Data Mining: Concepts and Techniques — Slides for Textbook — — Chapter 7 — ©Jiawei Han and Micheline Kamber Department of Computer Science University of Illinois at Urbana-Champaign www.cs.uiuc.edu/~hanj

Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by Neural Networks Classification by Support Vector Machines (SVM) Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

Classification Classification: predicts categorical class labels Typical Applications {credit history, salary}-> credit approval ( Yes/No) {Temp, Humidity} --> Rain (Yes/No) Mathematically

Linear Classification Binary Classification problem The data above the red line belongs to class ‘x’ The data below red line belongs to class ‘o’ Examples – SVM, Perceptron, Probabilistic Classifiers x x x x x x x x o x o o x o o o o o o o o o o

Discriminative Classifiers Advantages prediction accuracy is generally high (as compared to Bayesian methods – in general) robust, works when training examples contain errors fast evaluation of the learned target function (Bayesian networks are normally slow) Criticism long training time difficult to understand the learned function (weights) (Bayesian networks can be used easily for pattern discovery) not easy to incorporate domain knowledge (easy in the form of priors on the data or distributions)

Neural Networks Analogy to Biological Systems (Indeed a great example of a good learning system) Massive Parallelism allowing for computational efficiency The first learning algorithm came in 1959 (Rosenblatt) who suggested that if a target output value is provided for a single neuron with fixed inputs, one can incrementally change weights to learn to produce these outputs using the perceptron learning rule

Neural Networks Advantages prediction accuracy is generally high robust, works when training examples contain errors output may be discrete, real-valued, or a vector of several discrete or real-valued attributes fast evaluation of the learned target function Criticism long training time difficult to understand the learned function (weights) not easy to incorporate domain knowledge

Network Topology Input variables number of inputs number of hidden layers # of nodes in each hidden layer # of output nodes can handle discrete or continuous variables normalisation for continuous to 0..1 interval for discrete variables use k inputs for each level use k output for each level if k>2 A has three distinct values a1,a2,a3 three input variables I1,I2I3 when A=a1 I1=1,I2,I3=0 feed-forward:no cycle to input untis fully connected:each unit to each in the forward layer

Multi-Layer Perceptron Output vector Output nodes Hidden nodes wij Input nodes Input vector: xi

Variabe Encodings Continuous variables Ex: Dollar amounts Averages: averages sales,volume Ratio income-debt,payment to laoan Physical measures: area, temperature... Transfer between 0-1 or 0.1 – 0.9 -1.0 - +1.0 or -0.9 – 0.9 z scores z = x – mean_x/standard_dev_X

Continuous variables When a new observation comes it may be out of range What to do Plan for a larger range Reject out of range values Pag values lower then min to minrange higher then max to maxrange E.g.: new observation transformed value 1.2 Make it 1 1.2 to 1

Ordinal variables Discrete integers Ex: Age ranges : young mid old İncome : low,mid,high Number of children Transfer to 0-1 interval Ex: 5 categories of age 1 young,2 mid young,3 mid, 4 mid old 5 old Transfer between 0 to 1

Thermometer coding 0  0 0 0 0 0/16 = 0 1  1 0 0 0 8/16 = 0.5 2 1 1 0 0 12/16 = 0.75 3 1 1 1 0 14/16 =0.875 Useful for academic grades or bond ratings Difference on one side of the scale is more important then on the other side of the scale

Nominal Variables Ex: Gender marital status,occupation 1- treat like ordinary variables Ex marital status 5 codes: Single,divorced,maried,widowed,unknown Mapped to -1,-0.5,0,0.5,1 Network treat them ordinal Even though order does not make sence

2- break into flags One variable for each category 1 of N coding Gender has three values Male female unknown Male 1 -1 -1 or 1 0 0 Female -1 1 -1 0 1 0 Unknown -1 -1 1 0 0 1

1 of N-1 coding Male 1 -1 or 1 0 Female -1 1 0 1 Unknown -1 -1 0 0 3 replace the varible with an numerical one

