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The method requires an iterative process. That is, calculations must be repeated using different breaks in the dataset to determine which set of breaks has the smallest in-class variance. The process is started by dividing the ordered data into classes in some way which may be arbitrary. There are two steps that must be repeated:
Decision boundaries are not always clear cut. That is, the transition from one class in the feature space to another is not discontinuous, but gradual. This effect is common in fuzzy logic based classification algorithms, where membership in one class or another is ambiguous. Decision boundaries can be approximations of optimal stopping boundaries.
Suppose a pair (,) takes values in {,, …,}, where is the class label of an element whose features are given by .Assume that the conditional distribution of X, given that the label Y takes the value r is given by (=) =,, …, where "" means "is distributed as", and where denotes a probability distribution.
Otsu's method is related to Fisher's linear discriminant, and was created to binarize the histogram of pixels in a grayscale image by optimally picking the black/white threshold that minimizes intra-class variance and maximizes inter-class variance within/between grayscales assigned to black and white pixel classes.
In a Bayesian network, the Markov boundary of node A includes its parents, children and the other parents of all of its children.. In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless.
In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks) based on one or more variables.
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).