7,869 research outputs found

    VARMOG: A Co-Evolutionary Algorithm to Identify Manifolds on Large Data

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    Detecting clusters defining a specific shape or manifold is an open problem and has, indeed, inspired different machine learning algorithms. These methodologies normally lack scalability, as they depend on the performance of very sophisticated processes, such as extracting the Laplacian of a similarity graph in spectral clustering. When the algorithms need not only to identify manifolds on large amounts of data or streams, but also select the number of clusters, they failed either because of the robustness of their processes or by computational limitations. This paper introduces a general methodology that works in two levels: the initial step summarizes the data into a set of relevant features using the Euclidean properties of manifolds, and the second applies a robust methodology based on a co-evolutionary multi-objective clustering algorithm that identifies both, the number of manifolds and their associated manifold. The results show that this method outperforms different state of the art clustering processes for both, benchmark and real-world datasets

    Making Laplacians commute

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    In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data
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