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If debugging information is available, the stack trace includes the source file and program line number.The term cluster validation is used to design the procedure of evaluating the goodness of clustering algorithm results.

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Finally, we’ll provide R scripts for validating clustering results.In this section, we describe the most widely used clustering validation indices.Recall that the goal of partitioning clustering algorithms (Part @ref(partitioning-clustering)) is to split the data set into clusters of objects, such that: In this section, we’ll describe the two commonly used indices for assessing the goodness of clustering: the silhouette width and the Dunn index.These internal measure can be used also to determine the optimal number of clusters in the data.The silhouette analysis measures how well an observation is clustered and it estimates the average distance between clusters.This is important to avoid finding patterns in a random data, as well as, in the situation where you want to compare two clustering algorithms.

Generally, clustering validation statistics can be categorized into 3 classes In this chapter, we start by describing the different methods for clustering validation.

We also discuss the different user input validation techniques and cover how to use the Error Provider component to display error messages.

When an application encounters an unexpected situation such as a missing file or input parameter, or a logical error such as performing a division by zero, the application generates exceptions.

When you have linked data like you do, the natural solution is to use iteration. private static final Char Node ERRORNODE = new Char Node(....); private static final Char Node ENDOFDATA = new Char Node(....); boolean check Parenthesis(Char Node current) Char Node match Parenthesis(Char Node current, boolean toplevel) Your recursive solution works, as long as the input isn't too long.

I don't recommend using recursion for this problem, since a long input could easily cause a crash from stack overflow.

Table 3.1 details some of the important properties of the Exception class, inherited by the exception classes.