Functional data analysis (FDA) has attracted great attention from the statistical community, but there are few fuzzy systems approaches. Therefore, this is a great opportunity for the fuzzy systems community. Focusing on the function-on-function (FOF) regression problem in FDA, the existing models are batch learning models with fixed model structure and parameters, which makes them unsuitable for solving the time-varying regression problem that requires the model to be updated dynamically and continuously with streams of functional data. Furthermore, as far as we are aware, there is no work on the online learning approach for FOF regression problems. To fill this gap, this paper proposes a nonlinear online FOF regression approach called evolving functional fuzzy-neural system (EFFNS) to learn functional data streams in real-time, with both input and output being functions. As a completely new type of evolving fuzzy system designed to learn from data represented as functions rather than vectors or matrices, EFFNS has a flexible model structure which could start from an empty rule base, expand and shrink the rule base, and tune the parameters dynamically depending on the knowledge learned from the rapidly coming functions. Various benchmark examples verify that EFFNS outperforms many of the state-of-the-art approaches.

Visibility algorithm acts as a mapping that bridges graph representation learning with time series analysis, which has been broadly investigated for forecasting tasks. However, the intrinsic nature of visibility encoding yields graphs structured exclusively by binary adjacency matrix, leading to inevitable information loss of temporal sequence during the mapping. To this end, we introduce Angular Visibility Graph Networks (AVGNets), designed with two core features: (i) The framework reconstructs weighted graphs to encode time series by leveraging topological insights derived from visual angles of visibility networks, which capture sequential and structural information within weighted angular matrix. (ii) ProbAttention module is proposed for evaluating probabilistic attention of weighted networks, with remarkable capabilities to extract intrinsic and extrinsic temporal dependencies across multi-layer graphs. Extensive experiments and ablation studies on real-world datasets covering diverse ranges demonstrate that AVGNets achieve state-of-the-art performance, offering an innovative perspective on graph representation for sequence modeling.