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Christoph F. Eick Questions and Topics Review Nov. 22, 2011 1.Assume you have to do feature selection for a classification task. What are the characteristics of features (attributes) you might remove from the dataset prior to learning the classification algorithm? 2.How is region discovery in spatial datasets different from traditional clustering? 3.What are the unique characteristics of hierarchical clustering? 4.Compute the Silhouette of the following clustering that consists of 2 clusters: {(0,0), (0,1), (2,2)} {(3,2), (3,3)}. To be discussed in review on Dec. 1! Silhouette: For an individual point, i –Calculate a = average distance of i to the points in its cluster –Calculate b = min (average distance of i to points in another cluster) –The silhouette coefficient for a point is then given by: s = (b-a)/max(a,b) 5.Compare Decision Trees, Support Vector Machines, and K-NN with respect to the number of decision boundary each approach uses! 6.K-NN is a lazy approach; what does it mean? What are the disadvantages of K-NN’s lazy approach? Do you see any advantages in using K-NN’s lazy approach? 7.Why do some support vector machine approaches map examples from a lower dimensional space to a higher dimensional space? 8.What is the role of slack variables in the Linear/SVM/Non-separable approach (textbook pages 266-270)—what do they measure? What properties of hyperplanes are maximized by the objective function f(w) (on page 268) in the approach?

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Christoph F. Eick Support Vector Machines What if the problem is not linearly separable? Square hyperplane Circle hyperplane

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Tan, Steinbach, Kumar, Eick: NN-Classifiers and Support Vector Machines Linear SVM for Non-linearly Separable Problems What if the problem is not linearly separable? –Introduce slack variables Need to minimize: Subject to (i=1,..,N): C is chosen using a validation set trying to keep the margins wide while keeping the training error low. Measures error Inverse size of margin between hyperplanes Parameter Slack variable allows constraint violation to a certain degree

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Christoph F. Eick Answers Review Nov. 22, 2011 1.Assume you have to do feature selection for a classification task. What are the characteristics of features (attributes) you might remove from the dataset prior to learning the classification algorithm? Redundant attributes; irrelevant attributes 2.How is region discovery in spatial datasets different from traditional clustering? Clustering is performed in the subspace of spatial attributes; e.g. clusters are contiguous in the space of the spatial attributes; separation between spatial and non-spatial attributes---non- spatial attributes are on used by objective functions/cluster evaluation measures. 3.What are the unique characteristics of hierarchical clustering? Computes a dendrogram and multiple clusterings; a dendrogram captures hierarchical relationships between clusters; HC relies on agglomerative/divisive approaches to compute clusters based on an union operator: C=C1 C2 4.… 5.Compare Decision Trees, Support Vector Machines, and K-NN with respect to the number of decision boundary each approach uses! DT: many, rectangular for numerical attributes K-NN: many, convex polygons (Voronoi cells), SVM: one, a single hyperplane 7.Why do some support vector machine approaches map examples from a lower dimensional space to a higher dimensional space? To make them linearly separable.

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Christoph F. Eick Answers2 Review Nov. 22, 2011 6. K-NN is a lazy approach; what does it mean? What are the disadvantages of K-NN’s lazy approach? Do you see any advantages in using K-NN’s lazy approach. Lazy: postpones “learning a model” disadvantages: slow as the model is “obtained” when classifying an object and not beforehand…; (other disadvantage (not asked for here)): there is no explicit model and therefore no way to show it to a domain expert which makes it difficult to establish trust into the learnt model. Advantage of “being lazy”: for quickly changing streaming data learning the model might be a waste of time as the model changes quickly over time and a lazy approach might be better… 8. What is the role of slack variables in the Linear/SVM/Non-separable approach (textbook pages 266-270)—what do they measure? What properties of hyperplanes are maximized by the objective function f(w) (on page 268) in the approach? The slack variables i measure the distance of an object i to the object’s class hyperplane if it is on the wrong side of the object’s class hyperplane, and 0 if the example is on the correct side of the hyperplane. i measures the error associated with the i’s example. Soft Margin SVM solve a 2-objective optimization problem, trying to minimize the errors associated with the examples ( i ) while keeping the margins as wide as possible (minimizing ||w||)—the parameter C determines how much emphasis is put on each of the two objectives.

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