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Decision-Tree Induction

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Automatic Design of Decision-Tree Induction Algorithms

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

Abstract

Decision-tree induction algorithms are highly used in a variety of domains for knowledge discovery and pattern recognition. They have the advantage of producing a comprehensible classification/regression model and satisfactory accuracy levels in several application domains, such as medical diagnosis and credit risk assessment. In this chapter, we present in detail the most common approach for decision-tree induction: top-down induction (Sect. 2.3). Furthermore, we briefly comment on some alternative strategies for induction of decision trees (Sect. 2.4). Our goal is to summarize the main design options one has to face when building decision-tree induction algorithms. These design choices will be specially interesting when designing an evolutionary algorithm for evolving decision-tree induction algorithms.

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Notes

  1. 1.

    Coppersmith et al. [25] present an interesting heuristic procedure for finding subdomains \(d_{1}\) and \(d_{2}\) when the partition is based on a nominal attribute. Shih [105] also investigates the problem of efficiency on finding the best binary split for nominal attributes.

  2. 2.

    Data fragmentation is a well-known problem in top-down decision trees. Nodes with few instances usually lack statistical support for further partitioning. This phenomenon happens for most of the split criteria available, since their distributions depend on the number of instances in each particular node.

  3. 3.

    OC1 only allows the option of employing oblique splits when \(N > 2n\), though this threshold can be user-defined.

  4. 4.

    Grafting is a term introduced by Esposito et al. [34]. It is also known as subtree raising [127].

  5. 5.

    For inverting a matrix, the Gauss-Jordan procedure takes time proportional to \(O(n^{3})\). The fastest algorithm for inverting matrices to date is \(O(n^{2.376})\) (the Coppersmith-Winograd algorithm).

  6. 6.

    Nominal attributes are not used more than once in a given subtree.

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  1. Faculdade de Informática, Pontifícia Universidade Católica do Rio Grande do Sul, Porto Alegre, RS, Brazil

    Rodrigo C. Barros

  2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil

    André C. P. L. F. de Carvalho

  3. School of Computing, University of Kent, Canterbury, Kent, UK

    Alex A. Freitas

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Barros, R.C., de Carvalho, A.C.P.L.F., Freitas, A.A. (2015). Decision-Tree Induction. In: Automatic Design of Decision-Tree Induction Algorithms. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-14231-9_2

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