Time Series variables Stock market prediction Output IMKB100 at t Inputs: IMKB100 at t-1, at t-2, at t-3... Dollar at t-1, t-2,t-3.. İnterest rate at t-1,t-2,t-3 Day of week variables Ordinal Monday 1 0 0 0 0 ,...,Friday 0 0 0 0 1 Nominal Monday to Friday map from -1 to 1 or 0 to 1

A Neuron mk - f weighted sum Input vector x output y Activation function weight vector w å w0 w1 wn x0 x1 xn The n-dimensional input vector x is mapped into variable y by means of the scalar product and a nonlinear function mapping

- f A Neuron mk å weighted sum Input vector x output y Activation function weight vector w å w0 w1 wn x0 x1 xn

Network Training The ultimate objective of training obtain a set of weights that makes almost all the tuples in the training data classified correctly Steps Initialize weights with random values repeat until classification error is lower then a threshold (epoch) Feed the input tuples into the network one by one For each unit Compute the net input to the unit as a linear combination of all the inputs to the unit Compute the output value using the activation function Compute the error Update the weights and the bias

Example: Stock market prediction input variables: individual stock prices at t-1, t-2,t-3,... stock index at t-1, t-2, t-3, inflation rate, interest rate, exchange rates $ output variable: predicted stock price next time train the network with known cases adjust weights experiment with different topologies test the network use the tested network for predicting unknown stock prices

Other business Applications (1) Marketing and sales Prediction Sales forecasting Price elasticity forecasting Customer responce Classification Target marketing Customer satisfaction Loyalty and retention Clustering segmentation

Other business Applications (1) Risk Management Credit scoring Financial health Clasification Bankruptcy clasification Fraud detection Clustering Risk assesment

Other business Applications (1) Finance Prediction Hedging Future prediction Forex stock prediction Clasification Stock trend clasification Bond rating Clustering Economic rating Mutual fond selection

Perceptrons Mitchell 97 Sec 4.4, WK 91 sec 4.2 N inputs Ii i:1..N single output O two classes C0 and C1 denoted by 0 and 1 one node output: O=1 if w1I1+ w2I2+...+wnIn+w0>0 O=0 if w1I1+ w2I2+...+wnIn+w0<0 sometimes  is used for constant term for w0 called bias or treshold in ANN

Artificial Neural Nets: Perseptron x0=+1 x1 w1 w0 x2 g w2 y wd xd

Perceptron training procedure(rule) (1) Find w weights to separate each training sample correctly Initial weights randomly chosen weight updating samples are presented in sequence after presenting each case weights are updated: wi(t+1) = wi(t)+ wi(t) i(t+1) = i(t)+ i(t) wi(t) = (T -O)Ii i(t) = (T -O) O: output of perceptron,T true output for each case,  learning rate 0<<1 usually around 0.1

Perceptron training procedure (rule) (2) each case is presented and weights are updated after presenting each case if the error is not zero then present all cases ones each such cycle is called an epoch unit error is zero for perfectly separable samples

Perceptron convergence theorem: if the sample is linearly separable the perceptron will eventually converge: separate all the sample correctly error =0 the learning rate can be even one This slows down the convergence to increase stability it is gradually decreased linearly separable: a line or hyperplane can separate all the sample correctly

If classes are not perfectly linearly separable if a plane or line can not separate classes completely The procedure will not converge and will keep on cycling through the data forever

o o o o o o o o x o o o x o x o o x x x o x x x x x x o linearly separable not linearly separable

Example calculations O = 0.25*1.5+0.5*0.5-0.5=0.125>0 O=1 Two weights w1=0.25 w2=0.5 w0 or =-0.5 Inputs are :I1= 1.5 I2 =0.5 and T = 0 true output learning rate=0.1 perceptron separate this as: O = 0.25*1.5+0.5*0.5-0.5=0.125>0 O=1 O is not equal to true output T weight update required w1(t+1) = 0.25+0.1(0-1)1.5=0.1 w2(t+1) = 0.5+ 0.1(0-1)0.5 =0.45 (t+1) = -0.5+ 0.1(0-1)=-0.6 with the new weights: O = 0.1*1.5+0.45*0.5-0.6=-0.225 O =0 no error

