A new class of metrics for learning on real-valued and structured data
| Autor: | Matthew W. Hahn, Ruiyu Yang, Scott Mathews, Predrag Radivojac, Elizabeth A. Housworth, Yuxiang Jiang |
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| Rok vydání: | 2016 |
| Předmět: |
Clustering high-dimensional data
FOS: Computer and information sciences Jaccard index Theoretical computer science Computer Networks and Communications Computer science Machine Learning (stat.ML) 02 engineering and technology Directed acyclic graph Computer Science Applications Euclidean distance Exploratory data analysis Similarity (network science) Statistics - Machine Learning 020204 information systems Metric (mathematics) 0202 electrical engineering electronic engineering information engineering Probability distribution 020201 artificial intelligence & image processing Information Systems |
| DOI: | 10.48550/arxiv.1603.06846 |
| Popis: | We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Manhattan distance on vector spaces, and Marczewski-Steinhaus distance on integrable functions. We prove that the new metrics are complete and show useful relationships with f-divergences for probability distributions. To further extend our approach to structured objects such as ontologies, we introduce information-theoretic metrics on directed acyclic graphs drawn according to a fixed probability distribution. We conduct empirical investigation to demonstrate the effectiveness on real-valued, high-dimensional, and structured data. Overall, the new metrics compare favorably to multiple similarity and dissimilarity functions traditionally used in data mining, including the Minkowski ( $$L^p$$ ) family, the fractional $$L^p$$ family, two f-divergences, cosine distance, and two correlation coefficients. We provide evidence that they are particularly appropriate for rapid processing of high-dimensional and structured data in distance-based learning. |
| Databáze: | OpenAIRE |
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