Trai ning, Validati on and Test DataExample:(A) We have data on 16 data items , their attributes and class labels. RANDOMLY divide them into 8 for training, 4 for validation and 4 for testing.Trai ningItem No.d -AttributesClass1.02.03.KNOWN FOR ALL14.15.DATA ITEMS16.17.08.0Validati on9.010.011.112.0Test13.014.015.116.1(B) . Next, suppose we develop, three classification models A, B, C from the training data. Let the training errors on these models be as shown below (recall that the models do not necessarily provide perfect results on trai ning data n either they are required to).Classificati on results fromItem No.d- AttributesTrue ClassModel AModel BModel C1.00112.ALL KNOWN00003.10104.11015.10006.11117.00008.0000Classificati on Error2/83/83/8(C) . Next, use the three models A, B, C to classify each item in the validation set based on its attribute vales. Recall that we do know their true labels as well. Suppose we get the follow ing results:Classificati on results fromItem No.d- AttributesTrue ClassModel AModel BModel C9.010010.001011.101012.0010Classificati on Error2/42/41/4If we use minimum validation error as model selection criterion, we would select model C.(D) . Now use model C to determine class values for each data point in the test set. We do so by substitut ing the (known) attribute value into the classificati on model C. Again, recall that we know the true label of each of these data items so that we can compare the values obtained from the classification model with the true labels to determine classification error on the test set. Suppose we get the follow ing results.Classificati on results fromItem No.d- AttributesTrue ClassModel C13.0014.ALL KNOWN0015.1016.11Classificati on Error1/4(E) . Based on the above, an estimate of generalization error is 25%.What this means is that if we use Model C to classify future items for which only the attributes will be known, not the class labels, we are likely to make in correct classificati ons about 25% of the time.(F) . A summary of the above is as follows:ModelTrai ningValidati onTestA2550B50C2525Cross Validati onIf available data are limited, we employ Cross Validation (CV). In this approach, data are randomly divided into almost k equal sets. Training is done based on (k-1) sets and the k- th set is used for test. This process is repeated k times (k-fold CV). The average error on the k repetitions is used as a measure of the test error.For the special case whe n k=1, the above is called Leave- One -Out-Cross-Validatio n (LOO-CV).EXAMPLE:Consider the above data consisting of 16 items.(A). Let k= 4, ., 4- fold Cross Validatio n.Divide the data into four sets of 4 items each.Suppose the follow ing set up occurs and the errors obta ined are as show n.Set 1Set 2Set 3Set 4Trai ningItems 1 - 12Items 1 - 813-16Items 1 - 49-16Items 5-16TestItems 13-16Items 9-12Items 5 - 8Items 1 -4Error on test set(assume)25%35%28%32%Estimated Classification Error (CE) = 25+35+28+32= 30%4(B). LOO -CVFor this, data are divided into 16 sets, each con sisti ng of 15 training data and one test data.Set 1Set 2Set 15Set 16Trai ningItems 1 - 15Items 1 -14,16Item 1,3-8Items 2-16TestItem 16Item 15Item 2Item 1Error on test set(assume)0%100%100%100%Suppose Average Classification Error based on the values in the last row isCE)= 32%Then the estimate of test error is 32% .