Above ihe ine is class 1 Below the line is class 0 I2 0.25*I1+0.5*I2-0.5=0 1 true class is 0 but classified as class 1 o class 1 0.5 I1 2 1.5 class 0 I2 0.1*I1+0.45*I2-0.6=0 1.33 true class is 0 and classified as class 0 class 1 0.5 o class 0 6 I1

Least mean square or delta rule Output is just a linear function of inputs O = w1I1+ w2I2+...+wnIn+w0 T=0 or 1 again but O is a real number Minimize error E=(1/2)(T-O)2 least mean square error reduces the distance between output and the true answer Example

If there are two inputs the error surface has a global minimum see figure 4.4 in Mitchell 97 Start from an initial random weights the algorithm find the direction so that error is decreased most direction is negative of gradient gradient is the direction with steepest increase in error or wi=-(dE/dwi)=d(Td-Od)Ii,dSee table 4.1 in Mitchell 97

Note about gradient y=f(x1,x2....,xn) x1,..xn variables or inputs y output grad f = a vector of partial derivatives (dy/dx1, dy/dx2,..., dy/dxn) indicates the direction the function’s increases most

w2 global minimum x initial point o w1

proof of gradient decent (delta) rule wi=-(dE/dwi) but Od = ni=0wiIi,d where I0,d=1 dE/dwi=d/dwi[(1/2)d(Td-Od)2] apply chain rule = (1/2)d{2(Td-Od)*d/dwi[(Td-Od)]} = d{(Td-Od)*d/dwi[(Td-ni=0wiIi,d)]} but d/dwi[(Td-ni=0wiIi,d)]= -Ii,d so dE/dwi=d(Td-Od)(-Ii,d) hence wi=-(dE/dwi)=d(Td-Od)Ii,d

Stochastic gradient decent or Incremental gradient decent Update weights incrementally,after presenting each sample wi(t) = (T -O)Ii i(t) = (T -O) delta rule or LMS rule for all training samples new weights are wi(t+1) = wi(t)+ wi(t) i(t+1) = i(t)+ i(t) same as the perceptron training rule an approximation to the gradient decent learning rate small converge but slow high unstable but fast

Example Delta rule In the previous example weights w1=0.25 w2=0.5 w0 or =-0.5 İnputs are I1= 1.5 I2 =0.5 and T = 0 true output learning rate=0.1 perceptron separa this as: O = 0.25*1.5+0.5*0.5-0.5=0.125>0 O=0 closer to 0 Weigth update is necessary w1(t+1) = 0.25+0.1(0-.125)1.5=0.23 w2(t+1) = 0.5+ 0.1(0-.125)0.5 =0.49 (t+1) = -0.5+ 0.1(0-.125)=-0.51 with the new weights: O = 0.23*1.5+0.49*0.5-0.51=0.08

XOR: exclusive OR problem Two inputs I1 I2 when both agree I1=0 and I2=0 or I1=1 and I2=1 class 0, O=0 when both disagree I1=0 and I2=1 or I1=1 and I2=0 class 1, O=1 one line can not solve XOR but two ilnes can

I2 class 0 1 class 1 I1 1 a single line can not separate these classes

Multi-layer networks Study section 4.5(4.5.3 excluded) Mitchell and 4.3 In WK One layer networks can separate a hyperplane two layer networks can any convex region and three layer networks can separate any non convex boundary Examples see notes

ANN for classification x0=+1 oK xd x2 x1 o2 o1 wKd

inside the triangle ABC is class O outside the triangle is class + class =0 if I1+I2>=10 I1<=I2 I2<=10 C B o o o o o o + o + +1 o +1 + A + + + a + + + I1 I1 d b output of hidden node a: 1 if class O w11I1+w12I2+w10>=0 0 if class is + w11I1+w12I2+w10<0 I2 c so w1i s are W11=1,w12=1 and w10=-10

