Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Fractal, multifractal and sliding window correlation dimension analysis of sedimentary time series
Computers & Geosciences - Fractals and Multifractals
Temporal data mining for the quality assessment of hemodialysis services
Artificial Intelligence in Medicine
An IFS-based similarity measure to index electroencephalograms
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part II
Local fuzzy fractal dimension and its application in medical image processing
Artificial Intelligence in Medicine
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This paper attempts to characterize medical time series using fractal dimensions. Existing fractal dimensions like box, information and correlation dimensions characterize the time series by measuring the rate at which the distribution of the time series changes when the length (or radius) of the box (or hypersphere) is changed. However, the measured dimensions significantly vary when the box (or hypersphere) position is changed slightly. It happens because the data points just outside the box (or hypersphere) are not accounted for, and all the data points inside the box or hypersphere are treated equally. To overcome these problems, the hypersphere is converted to a Gaussian, and thus the hard boundary becomes soft. The Gaussian represents the fuzzy similarity between the neighbors and the point around which the Gaussian is constructed. This concept of similarity is exploited to propose a fuzzy similarity-based fractal dimension. The proposed dimension aims to capture the regularity of the time series in terms of how the fuzzy similarity scales up/down when the resolution of the time series is decreased/increased. Experiments on intensive care unit (ICU) data sets show that the proposed dimension characterizes the time series better than the correlation dimension.