Knowledge Discovery and Data Mining 1 (VO) ( )
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1 Knowledge Discovery and Data Mining 1 (VO) ( ) Sample Examination Questions Denis Helic KTI, TU Graz Jan 16, 2014 Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
2 Exercise Suppose we have a utility matrix of a movie recommender system. This matrix keeps the user ratings for various movies. In our movies database we have only movies of two genres: science fiction and romance. The utility matrix: User Movie Matrix Alien Star Wars Casablanca Titanic Joe Jim John Jack Jill Jenny Jane Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
3 Exercise For the purposes of recommending movies to new users we decompose the utility matrix using SVD decomposition. Thus, we map the users and movies into the concept space spawned by two movie genres: science fiction and romance. The SVD decomposition is given by: = ( ) ( ) Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
4 Exercise 1 What are these four matrices? 2 How do we interpret them? 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? 4 Which other movies should we recommend to Quincy? 5 What about Leslie who rated Alien with 3 and Titanic with 4 stars. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
5 1 What are these four matrices? The matrices are: the utility matrix M U is a matrix of eigenvectors of MM T V is a matrix of eigenvectors of M T M Σ is the matrix of the square roots of eigenvalues (singular values) of MM T or M T M. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
6 2 How do we interpret them? Interpretation: M connects users to movies U connects users to concepts (genres) V connects movies to concepts Σ gives importance of concepts Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
7 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? First we need to represent Quincy in the utility matrix M. How can we do that? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
8 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? First we need to represent Quincy in the utility matrix M. How can we do that? Each row of M is a user. We represent Quincy with a row vector: q T = ( ) Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
9 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? Now we need to assess Quincy s interests in different genres. How can we do that? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
10 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? Now we need to assess Quincy s interests in different genres. How can we do that? We need to map Quincy into concept space. How? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
11 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? Now we need to assess Quincy s interests in different genres. How can we do that? We need to map Quincy into concept space. How? What does q T connect? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
12 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? Now we need to assess Quincy s interests in different genres. How can we do that? We need to map Quincy into concept space. How? What does q T connect? A user with movies What do we need? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
13 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? Now we need to assess Quincy s interests in different genres. How can we do that? We need to map Quincy into concept space. How? What does q T connect? A user with movies What do we need? The connection between the user and concepts Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
14 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? How to relate the user with concepts? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
15 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? How to relate the user with concepts? q T connects a user with movies, V connects movies to concepts q T V gives us connection between the user and concepts q T V =? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
16 3 Suppose we have a new user Quincy. Quincy has only seen Matrix and rated it 4. How are Quincy s interests in different movie genres? How to relate the user with concepts? q T connects a user with movies, V connects movies to concepts q T V gives us connection between the user and concepts q T V =? q T V = ( ) Quincy s interest in science fiction is 2.32 and he does not have interest in romance Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
17 4 Which other movies should we recommend to Quincy? Now we need to assess how Quincy would like other movies according to his interests. How we can do that? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
18 4 Which other movies should we recommend to Quincy? Now we need to assess how Quincy would like other movies according to his interests. How we can do that? We need again a relation between the user and movies, i.e. we need a row from the utility matrix M q T V relates the user with concepts V relates movies with concepts Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
19 4 Which other movies should we recommend to Quincy? How do we obtain the relation between users and movies? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
20 4 Which other movies should we recommend to Quincy? How do we obtain the relation between users and movies? q T VV T q T VV T = ( ) Quincy would like Alien and Star wars Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
21 5 What about Leslie who rated Alien with 3 and Titanic with 4 stars. We represent Leslie with a row vector: q T = ( ) Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
22 5 What about Leslie who rated Alien with 3 and Titanic with 4 stars. Leslie s interests in genres: q T V = ( ) Leslie s interest in science fiction is 1.74 and interest in romance is stronger: 2.84 Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
23 5 What about Leslie who rated Alien with 3 and Titanic with 4 stars. User-movie matrix q T VV T = ( ) Leslie would like Casablanca at most Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
24 Example 2 Exercise For evaluation of the quality of a classifier we use the contingency table. 1 Sketch this table and write down the names for the table cells. 2 Using the terms from the contingency table explain how we measure accuracy of a classifier. 3 Explain what happens with accuracy in the presence of a skewed class distribution? Do we need alternative measures? 4 Define the precision and recall. 5 Explain precision-recall trade-off and F1 measure. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
25 Example 2 1 Sketch this table and write down the names for the table cells. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
26 Example 2 1 Sketch this table and write down the names for the table cells. Prediction Real class c true positive (tp) false positive (fp) c c false negative (fn) true negative (tn) c c c Table: Contingency table Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
27 Example 2 2 Using the terms from the contingency table explain how we measure accuracy of a classifier. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
28 Example 2 2 Using the terms from the contingency table explain how we measure accuracy of a classifier. tp + tn A = tp + fp + fn + tn Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
29 Example 2 3 Explain what happens with accuracy in the presence of a skewed class distribution? Do we need alternative measures? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
30 Example 2 3 Explain what happens with accuracy in the presence of a skewed class distribution? Do we need alternative measures? We have one small and one huge class P(cancer) = P(cancer c ) = Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
31 Example 2 3 Explain what happens with accuracy in the presence of a skewed class distribution? Do we need alternative measures? Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
32 Example 2 3 Explain what happens with accuracy in the presence of a skewed class distribution? Do we need alternative measures? We always predict: cancer c : Prediction Real class c c c c 0 0 c c tp+tn A = tp+fp+fn+tn = = We need alternatives Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
33 Example 2 4 Define the precision and recall. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
34 Example 2 4 Define the precision and recall. Recall R = Precision P = tp tp+fn tp tp+fp Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
35 Example 2 5 Explain precision-recall trade-off and F1 measure. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
36 Example 2 5 Explain precision-recall trade-off and F1 measure Evaluation in information retrieval Precision Recall Figure 8.2 Precision/recall graph. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
37 Example 2 5 Explain precision-recall trade-off and F1 measure. Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
38 Example 2 5 Explain precision-recall trade-off and F1 measure. F 1 = 2PR P+R Denis Helic (KTI, TU Graz) KDDM1 Jan 16, / 22
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