Abstract
This chapter focuses on algorithms. Evolutionary computing gets special attention because of its roots in biological evolution. Pattern recognition and clustering are considered in some detail because of their practical importance in solving many problems in bioinformatics. Multidimensional scaling, a technique that could probably find many applications in bioinformatics, receives attention. The chapter closes with some remarks on visualization as a mode of knowledge representation.
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Notes
- 1.
I.e., an algorithm.
- 2.
For example, imagine a typical time-varying signal such as the output of a microphone. This can be converted to a square wave of uniform amplitude and varying period.
- 3.
E.g., using principal component analysis (PCA) (q.v.).
- 4.
See Gorban et al. (2005) for an example.
- 5.
We also have the intermediate process of semisupervised learning, which deals with the problem of combining small amounts of labelled data with large amounts of unlabelled data—the classic paper is Zhu et al. (2003).
- 6.
Fourier’s assertion was that any \(2\pi \)-periodic function \(f(x) = a_0 + \sum _{k=1}^\infty (a_k\cos kx + b_k\sin kx)\). The coefficients are defined as \(a_0 = (2\pi )^{-1}\int _0^{2\pi }f(x)\, \mathrm{{d}}x\), \(a_k = \pi ^{-1}\int _0^{2\pi }f(x)\cos (kx)\, \mathrm{{d}}x\), and \(b_k = \pi ^{-1}\int _0^{2\pi }f(x)\sin (kx)\, \mathrm{{d}}x\).
- 7.
See Kruskal (1964).
- 8.
This was famously applied by Kendall (1970) to the problem of chronology of early Egyptian tombs found at a certain site. The features in that case are artisanal artefacts characteristic of a certain epoch found in the tombs.
- 9.
Cf. Sect. 22.2.
- 10.
It is said that Leibniz was the first to raise this possibility in a letter to one of the Bernoulli brothers, in which he wondered whether it might be possible to discern a pattern in the binary expansion of \(\pi \).
References
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Ramsden, J. (2015). Algorithms. In: Bioinformatics. Computational Biology, vol 21. Springer, London. https://doi.org/10.1007/978-1-4471-6702-0_8
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DOI: https://doi.org/10.1007/978-1-4471-6702-0_8
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