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In addition to a precision automated X– Y sample stage, the confocal optics provides discrimination between points of different depths within the cell, enabling chemical mapping in three dimensions.
Similarly, support vector machines represent a third approach to machine learning, in which the learning set of data points are mapped into a higher dimensional space via a kernel function, and a hyperplane identified that provides the greatest separation between points of different class (ADHD, control).
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For example, values smaller than 1 for g ij (r) indicate some tendency of repulsion or inhibition between points of the different types i and j.
Then, MMD-Isomap aims at seeking an optimal nonlinear subspace to preserve the geometrical structure of each manifold according to the Isomap criterion, meanwhile, to enhance the discriminating capability by maximizing the distances between data points of different manifolds.
The idea of the support vector machines (SVMs) is to find the optimal hyperplanes between data points of different groups; see [ 3] for a detailed description about the method.
The list of codes used for feature names is given in the Additional file 7. SVMs are a class of algorithms based on statistical learning theory, which find the hyperplane that separates the data points (here: proteomes) of different classes so that the width of the margin between the points of different classes is maximized; wider margins imply lower generalization error.
On the other hand, SVMs are algorithms based on statistical learning theory, which find the hyperplane that separates the data points (here: proteomes) of different classes so that the width of the margin between the points of different classes is maximized [ 15].
At this step, no differentiation between the data points of different isotopic compositions can be accomplished.
We only evaluated the cut points at the boundary between two classes (boundary of binding sites), because the cut point T that minimizes the average class entropy Ent(S, T) is always a value between two data points of different classes in a sorted array (Fayyad and Irani, 1993).
If considered a ball of certain size defined by fuzzy cardinality, the exchange of two such fuzzy sets as points disturbs the position of all the others, if the exchange takes place between two fuzzy sets as points of different size.
Figure 3 illustrates the relationship between point charge of different class and corresponding IEFP.
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