In this paper, we develop a new classification method based on nearest centroid, and it is called the nearest disjoint centroid classifier. Our method differs from the nearest centroid classifier in the following two aspects: (1) the centroids are defined based on disjoint subsets of features instead of all the features, and (2) the distance is induced by the dimensionality-normalized norm instead of the Euclidean norm. We provide a few theoretical results regarding our method. In addition, we propose a simple algorithm based on adapted k-means clustering that can find the disjoint subsets of features used in our method, and extend the algorithm to perform feature selection. We evaluate and compare the performance of our method to other closely related classifiers on both simulated data and real-world gene expression datasets. The results demonstrate that our method is able to outperform other competing classifiers by having smaller misclassification rates and/or using fewer features in various settings and situations.

In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In particular, randomized algorithms are currently having a resurgence, given their generalized elementary approach. By using randomized neural networks, we study distributed classification, which can be employed in situations were data cannot be stored at a central location nor shared. We propose a more efficient solution for distributed classification by making use of a lossy compression approach applied when sharing the local classifiers with other agents. This approach originates from the framework of hyperdimensional computing, and is adapted herein. The results of experiments on a collection of datasets demonstrate that the proposed approach has usually higher accuracy than local classifiers and getting close to the benchmark - the centralized classifier. This work can be considered as the first step towards analyzing the variegated horizon of distributed randomized neural networks.

The nearest-centroid classifier is a simple linear-time classifier based on computing the centroids of the data classes in the training phase, and then assigning a new datum to the class corresponding to its nearest centroid. Thanks to its very low computational cost, the nearest-centroid classifier is still widely used in machine learning, despite the development of many other more sophisticated classification methods. In this paper, we propose two sparse variants of the nearest-centroid classifier, based respectively on $\ell_1$ and $\ell_2$ distance criteria. The proposed sparse classifiers perform simultaneous classification and feature selection, by detecting the features that are most relevant for the classification purpose. We show that training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) and at a quasi-linear computational cost. The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection techniques, while having a significantly lower computational cost.