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Topological analysis of gene expression arrays identifies high risk molecular subtypes in breast cancer

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Genomic technologies measure thousands of molecular signals with the goal of understanding complex biological processes. In cancer these molecular signals have been used to characterize disease subtypes, signaling pathways and to identify subsets of patients with specific prognosis. However molecular signals for any disease type are so vast and complex that novel mathematical approaches are required for further analyses. Persistent and computational homology provide a new method for these analyses. In our previous work we presented a new homology-based supervised classification method to identify copy number aberrations from comparative genomic hybridization arrays. In this work we first propose a theoretical framework for our classification method and second we extend our analysis to gene expression data. We analyze a published breast cancer data set and find that that our method can distinguish most, but not all, different breast cancer subtypes. This result suggests that specific relationships between genes, captured by our algorithm, help distinguish between breast cancer subtypes. We propose that topological methods can be used for the classification and clustering of gene expression profiles.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, San Francisco, CA, 94132, USA

    Javier Arsuaga & Aleksandr Pankov

  2. Department of Mathematics, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Nils A. Baas

  3. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Daniel DeWoskin

  4. Discovery Science and Technology Department, Chugai Pharmaceuticals Co. Ltd., Kamakura, Kanagawa, Japan

    Hideaki Mizuno

  5. Department of Radiation Oncology, Helen Diller Family Comprehensive Cancer Center, University of California San Francisco, San Francisco, CA, 94115, USA

    Catherine Park

Authors
  1. Javier Arsuaga
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  2. Nils A. Baas
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  3. Daniel DeWoskin
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  4. Hideaki Mizuno
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  5. Aleksandr Pankov
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  6. Catherine Park
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Correspondence to Javier Arsuaga.

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Arsuaga, J., Baas, N.A., DeWoskin, D. et al. Topological analysis of gene expression arrays identifies high risk molecular subtypes in breast cancer. AAECC 23, 3–15 (2012). https://doi.org/10.1007/s00200-012-0166-8

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  • DOI: https://doi.org/10.1007/s00200-012-0166-8

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