I2 C B +1 +1 A a I1 I1 d b I2 c output of hidden node b: 1 if that is O w21I1+w22I2+w20>=0 0 if that is + w21I1+w22I2+w20<0 so w2i s are W21=-1,w22=1 and w10=-0 I2 + + C + B o o o o o o + o + +1 o +1 + A + + + a + + + I1 I1 d b output of hidden node c: 1 if w31I1+w32I2+w30>=0 0 if w11I1+w12I2+w10<=0 I2 c so w1i s are W31=0,w32=-1 and w10=10

an object is class O if all hidden units predict is as class 0 output is 1 if w’aHa+w’bHb+w’cHc+wd>=0 output is 0 if w’aHa+w’bHb+w’cHc+wd<0 I2 + + C + B o o o o o o + o + +1 o +1 + A + + + a + + + I1 I1 d b weights of output node d: wa=1,wb=1wc=1 wd=-3+x where x a small number I2 c

ADBC is the union of two convex regions in this case triangles each triangular region can be separated by a two layer network I2 + + C + B +1 o o o +1 o o o o o + o + o a o + A + o w’’f0 + + + + + I1 I1 D b w’’f1 d d separates ABC e separates ADB ADBC is union of ABC and ADB f I2 c w’’f2 e output is class O if w’’f0+w’’f1He+w’’f2Hf>=0 w’’f0=--0.99,w’’f=1,w’’f2=1 first hidden layer second hidden layer

In practice boundaries are not known but increasing number of hidden node: two layer perceptron can separate any convex region if it is perfectly separable adding a second hidden layer and or ing the convex regions any nonconvex boundary can be separated Weights are unknown but are found by training the network

Network Training The ultimate objective of training obtain a set of weights that makes almost all the tuples in the training data classified correctly Steps Initialize weights with random values Feed the input tuples into the network one by one For each unit Compute the net input to the unit as a linear combination of all the inputs to the unit Compute the output value using the activation function Compute the error Update the weights and the bias

Multi-Layer Perceptron Output vector Output nodes Hidden nodes wij Input nodes Input vector: xi

Back propagation algorithm LMS uses a linear activation function not so useful threshold activation function is very good in separating but not differentiable back propagation uses logistic function O = 1/(1+exp(-N))=(1+exp(-N))-1 N: net input to a node = w1I1+w2I2+... wNIN+ the derivative of logistic function dO/dN = -(1+exp(-N))-2(-exp(-N)) (1+exp(-N))-2(1-1+exp(-N))=O(1-O) dO/dN = O*(1-O) expressed as a function of output where O =1/(1+exp(-N)), 0<=O<=1

Minimize total error again E= (1/2)Nd=1Mk=1(Tk,d-Ok,d)2 where N is number of cases M number of output units Tk,d:true value of sample d in output unit k Ok,d:predicted value of sample d in output unit k the algorithm updates weights by a similar method to the delta rule for each output units wij=-(dE/dwi)=d=1 Od(1- Od)(Td-Od)Ii,d or wij(t) = O(1-O)(T -O)Ii | when objects are ij(t) = O(1-O)(T -O) | presented sequentially here O(1-O)(T -O)= is the error term

so wij(t)= *errorj*Ii or ij(t)= *errorj for all training samples new weights are wi(t+1) = wi(t)+ wi(t) i(t+1) = i(t)+ i(t) but for hidden layer weights no target value is available wij(t) = Od(1- Od) (Mk=1errork*wkh)Ii ij(t) = Od(1- Od)(Mk=1errork*wkh) the error rate of each output is weighted by its weight and summed up to find the error derivative The weights from hidden unit h to output unit k is responsible for the error in output unit k

