Kernel methods are algorithms that, by replacing the inner product with an appropriate positive definite function, implicitly perform a nonlinear mapping of the input data into a high-dimensional feature space. In this paper, we present a kernel method for clustering inspired by the classical k-means algorithm in which each cluster is iteratively refined using a one-class support vector machine. Our method, which can be easily implemented, compares favorably with respect to popular clustering algorithms, like k-means, neural gas, and self-organizing maps, on a synthetic data set and three UCI real data benchmarks (IRIS data, Wisconsin breast cancer database, Spam database).

A time series is a sequence of time-ordered data, and it is generally used to describe how a phenomenon evolves over time. Time series forecasting, estimating future values of time series, allows the implementation of decision-making strategies. Deep learning, the currently leading field of machine learning, applied to time series forecasting can cope with complex and high-dimensional time series that cannot be usually handled by other machine learning techniques. The aim of the work is to provide a review of state-of-the-art deep learning architectures for time series forecasting, underline recent advances and open problems, and also pay attention to benchmark data sets. Moreover, the work presents a clear distinction between deep learning architectures that are suitable for short-term and long-term forecasting. With respect to existing literature, the major advantage of the work consists in describing the most recent architectures for time series forecasting, such as Graph Neural Networks, Deep Gaussian Processes, Generative Adversarial Networks, Diffusion Models, and Transformers.