By Iske A , Levesley J (Eds)
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Extra resources for Algorithms For Approximation Proc, Chester 2005
Wunsch II K is the prior probability and i=1 P (Ci ) = 1, and p(x|Ci , ηi ) is the conditional probability density. The component density can be different types of functions, or the same family, but with different parameters. If these distributions are known, finding the clusters of a given data set is equivalent to estimating the parameters of several underlying models, where Maximum Likelihood (ML) estimation can be used . In the case that the solutions of the likelihood equations of ML cannot be obtained analytically, the Expectation-Maximization (EM) algorithm can be utilized to approximate the ML estimates through an iterative procedure .
Cluster validation. Effective evaluation standards and criteria are important to provide the users with a degree of confidence for the clustering results derived from the used algorithms. 4. Results interpretation. Experts in the relevant fields interpret the data partition. Further analysis, even experiments, may be required to guarantee the reliability of extracted knowledge. The remainder of the paper is organized as follows. In Section 2, we briefly review major clustering techniques rooted in machine learning, computer science, and statistics.
This is represented through a weight matrix, describing how each point is related to the reconstruction of another data point. Therefore, the procedure for dimensional reduction can be constructed as the problem that finding L-dimensional vectors yi so that the criterion function i |yi − j wij yj | is minimized. This process makes LLE different from other nonlinear projection techniques, such as Multidimensional Scaling (MDS)  and the isometric feature mapping algorithm (ISOMAP), which extends MDS and aims to estimate the shortest path between a pair of points on a manifold, by virtue of the measured inputspace distances .
Algorithms For Approximation Proc, Chester 2005 by Iske A , Levesley J (Eds)