Example: Sample iterations A network suggested to solve the XOR problem figure 4.7 of WK page 96-99 learning rate is 1 for simplicity I1=I2=1 T =0 true output

1 0.1 3 O3:0.65 I1:1 0.5 O5:0.63 0.3 5 -0.2 -0.4 2 I2:1 4 0.4 O4:0.48

Exercise Carry out one more iteration for the XOR problem

Practical Applications of BP Revision by epoch or case dE/dwj = Ni=1Oi(1-Oi)(Ti-Oi)Iij where i= 1,..,N index for samples N sample size j: index for inputs Iij input variable j for sample i This is the theoretical and actual derivtives information in all samples are used in one update of the weight j weights are revised after each epoch

If samples are presented one by one weight j is updated after presenting each sample by dE/dwj = Oi(1-Oi)(Ti-Oi)Iij this is just one term in the epoch update or gradient formula of derivative called case update updating by case is more common and give better results less likely to stack to local minima Random or sequential presentation in each epoch case are presented in sequential order or in random order

sequential presentation 1 2 3 3 5.. 1 2 3 4 5..1 2 3 4 5.. 1 2 3 4 5.. epoch 1 epoch 2 epoch 3 random presentation 1 2 5 4 3.. 3 2 1 4 5..5 1 4 2 3.. 2 5 4 1 3.. epoch 1 epoch 2 epoch 3

Neural Networks Random initial state weights and biases are initialized to random values usually between -0.5 to 0.5 the final solution may depend on the initial values of weights the algorithm may converge to different local minima Learning rate and local minima learning rate  too small: slow convergence too large: much fast but osilations With a small learning rate local minimum is less likely

Momentum Momentum is added to the update equations wij(t+1) = *errorderivativej*Ii+ mon*wij(t) ij(t+1) = *errorderivativej+ mom*ij(t) momentum term slows down the change of direction avoids falling into a local minima or speed up convergence by increasing the gradient by adding a value to it when it falls into flat regions

Stoping criteria Limit the number of epochs improvement in error is so small sample error after a fixed number of epochs measure the reduction in error no change in w values above a threshold

Overfitting Sec 4.6.5 pp 108-112 Mitchell E monotonically decreases as number of iterations increases Fig 4.9 in Mitchell Validation or test case error in general decreases first then start increasing Why as training progress some weights values are high fit noise in training data not representative features of the population

What to do Weight decay slowly decrease weights put a penalty to error function for high weights Monitoring the validation set error as well as the training set error as a function of iterations see figure 4.9 in Mitchell

Error and Complexity Sec 4.4 of WK pp 102-107 error rate on the training set decreases as number of hidden units is increased error rate on test set first decreases flatten out then start increasing as number of hidden layers is increased Start with zero hidden units increase gradually the number of units in hidden layer at each network size 10 fold cross validation or sampling the different initial weights may be used to estimate error. error may be averaged

A General Network Training Procedure Define the problem Select input and output variables Make necessary transformations Decide on algorithm gradient decent or stochastic approximation (delta rule) Choose the transfer function logistic, hyperbolic tangent Select a learning rate a momentum after experimenting with possibly different rates

A General Network Training Procedure cnt Determine the stopping criteria after error decreases by to a level or number of epochs Start from zero hidden units increment number of hidden units for each number of hidden units repeat train the network on training data set perform cross validation to estimate test error rate by averaging on different test samples for a set of initial weights find best initial weights

Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by Neural Networks Classification by Support Vector Machines (SVM) Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

Other Classification Methods k-nearest neighbor classifier case-based reasoning Genetic algorithm Rough set approach Fuzzy set approaches

Instance-Based Methods Instance-based learning: Store training examples and delay the processing (“lazy evaluation”) until a new instance must be classified Typical approaches k-nearest neighbor approach Instances represented as points in a Euclidean space. Locally weighted regression Constructs local approximation Case-based reasoning Uses symbolic representations and knowledge-based inference

