Fractional norms and quasinorms do not help to overcome the curse of dimensionality

The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using of the Manhattan distance and even fractional quasinorms lp (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we systematically test this hypothesis. We confirm that fractional quasinorms have a greater relative contrast or coefficient of variation than the Euclidean norm l2, but we also demonstrate that the distance concentration shows qualitatively the same behaviour for all tested norms and quasinorms and the difference between them decays as dimension tends to infinity. Estimation of classification quality for kNN based on different norms and quasinorms shows that a greater relative contrast does not mean better classifier performance and the worst performance for different databases was shown by different norms (quasinorms). A systematic comparison shows that the difference of the performance of kNN based on lp for p=2, 1, and 0.5 is statistically insignificant

Feature-domain super-resolution framework for Gabor-based face and iris recognition

The low resolution of images has been one of the major limitations in recognising humans from a distance using their biometric traits, such as face and iris. Superresolution has been employed to improve the resolution and the recognition performance simultaneously, however the majority of techniques employed operate in the pixel domain, such that the biometric feature vectors are extracted from a super-resolved input image. Feature-domain superresolution has been proposed for face and iris, and is shown to further improve recognition performance by capitalising on direct super-resolving the features which are used for recognition. However, current feature-domain superresolution approaches are limited to simple linear features such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which are not the most discriminant features for biometrics. Gabor-based features have been shown to be one of the most discriminant features for biometrics including face and iris. This paper proposes a framework to conduct super-resolution in the non-linear Gabor feature domain to further improve the recognition performance of biometric systems. Experiments have confirmed the validity of the proposed approach, demonstrating superior performance to existing linear approaches for both face and iris biometrics

A memory-based method to select the number of relevant components in Principal Component Analysis

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an exponential, giving rise to long memory effects. In comparison with other available methods present in the literature, our procedure does not rely on subjective evaluations and is computationally inexpensive. The underlying basic idea is to use a suitable factor model to analyse the residual memory after sequentially removing more and more components, and stopping the process when the maximum amount of memory has been accounted for by the retained components. We validate our methodology on both synthetic and real financial data, and find in all cases a clear and computationally superior answer entirely compatible with available heuristic criteria, such as cumulative variance and cross-validation.Comment: 29 pages, publishe