Remarkable achievements have been made in utilizing information granulation for improving the accuracy and interpretability of time series forecasting. However, existing information granule-based methods suffer from multiple limitations, including the loss of scale information and the neglect of nonlinear trends and magnitude information, which compromise prediction quality. To address these issues, this article proposes an information granule-based time series prediction method by synergizing multiscale and multitype information granulations. Firstly, an adaptive multiscale sequence generation method is designed to generate the multiscale subsequences, which provide the multiscale views of time series. Then, the dual-mode granulation mechanism integrating magnitude-type and trend-type information granulations is proposed to comprehensively exploit linear trends, non-linear trends, and magnitude information of time series. Thirdly, the cross-scale information granule fusion is designed to model the inherent interrelationships between multiscale information granules, which can promote the collaboration across different-scale information granules. Finally, multitype information granules are synergized to perform prediction, and the prediction process also benefits from the fused multiscale information. Experiments on small, medium, and large size time series datasets demonstrate that the proposed method achieves significant performance compared with the state-of-the-art methods.

Impressive advancements have been achieved in utilizing information granulation for solving long-term time series prediction problems. However, most state-of-the-art methods suffer from limitations due to not only using the single-scale information granulation but also the lack of trend information. As a result, the prediction models are difficult to capture the multiscale temporal dependencies and dynamic behavior of time series. To address these problems, this article proposes a multiscale information granule-based time series forecasting model. First, the trend-based information granulation strategy is proposed to generate trend information granules that can capture dynamic behavior and trend information in an incremental manner. Then, the multiscale fusion mechanism is proposed to form multiscale information granules with diversified information, which fuses local and global information at different scales. Finally, the two-stage prediction mechanism is proposed to capture multiscale temporal dependencies and perform long-term prediction. A series of experiments were conducted on publicly available time series. Comparative analysis shows that the proposed method outperforms existing numeric models and granular models in long-term prediction on regular and large data time series.

Time-series prediction based on information granule in which the algorithm is developed by deriving the relations existing in the granular time series, has achieved excellent success. However, the existing uncertainty in data and the computational demand of the granulation process make it difficult for these methods to accurately and efficiently achieve long-term prediction. In this article, a fuzzy-probabilistic prediction approach with evolving clustering-based granulation is proposed. First, the evolving clustering-based granulation strategy is proposed to transform the original numerical data into information granules. The granulation process is performed in an incremental way and the information granules are represented with the triplets, which can efficiently reduce the computation overhead. Then, the proposed information granule clustering is used to derive the group relations in the information granules. Based on the logical relationships of information granules in the temporal order, the information granule forecasting the integrated fuzzy and probability theory is proposed to deal with uncertainties and perform final long-term prediction. A series of experiments using publicly available time series are conducted, and the comparative analysis demonstrates that the proposed approach can achieve a better performance for regular and Big Data time series than the existing granular and numeric models for long-term prediction.

Most traditional methods for extracting key points from the 3D point cloud are based on the geometric features of points and they pose problems such as low accuracy. In order to solve these problems, this paper proposes a novel approach based on 2D image mapping, making it able to achieve highly accurate localization of key points. Specifically, it works as follows: input images are first selected for Harris corner detection; the three pairs of marker points of the images and the point cloud are then selected to calculate the transformation matrix T between them; next, the image key points are mapped onto the three-dimensional points through the transformation matrix T, for which the extraction of key points is achieved. Experimental results show that the proposed algorithm is able to greatly improve the extraction accuracy of key points in comparison with traditional algorithms.

Long-term time series prediction is a challenging and essential task both in theory and practice. Recently, information granulation is shown to be an appropriate tool for the long-term forecast. Though some models for the long-term prediction problem have been proposed using information granulation recently, there is still a growing need to develop new prediction approaches for time series data based on information granule, which can capture the dynamic trend change with high accuracy. In this article, a long-term prediction approach, based on back-propagation neural network and information granule, is proposed. First, the individual numerical intervals for the time series are obtained by using the principle of justifiable granularity in information granule. Then, an automatic linear trend extraction method is developed to extract the trend change, which is inherited in granules. Finally, a hierarchy of neural network is constructed to carry out prediction by using information granule as input. Experiments using publicly available time series datasets demonstrate that the proposed approach can achieve better performance than the existing models for long-term prediction.