Addressing complexity helps to better leverage ML and explain AI

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Addressing complexity helps to better leverage ML and explain AI

Hunting the Hidden Dimension — PBS

Both ML and AI involve feature extraction procedures either explicitly or implicitly, such as shape or texture features. Such features may however exhibit complex and fractal behavior that can be a challenge to capture using Euclidean geometry. Addressing such complexity can help tremendously in better leveraging ML and explain AI. This was based on an early work that I have conducted with colleagues, some years ago using Matlab and Neural Network with fractals to capture features of gene expression. Fractals with ML helped us to capture subtle variation in gene expression when compared with Euclidean geometry.

Fractals is helping vastly in today’s information technology with its use in mobile phone. Fractal-based models are helping in the description and classification of scale-related phenomena in life sciences, from molecular to higher ecosystem levels of organization.

Fractal feature extraction types

Fractal features can be captured as dimensions (D) to detect whether data exhibit patterns and surface roughness in engineering. The fractal dimension such as box counting (Db) is measured by counting the numbers of boxes occupied by the black pixels of black and white images. The box size started first with 2 large squares on one side, and then 2n squares, with n varying depending on the box size.

Image features extraction possibilities based on fractal geometry

There are several other procedure to measure texture in addition to box counting where Db is then estimated by plotting the number of boxes N(d) against the box-side length d. This method is similar to the areography technique in which boxes are fixed ‘sub-regions” defined by geographical coordinates instead of grids of changing sizes.

Since the box counting values can change with re-orientation and the relatively low resolution of digitized images it could produce an underestimation of counts for smaller boxes, variogram approach can be also used to capture fractal dimensions (Dv). The variogram approach can be also used measure the surface texture through the measurement of surface fractal dimension (Dv) and to reconstruct images (surfaces).

The variogram has also a link to Hurst exponent. The standard deviation SD2(h) of the difference between Z(i) and Z(0), which follows a normal distribution, is proportional to h2H. The Hurst exponent, referred to by H, is a measure used in time series commonly used to capture trends in financial data. Similar to AUC when H=0.5 indicates a random series and when AUC >0.5 as indication of presence of a pattern in data in the case of H>0.5 it is an indication of presence of a trend supporting times series.


Some of the work conducted using fractals and neural networks to capture gene expression can be found in Complexity and Fractals in Nature at


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