HOMEWORK ABOUT DATA MİNİNG

Metrics (25 points) – NAME:____________________________(in uppercase) Metrics: Cosine, Correlation, Distance, Similarity, Normalization, Norm, etc NOTE: Provide your answer in pencil & paper on this file. Additionally, you are welcome to validate your answer with Python Code (if necessary). What does each of condition tell you? Please provide your answer concisely and accurately. (Q01) (Cosine) Two attributes have a cosine similarity of 1. (Q02) (Correlation) Two attributes have a Pearson’s correlation coefficient of 1. (Q03) (Jaccard) Two binary attributes have a jaccard similarity of 1. (Q04) (Distance) Two attributes have a (normalized) distance of 1. (Q05) (Similarity) Two attributes have a (normalized) similarity of 0. Let’s further explore cosine, correlation, and z-score with the following questions. (Q06) What is the range of values that are possible for the cosine measure? (Q07) What is the range of values that are possible for the Pearson’s correlation measure? (Q08) If two objects have a cosine measure of 1, are they identical? Explain. (Hint) What is the cosine of 𝑥 𝑇 = [3, 3] and 𝑦 𝑇 = [6, 6]? What do you infer from this result? (Q09) 𝑥 𝑇 = [2, 4] a. 1-norm normalization of vector x b. How do you interpret 1-norm normalization? c. What is the 1-norm of the 1-norm normalized vector after step a? d. 2-norm normalization of vector x e. How do you interpret 2-norm normalization? f. What is the 2-norm of the 2-norm normalized vector after step d? (Q10) 𝑥 𝑇 = [1, 2, 3, 4, 5] a. Mean-centering of vector x b. What is the characteristic of mean-centering? c. z-score transformation of vector x d. What is/are characteristic(s) of z-score transformation? (Q11) 𝑥 𝑇 = [0, 1, 0, 1, 1, 1] and 𝑦 𝑇 = [1, 0, 1, 0, 1, 0] a. Cosine similarity b. Euclidian distance c. Simple matching coefficient d. Simple matching distance e. Jaccard similarity coefficient (= Jaccard index) f. Jaccard distance g. Hamming distance (OPTIONAL) What is the relationship among cosine, correlation, & z-score, if any? (HINT) Referring to their definitions, please try to explain how you can make a connection among the measures. You are welcome to write your answer on an extra page.