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The binomial-neighbour instance-based learner on a multiclass performance measure scheme

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Abstract

This paper presents a novel instance-based learning methodology the Binomial-Neighbour (B-N) algorithm. Unlike to other k-Nearest Neighbour algorithms, B-N employs binomial search through vectors of statistical features and distance primitives. The binomial combinations derived from the search with best classification accuracy are distinct primitives which characterise a pattern. The statistical features employ a twofold role; initially to model the data set in a dimensionality reduction preprocessing, and finally to exploit these attributes to recognise patterns. The paper introduces as well a performance measure scheme for multiclass problems using type error statistics. We harness this scheme to evaluate the B-N model on a benchmark human action dataset of normal and aggressive activities. Classification results are being compared with the standard IBk and IB1 models achieving significantly exceptional recognition performance.

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Notes

  1. The expression \(e_i \ne a_i\) denotes a misclassified instance.

  2. The expression \(e_i = -1\) denotes an out-of-scope misclassified instance (\(e_i \notin C\)).

  3. The original statistical functions derived from performance metrics, which have been used for the multiclass problem, are included in the work of Sokolova et al. (2006).

  4. All primitive abbreviations can be found in the primitive table presented in Theodoridis and Hu (2008).

    Fig. 2
    figure 2

    Primitive function usage of the B-N representation. a Features, b Distances, c Voronoi diagram. (Primitive abbreviations can be found at Theodoridis and Hu (2008)). Features SUM adder, MAX maximum, MIN minimum, WAMP Willison amplitude, SSC slope sign changes, ZC zero crossing, WL waveform length, EPR error propagation, KUR Kurtosis, SKE skewness, VAR variance, SDV standard deviation, MDR mid-range, MAVS MAV slope, MAV mean absolute value, RMS root mean square, GOM geometric-mean, HRM harmonic mean, GNM generalised mean, IQM interquartile mean, MEAN mean, Distances BHD Bhattacharyya dist., TVD total variation, PDD probability distribution, MCV Pearsons coefficient, MSE mean square error, SQR square error, ABS absolute dist., ERR error difference, LEE Lee dist., BRD Bregman divergence, MNE Mahalanobis Norm., EUC Euclidean dist

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Authors and Affiliations

  1. University of Salford, Salford, UK

    Theodoros Theodoridis

  2. University of Essex, Colchester, UK

    Huosheng Hu

Authors
  1. Theodoros Theodoridis
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  2. Huosheng Hu
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Corresponding author

Correspondence to Theodoros Theodoridis.

Additional information

Communicated by V. Loia.

Primitive feature, distance, and statistical vectors (\(\varvec{f}\), \(\varvec{d}\), \(\varvec{z}\)) have been used extensively in this work, taken from the primitive table presented in Theodoridis and Hu (2008).

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Theodoridis, T., Hu, H. The binomial-neighbour instance-based learner on a multiclass performance measure scheme. Soft Comput 19, 2973–2981 (2015). https://doi.org/10.1007/s00500-014-1461-z

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