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Efficient Approaches for Solving the Large-Scale k-Medoids Problem: Towards Structured Data

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Computational Intelligence (IJCCI 2017)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 829))

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Abstract

The possibility of clustering objects represented by structured data with possibly non-trivial geometry certainly is an interesting task in pattern recognition. Moreover, in the Big Data era, the possibility of clustering huge amount of (structured) data challenges computer science and pattern recognition researchers alike. The aim of this paper is to bridge the gap on large-scale structured data clustering. Specifically, following a previous work, in this paper a parallel and distributed k-medoids clustering implementation is proposed and tested on real-world biological structured data, namely pathway maps (graphs) and primary structure of proteins (sequences). Furthermore, two methods for medoids’ evaluation are proposed and compared in terms of scalability, based on exact and approximate procedures, respectively. Computational results show that the proposed implementation is flexible with respect to the dissimilarity measure and the input space adopted, with satisfactory results in terms of scalability.

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Notes

  1. 1.

    In Spark, workers are the elementary computational units, which can be either single cores on a CPU or entire computers, depending on the environment configuration (i.e. the Spark Context).

  2. 2.

    For a more extensive list, we refer the interested reader to the official Apache Spark RDD API at https://spark.apache.org/docs/latest/api/python/pyspark.html#pyspark.RDD.

  3. 3.

    In the following subsections and pseudocodes every variable whose name ends with RDD shall be considered as an RDD, therefore a data structure whose shards are distributed across the workers or, similarly, with no guarantee that a single worker has its entire content in memory.

  4. 4.

    Not to be confused with i in datasetRDD, distancesRDD and nearestClusterRDD, which is a within-dataset pattern ID.

  5. 5.

    Indeed, in many cases the pattern-to-medoid assignments rather than the WCSoD are compared between consecutive iterations.

  6. 6.

    In the following, we suppose that the dissimilarity measure \(d(\cdot ,\cdot )\), although it might not be metric, is at least symmetric, i.e. \(d(a,b)=d(b,a)\). For symmetric dissimilarity measures the pairwise distance matrix is symmetric by definition and the sum by rows or columns leads to the same result. In case of not-symmetric dissimilarity measures, it is possible to ‘force’ symmetry by letting (for example) \(\bar{d}(a,b)=\frac{1}{2}(d(a,b)+d(b,a))\).

  7. 7.

    Indeed, for very small clusters a Spark-driven parallelisation is discouraged as the majority of the execution time will be spent on thread scheduling and worker communication rather than processing.

  8. 8.

    http://www.kegg.jp/kegg/rest/keggapi.html.

  9. 9.

    http://www.kegg.jp/kegg/xml/docs/.

  10. 10.

    It is sufficient for a given node to exist in a single network to be included.

  11. 11.

    For the sake of comparison, it is worth remarking that both the Euclidean distance and the Hamming distance have complexity \(\mathcal {O}(n)\), where n is the number of attributes. However, in this work, the number of attributes ranges from \(2136^2\) to \(4431^2\) whereas in [12] it ranged from 4 to 28102.

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Authors and Affiliations

  1. Department of Information Engineering, Electronics and Telecommunications, University of Rome “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    Alessio Martino, Antonello Rizzi & Fabio Massimo Frattale Mascioli

Authors
  1. Alessio Martino
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  2. Antonello Rizzi
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  3. Fabio Massimo Frattale Mascioli
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Correspondence to Alessio Martino .

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Editors and Affiliations

  1. IUT Sénart, Université Paris-Est Créteil (UPEC), Créteil, France

    Christophe Sabourin

  2. Department of Computer Architecture and Technology, University of Granada, Granada, Spain

    Juan Julian Merelo

  3. Université Paris-Est Créteil (UPEC), Créteil, France

    Kurosh Madani

  4. University of Reading, Reading, UK

    Kevin Warwick

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Martino, A., Rizzi, A., Frattale Mascioli, F.M. (2019). Efficient Approaches for Solving the Large-Scale k-Medoids Problem: Towards Structured Data. In: Sabourin, C., Merelo, J.J., Madani, K., Warwick, K. (eds) Computational Intelligence. IJCCI 2017. Studies in Computational Intelligence, vol 829. Springer, Cham. https://doi.org/10.1007/978-3-030-16469-0_11

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