Data Mining Mehmed Kantardzic (good english books to read .txt) 📖

training samples, and then it is evaluated based on its performance on the test samples. In order for this error estimate to be reliable in predicting future model performance, not only should the training and the testing sets be sufficiently large, they must also be independent. This requirement of independent training and test samples is still often overlooked in practice.

How should the available samples be split to form training and test sets? If the training set is small, then the resulting model will not be very robust and will have low generalization ability. On the other hand, if the test set is small, then the confidence in the estimated error rate will be low. Various methods are used to estimate the error rate. They differ in how they utilize the available samples as training and test sets. If the number of available samples is extremely large (say, 1 million), then all these methods are likely to lead to the same estimate of the error rate. If the number of samples is smaller, then the designer of the data-mining experiments has to be very careful in splitting the data. There are no good guidelines available on how to divide the samples into subsets. No matter how the data are split, it should be clear that different random splits, even with the specified size of training and testing sets, would result in different error estimates.

Let us discuss different techniques, usually called resampling methods, for splitting data sets into training and test samples. The main advantage of using the resampling approach over the analytical approach for estimating and selecting models is that the former does not depend on assumptions about the statistical distribution of the data or specific properties of approximating functions. The main disadvantages of resampling techniques are their high computational effort and the variation in estimates depending on the resampling strategy.

The basic approach in model estimation is first to prepare or to learn a model using a portion of the training data set and then to use the remaining samples to estimate the prediction risk for this model. The first portion of the data is called a learning set, and the second portion is a validation set, also called a testing set. This naïve strategy is based on the assumption that the learning set and the validation set are chosen as representatives of the same, unknown distribution of data. This is usually true for large data sets, but the strategy has an obvious disadvantage for smaller data sets. With a smaller number of samples, the specific method of splitting the data starts to have an impact on the accuracy of the model. The various methods of resampling are used for smaller data sets, and they differ according to the strategies used to divide the initial data set. We will give a brief description of the resampling methods that are common in today’s data-mining practice, and a designer of a data-mining system will have to make a selection based on the characteristics of the data and the problem.

1. Resubstitution Method. This is the simplest method. All the available data are used for training as well as for testing. In other words, the training and testing sets are the same. Estimation of the error rate for this “data distribution” is optimistically biased (estimated error is often smaller than could be expected in real applications of the model), and therefore the method is very seldom used in real-world data-mining applications. This is especially the case when the ratio of sample size to dimensionality is small.

2. Holdout Method. Half the data, or sometimes two-thirds of the data, is used for training and the remaining data are used for testing. Training and testing sets are independent and the error estimation is pessimistic. Different partitioning will give different estimates. A repetition of the process, with different training and testing sets randomly selected, and integration of the error results into one standard parameter, will improve the estimate of the model.

3. Leave-One-Out Method. A model is designed using (n − 1) samples for training and evaluated on the one remaining sample. This is repeated n times with different training sets of size (n − 1). This approach has large computational requirements because n different models have to be designed and compared.

4. Rotation Method (n-Fold Cross-Validation). This approach is a compromise between holdout and leave-one-out methods. It divides the available samples into P disjoint subsets, where 1 ≤ P ≤ n. (P − 1) subsets are used for training and the remaining subset for testing. This is the most popular method in practice, especially for problems where the number of samples is relatively small.

5. Bootstrap Method. This method resamples the available data with replacements to generate a number of “fake” data sets of the same size as the given data set. The number of these new sets is typically several hundreds. These new training sets can be used to define the so-called bootstrap estimates of the error rate. Experimental results have shown that the bootstrap estimates can outperform the cross-validation estimates. This method is especially useful in small data set situations.

4.8 MODEL ESTIMATION

A model realized through the data-mining process using different inductive-learning techniques might be estimated using the standard error rate parameter as a measure of its performance. This value expresses an approximation of the true error rate, a parameter defined in SLT. The error rate is computed using a testing data set obtained through one of applied resampling techniques. In addition to the accuracy measured by the error rate, data-mining models can be compared with respect to their speed, robustness, scalability, and interpretability; all these parameters may have an influence on the final verification and validation of the model. In the short overview that follows, we will illustrate the characteristics of the error-rate parameter for classification tasks; similar approaches and analyses are possible for other common data-mining tasks.

The computation of error rate is based on counting of errors in a testing process. These