187,885 research outputs found
Topological Hierarchies and Decomposition: From Clustering to Persistence
Hierarchical clustering is a class of algorithms commonly used in exploratory data analysis (EDA) and supervised learning. However, they suffer from some drawbacks, including the difficulty of interpreting the resulting dendrogram, arbitrariness in the choice of cut to obtain a flat clustering, and the lack of an obvious way of comparing individual clusters. In this dissertation, we develop the notion of a topological hierarchy on recursively-defined subsets of a metric space. We look to the field of topological data analysis (TDA) for the mathematical background to associate topological structures such as simplicial complexes and maps of covers to clusters in a hierarchy. Our main results include the definition of a novel hierarchical algorithm for constructing a topological hierarchy, and an implementation of the MAPPER algorithm and our topological hierarchies in pure Python code as well as a web app dashboard for exploratory data analysis. We show that the algorithm scales well to high-dimensional data due to the use of dimensionality reduction in most TDA methods, and analyze the worst-case time complexity of MAPPER and our hierarchical decomposition algorithm. Finally, we give a use case for exploratory data analysis with our techniques
A Design Methodology for Space-Time Adapter
This paper presents a solution to efficiently explore the design space of
communication adapters. In most digital signal processing (DSP) applications,
the overall architecture of the system is significantly affected by
communication architecture, so the designers need specifically optimized
adapters. By explicitly modeling these communications within an effective
graph-theoretic model and analysis framework, we automatically generate an
optimized architecture, named Space-Time AdapteR (STAR). Our design flow inputs
a C description of Input/Output data scheduling, and user requirements
(throughput, latency, parallelism...), and formalizes communication constraints
through a Resource Constraints Graph (RCG). The RCG properties enable an
efficient architecture space exploration in order to synthesize a STAR
component. The proposed approach has been tested to design an industrial data
mixing block example: an Ultra-Wideband interleaver.Comment: ISBN : 978-1-59593-606-
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