RESUMO
The number of spatiotemporal data sets has increased rapidly in the last years, which demands robust and fast methods to extract information from this kind of data. Here, we propose a network-based model, called Chronnet, for spatiotemporal data analysis. The network construction process consists of dividing a geometric space into grid cells represented by nodes connected chronologically. Strong links in the network represent consecutive recurrent events between cells. The chronnet construction process is fast, making the model suitable to process large data sets. Using artificial and real data sets, we show how chronnets can capture data properties beyond simple statistics, like frequent patterns, spatial changes, outliers, and spatiotemporal clusters. Therefore, we conclude that chronnets represent a robust tool for the analysis of spatiotemporal data sets.
RESUMO
In this paper we demonstrate numerically that random networks whose adjacency matrices A are represented by a diluted version of the power-law banded random matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one-dimensional samples with random long-range bonds. The bond strengths of the model, which decay as a power-law, are tuned by the parameter µ as A_{mn}â|m-n|^{-µ}; while the sparsity is driven by the average network connectivity α: for α=0 the vertices in the network are isolated and for α=1 the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value µ=µ_{c}=1, we clearly show [from the scaling of the relative fluctuation of the participation number I_{2} as well as the scaling of the probability distribution functions P(lnI_{2})] the existence of the critical value µ_{c}≡µ_{c}(α) for α<1. Moreover, we characterize the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions D_{q}, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers expãlnI_{q}ã.