The k-Nearest Neighbor Algorithm All instances correspond to points in the n-D space. The nearest neighbor are defined in terms of Euclidean distance. The target function could be discrete- or real- valued. For discrete-valued, the k-NN returns the most common value among the k training examples nearest to xq. Vonoroi diagram: the decision surface induced by 1-NN for a typical set of training examples. . _ _ . _ _ + . . + . _ xq + . _ +

V: v1,...vn fp(xq) = argmaxvVki=1(v,f(xi)) (a,b) =1 if a=b otherwise 0 for real valued target functions fp(xq) = ki=1f(xi)/k

Discussion on the k-NN Algorithm The k-NN algorithm for continuous-valued target functions Calculate the mean values of the k nearest neighbors Distance-weighted nearest neighbor algorithm Weight the contribution of each of the k neighbors according to their distance to the query point xq giving greater weight to closer neighbors Similarly, for real-valued target functions Robust to noisy data by averaging k-nearest neighbors Curse of dimensionality: distance between neighbors could be dominated by irrelevant attributes. To overcome it, axes stretch or elimination of the least relevant attributes.

Robust to noisy data by averaging k-nearest neighbors Curse of dimensionality: distance between neighbors could be dominated by irrelevant attributes. To overcome it, axes stretch or elimination of the least relevant attributes. stretch each variable with a different factor experiment on the best stretching factor by cross validation zi =kxi irrelevant variables has small k values k=0 completely eliminates the variable

Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by Neural Networks Classification by Support Vector Machines (SVM) Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

Classification Accuracy: Estimating Error Rates Partition: Training-and-testing use two independent data sets, e.g., training set (2/3), test set(1/3) (holdout method) used for data set with large number of samples Cross-validation divide the data set into k subsamples use k-1 subsamples as training data and one sub-sample as test data—k-fold cross-validation for data set with moderate size Bootstrapping (leave-one-out) for small size data

cross-validation divide the data set into k subsamples S1,S2,..Sk use k-1 subsamples as training data and one sub-sample as test data --- k-fold cross-validation for data set with moderate size stratified cross validation folds are stratified so that the class distribution in each fold approximately the same as in the initial data 10-fold stratified cross validation is most common

leave-one-out for small size data k = S sample size in cross validation one sample is used for testing S-1 for training repeat for each sample

Bootstrapping sampling with replacement to form a training set a date set of N instances is samples N times with replacement some elements in the new data set are repeated test instances: not picked in the new data set but in the original data set 0.632 Bootstrap out of n cases with 1-1/n probability an object is not selected at each drawing after n drawings probability of not selecting a case is (1-1/n)n =e-1=0.368 so %36.8 of the objects are not in the training sample or they constitute the test data error = 0.632*etest + 0.368*etrainingg The whole bootstrap is repeated several times and error rate is averaged

Bagging and Boosting General idea Training data …….. Aggregation …. Altered Training data …….. Aggregation …. Classification method (CM) Classifier C CM Classifier C1 CM Classifier C2 Classifier C*

Bagging Given a set S of s samples Generate a bootstrap sample T from S. Cases in S may not appear in T or may appear more than once. Repeat this sampling procedure, getting a sequence of k independent training sets A corresponding sequence of classifiers C1,C2,…,Ck is constructed for each of these training sets, by using the same classification algorithm To classify an unknown sample X,let each classifier predict or vote The Bagged Classifier C* counts the votes and assigns X to the class with the “most” votes

Increasing classifier accuracy-Bagging WF pp 250-253 take t samples from data S sampling with replacement each case may occur more than ones a new classifier Ct is learned for each set St Form the bagged classifier C* by voting classifiers equally the majority rule For continuous valued prediction problems take the average of each predictor

Increasing classifier accuracy-Boosting WF pp 254-258 Boosting increases classification accuracy Applicable to decision trees or Bayesian classifier Learn a series of classifiers, where each classifier in the series pays more attention to the examples misclassified by its predecessor Boosting requires only linear time and constant space

