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Putting these values in the equation gives: The probability of red is P(x0) = 2/6 = 0.33. X is a vector of zero-indexed symbols, and P means 'probability of.' The log2 function (log to base 2) assumes that log2(0) = 0.0 rather than the true value of negative infinity. Expressed mathematically, Shannon's entropy is: The most common is called Shannon's entropy. Entropy is a metric that's a measure of the amount of disorder in a vector. The second problem is determining an effective technique to search through all possible combinations of clustering to find the best clustering. The first problem is defining exactly what makes a good clustering of data. Дata clustering involves solving two main problems.

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You can download the complete source code for the demo program here. The demo program code is too long to present in its entirety in this article, so I'll focus on the EMIAC algorithm so that you'll be able to modify the demo code to meet your own needs. I've removed all normal error-checking for clarity. I coded the demo program using a non-OOP approach with the C# language, but you shouldn't have too much trouble refactoring the demo code to OOP or another language.

This article assumes you have advanced programming skills with a C-family language but doesn't assume you know anything about data clustering. The demo program displays the final, best clustering found in string format for readability, and also displays a key metric called the entropy of the best clustering, 1.5331 in this example.

In Figure 1, the final clustering obtained by the algorithm is, which means tuple 0 ('Red Medium Hard') is in cluster 1, tuple 1 ('Red Small Soft') is in cluster 0, tuple 2 ('Blue Large Hard') is in cluster 2 and so on. The index of the array indicates a tuple index, and the cell value in the array indicates a cluster. Internally, the demo program encodes a clustering as an array of int. Because clustering doesn't use any kind of training data, clustering is called 'unsupervised learning.' After a preliminary clustering pass, the EMIAC algorithm performs a refining pass to try and improve the clustering. Then the clustering algorithm iterates through the tuples, assigning each tuple to the cluster that generates the best overall clustering, based on entropy. Behind the scenes, the algorithm starts by placing seed tuples 1, 4 and 7 into clusters 0, 1 and 2, respectively. The demo program then uses EMIAC to find the best clustering of the data. In this case the number of clusters is set to 3. Many clustering algorithms, including EMIAC, require the number of clusters to be specified. So the first raw data item, 'Red Medium Hard,' is encoded as '0 1 0.' For texture, hard is encoded as 0 and soft is encoded as 1. For size, small, medium and large are encoded as 0, 1, 2, respectively. For color, red, blue, green and orange are encoded as 0, 1, 2 and 3, respectively. The demo program converts the raw string data into integer form for more-efficient processing. Color can take on one of four possible values: red, blue, green or orange. Each tuple has three categorical attributes: color, size and texture. The demo program shown in the figure is clustering a small set of eight dummy data items. The best way to understand what clustering is and see where I'm headed in this article is to take a look at Figure 1. I call this algorithm and its implementation Entropy Minimization Iterative Agglomerate Clustering (EMIAC) to distinguish it from other clustering techniques. Although all the ideas used in the clustering algorithm presented here are known, the overall algorithm and specific implementation, to the best of my knowledge, have not been published before. The algorithm works with categorical and numeric data and scales well to extremely large data sets. In this article I present a clustering algorithm that's based on a concept called entropy. Unfortunately, k-means clustering directly applies only in situations where the data items to be clustered are completely numeric. The most basic algorithm is called k-means clustering. There are many different clustering algorithms because the effectiveness of a particular algorithm depends on the characteristics of the data being clustered.

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For example, cluster analysis can be used to determine what types of items are often purchased together so that targeted advertising can be aimed at consumers, or to group events in a log file to analyze the behavior of a software system. Clustering is a machine-learning technique that has many important practical uses.

Data clustering is the process of placing data items into different groups (clusters) in such a way that items in a particular group are similar to each other and items in different groups are different from each other.

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