Within-class multimodal classification

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Within-class multimodal classification Huan Wan1

· Hui Wang1 · Bryan Scotney2 · Jun Liu1 · Wing W. Y. Ng3

Received: 10 June 2019 / Revised: 25 May 2020 / Accepted: 24 June 2020 / © The Author(s) 2020

Abstract In many real-world classification problems there exist multiple subclasses (or clusters) within a class; in other words, the underlying data distribution is within-class multimodal. One example is face recognition where a face (i.e. a class) may be presented in frontal view or side view, corresponding to different modalities. This issue has been largely ignored in the literature or at least under studied. How to address the within-class multimodality issue is still an unsolved problem. In this paper, we present an extensive study of within-class multimodality classification. This study is guided by a number of research questions, and conducted through experimentation on artificial data and real data. In addition, we establish a case for within-class multimodal classification that is characterised by the concurrent maximisation of between-class separation, between-subclass separation and within-class compactness. Extensive experimental results show that within-class multimodal classification consistently leads to significant performance gains when within-class multimodality is present in data. Furthermore, it has been found that within-class multimodal classification offers a competitive solution to face recognition under different lighting and face pose conditions. It is our opinion that the case for within-class multimodal classification is established, therefore there is a milestone to be achieved in some machine learning algorithms (e.g. Gaussian mixture model) when within-class multimodal classification, or part of it, is pursued. Keywords Within-class multimodality · Linear discriminant analysis · Subclass discriminant analysis · Separability-oriented subclass discriminant analysis

1 Introduction Understanding the underlying data distribution before applying a machine learning process is an important step in the analysis of data, as otherwise, wrong choices may be made in the different stages of the machine learning process. Every single algorithm used in machine learning has, either explicitly or implicitly, some assumptions about the data for it to work

 Huan Wan

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Extended author information available on the last page of the article.

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effectively. For linear regression, the typical assumptions include linearity (there is linear relationship between the independent and dependent variables), exogeneity (the errors between observed and predicted values should have conditional mean zero), multicollinearity (the independent variables must all be linearly independent), homoscedasticity (the errors have the same variance in each observation) and normality (the errors have normal distribution) [7, 23]. For random forests [2], one assumption is that changes in the dependent variable are best described by hyper-rectangles in the independent variables (b