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Scan number and 3D coordinates are used as the inputs of the proposed neural networks to determine the curve which a data point belongs to and the sequence number of the data point on the curve.
A data point belongs to a cluster if its neighborhood density is high enough.
Under the fuzzy modelling paradigm, each data point belongs to a cluster to a degree specified by a membership value.
In general, as no membership is exactly null, a data point belongs to all clusters with different degrees.
To determine if a data point belongs to multiple clusters, consider the distance of the data point to each cluster center.
The clustering algorithm takes a length scale as input, which determines whether or not a stationary data point belongs to a location cluster.
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The degree of each data point belong to the corresponding data cluster can be calculated from membership function matrix.
The resulting probabilities were then compared in order to establish which class the data point belonged to.
Multinomial logistic regression is one such supervised classification method that models the posterior probability of a data point belonging to one of the C possible classes as a linear function of z [ 27, 28].
The model thus obtained is then used to predict the posterior probability of a given data point belonging to one of the C classes and consequently assigning it to the class with the maximum probability.
A careful insight into Fig. 4 reveals only small portion of data points belongs to region in which bubble point pressure is less than 1,000 Psi.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com