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Classification is a data mining approach used to forecast team membership for data instances. It is a two-step procedure. In the first step, a model is built defining a predetermined set of data classes or approaches. The model is developed by considering database tuples defined by attributes.

It is the task of analyzing the features of a freshly presented object and creating it to one of a pre-defined collection of classes. For learning classification rules, the system has to discover the rules that predict the class from the predicting attributes, therefore firstly the conditions must be represented for each class. The system must be given a case or tuple with specific known attributes values to be able to predict what class this case applies to.

Once classes are defined, the system must infer rules that govern the classification, thus the system must be able to discover the representation of each class. The descriptions should only define the predicting attributes of the training set so that only the positive examples must satisfy the characterization, not the negative examples. A rule is correct if its definition covers all the positive examples and none of the negative examples of a class is covered.

**Bayesian Classification** − Bayesian classifiers are statistical classifiers. They can predict class membership probabilities, including the probability that a given sample belongs to a specific class. Bayesian classifiers have also shown high efficiency and speed when used to a high databases.

Naïve Bayesian classifiers consider that the effect of an attribute value on a given class is autonomous of the values of the different attributes. This assumption is referred to as class conditional independence. It is created to define the evaluation contained and is treated Naïve.

**Bayes Theorem** − **Bayes Theorem** − Let X be a data tuple. In the Bayesian method, X is treated as “evidence.” Let H be some hypothesis, including that the data tuple X belongs to a particularized class C. The probability P (H|X) is decided to define the data. This probability P (H|X) is the probability that hypothesis H’s influence has given the “evidence” or noticed data tuple X.

P (H|X) is the posterior probability of H conditioned on X. For instance, consider the nature of data tuples is limited to users defined by the attribute age and income, commonly, and that X is 30 years old users with Rs. 20,000 income. Assume that H is the hypothesis that the user will purchase a computer. Thus P (H|X) reverses the probability that user X will purchase a computer given that the user’s age and income are acknowledged.

P (H) is the prior probability of H. For instance, this is the probability that any given user will purchase a computer, regardless of age, income, or some other data. The posterior probability P (H|X) is located on more data than the prior probability P (H), which is free of X.

Likewise, P (X|H) is the posterior probability of X conditioned on H. It is the probability that a user X is 30 years old and gains Rs. 20,000.

P (H), P (X|H), and P (X) can be measured from the given information. Bayes theorem supports a method of computing the posterior probability P (H|X), from P (H), P (X|H), and P(X). It is given by

$$P(H|X)=\frac{P(X|H)P(H)}{P(X)}$$

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