Boosting Technique — Algorithm Assign every example an equal weight 1/N For t = 1, 2, …, T Do Obtain a hypothesis (classifier) h(t) under w(t) Calculate the error of h(t) and re-weight the examples based on the error . Each classifier is dependent on the previous ones. Samples that are incorrectly predicted are weighted more heavily Normalize w(t+1) to sum to 1 (weights assigned to different classifiers sum to 1) Output a weighted sum of all the hypothesis, with each hypothesis weighted according to its accuracy on the training set

Boosting Technique (II) — Algorithm Assign every example an equal weight 1/N For t = 1, 2, …, T Do Obtain a hypothesis (classifier) h(t) under w(t) Calculate the error of h(t) and re-weight the examples based on the error decrease the weights of correctly classified cases weights(t+1) = weightst*e/1-e e:current classifiers overall error for correctly classified cases weights for incorrectly classified cases are unchanged Normalize w(t+1) to sum to 1 when error > 0.5 delete current classifier and stop or e=0 stop Output a weighted sum of all the hypothesis, with each hypothesis weighted according to its accuracy on the training set weight = -log(e/1-e)

Bagging and Boosting Experiments with a new boosting algorithm, freund et al (AdaBoost ) Bagging Predictors, Brieman Boosting Naïve Bayesian Learning on large subset of MEDLINE, W. Wilbur

Is accuracy enough to judge a classifier? Speed robustness (accuracy on noisy data) scalability number of I/O opp. For large datasets interpretability subjective objective: number of hidden units for ANN number of tree notes for decision trees

Alternatives to accuracy measure Ex: cancer or not_cancer cancer samples are positive not_cancer samples are negative sensitivity = t_pos/pos specificity = t_neg/neg precision = t_pos/(t_pos+f_pos) t_pos:#true positives cancer samples that were correctly classified as such

pos:# positive (cancer samples) t_neg:#true negatives not cancer samples that were correctly classified as such neg:# negative (not_cancer samples) f_pos:# false positives (not_cancer samples that were incorrectly labelled as cancer) accuracy = f(sensitivity,specificity) accuracy = sensitivity*pos/(pos+neg)+ specificity*neg/(pos+neg)

actual pos negative pos t_pos f_pos predicted f_neg t_neg neg

Evaluating numeric prediction Same strategies: independent test set, cross-validation, significance tests, etc. Difference: error measures Actual target values: a1 a2 …an Predicted target values: p1 p2 … pn Most popular measure: mean-squared error Easy to manipulate mathematically

Other measures The root mean-squared error : The mean absolute error is less sensitive to outliers than the mean-squared error: Sometimes relative error values are more appropriate (e.g. 10% for an error of 50 when predicting 500)

Lift charts In practice, costs are rarely known Decisions are usually made by comparing possible scenarios Example: promotional mailout to 1,000,000 households Mail to all; 0.1% respond (1000) Data mining tool identifies subset of 100,000 most promising, 0.4% of these respond (400) 40% of responses for 10% of cost may pay off Identify subset of 400,000 most promising, 0.2% respond (800) A lift chart allows a visual comparison

Generating a lift chart Sort instances according to predicted probability of being positive: x axis is sample size y axis is number of true positives Predicted probability Actual class 1 0.95 Yes 2 0.93 3 No 4 0.88 …

A hypothetical lift chart 40% of responses for 10% of cost 80% of responses for 40% of cost

Chapter 7. Classification and Prediction What is classification? What is prediction? Issues regarding classification and prediction Classification by decision tree induction Bayesian Classification Classification by Neural Networks Classification by Support Vector Machines (SVM) Classification based on concepts from association rule mining Other Classification Methods Prediction Classification accuracy Summary

Summary Classification is an extensively studied problem (mainly in statistics, machine learning & neural networks) Classification is probably one of the most widely used data mining techniques with a lot of extensions Scalability is still an important issue for database applications: thus combining classification with database techniques should be a promising topic Research directions: classification of non-relational data, e.g., text, spatial, multimedia, etc..

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