against laboratory measurements of the same circuit.
We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ implementations. The librarys ability to handle various types of data is rooted in a wide range of preprocessing techniques, and its strong focus on data exploration and interpretability is aided by an intuitive plotting API. Source code, binaries, examples, and documentation can be found at https://github.com/giotto-ai/giotto-tda.
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