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A fractal dimension is a ratio for figuring out the complexity of a system given its measurement. Fractal dimensions can be useful in machine learning (ML) as part of dimensionality reduction, in order to change how machine learning systems deal with data.
As ratios of a figure's complexity at scale, fractal dimensions are helpful tools for some kinds of technical evaluations. For example, fractal dimension is often used in dimensionality reduction, which is a problem in ML that is based on a kind of simplification of data set analysis – the system can produce a different model given a lower number of parameters. Feature selection and feature extraction are two techniques for implementing dimensionality reduction, which changes the model according to the user’s needs. The fractal dimension is a statistic that can have a bearing on how these methods are applied.
In general, fractal dimensions help to show how scaling changes a model or modeled object. For example, take a very complex shape, graphed to a scale, and then reduce the scale. The data points converge and become fewer. This is the kind of work that can be measured and judged with fractal dimensions.