DATA MINING Desktop Survival Guide by Graham Williams
Desktop Survival Project Home List of Figures List of Tables Data Mining Data Mining Data Mining with Rattle Introduction Data Transform Explore A Model Building Framework Unsupervised Modelling Two Class Models Multi Class Models Regression Models Text Mining Evaluation and Deployment Moving into R Troubleshooting R for the Data Miner R Data Graphics in R Understanding Data Preparing Data Building Models Evaluating Models Algorithms Apriori Bagging Bayes Classifier Boosting Cluster Analysis Conditional Trees Hierarchical Clustering K-Means K-Nearest Neighbours Linear Models Logistic Regression Neural Networks Support Vector Machines Text Mining Open Products AlphaMiner Borgelt Data Mining Suite KNime R Rattle Weka Closed Products C4.5 Clementine Equbits Foresight GhostMiner InductionEngine ODM Enterprise Miner Statistica Data Miner TreeNet Virtual Predict Appendicies Glossary Bibliography Index

Example

Suppose we have a database of patients for whom we have, in the past, identified suitable types of contact lenses. Four categorical variables might describe each patient: Age (having possible values young, pre-presbyopic, and presbyopic), type of Prescription (myope and hypermetrope), whether the patient is Astigmatic (boolean), and TearRate (reduced or normal). The patients are already classified into one of three classes indicating the type of contact lens to fit: hard, soft, none.

Sample data is presented in Table .

Table: Contact lens training data.

We can make use of this historic data to talk about the probabilities of requiring soft, hard, or no lenses, according to a patient's Age, Prescription, Astigmatic condition and TearRate. Having a probabilistic model we could then make predictions using the model about the suitability of particular lens types for new clients. Thus, if we know historically that the probability of a patient requiring a soft contact lens, given that they were young and had a normal rate of tear production, was 0.9 (i.e., 90%) then we would supply soft lens to most such patients in the future. Symbolically we write this probability as:

$$P(soft\vert young,normal) = 0.9$$

Generally the real problem is to determine something like:

$$P(soft\vert young,myope,no,normal)$$

To do this we would need to have a sufficient number of examples of $(young,myope,no,normal)$ in the database. For databases with many variables, and even for very large databases, it is not likely that we will have sufficient (or even any) examples of all possible combinations of all variable values. This is where naïve Bayes helps.

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