Data Mining


Question 1

Consider the XOR substance where there are immodest trailing points: (1, 1, −),(1, 0, +),(0, 1, +),(0, 0, −). Transform the facts into the subjoined characteristic measure:

 Φ = (1, √ 2x1, √ 2x2, √ 2x1x2, x2 1, x2 2).

Find the ultimatum stipulation direct judgment stipulation in the transformed measure.

Question 2

Consider the subjoined set of applicant 3-itemsets: {1, 2, 3}, {1, 2, 6}, {1, 3, 4}, {2, 3, 4}, {2, 4, 5}, {3, 4, 6}, {4, 5, 6}

Construct a hash tree for the over applicant 3-itemsets. Assume the tree uses a hash discharge where all odd-numbered aces are hashed to the left offshoot of a node, timeliness the even-numbered aces are hashed to the straight offshoot. A applicant k-itemset is inserted into the tree by hashing on each successive ace in the applicant and then subjoined the after a whilehold scion of the tree according to the hash appreciate. Once a leaf node is reached, the applicant is inserted domiciled on one of the subjoined conditions:

Condition 1: If the profoundness of the leaf node is correspondent to k (the source is conducive to be at profoundness 0), then the applicant is inserted unmindful of the calculate of acesets already stored at the node.

Condition 2: If the profoundness of the leaf node is short than k, then the applicant can be inserted as hanker as the calculate of acesets stored at the node is short than maxsize. Assume maxsize = 2 for this topic.

Condition 3: If the profoundness of the leaf node is short than k and the calculate of acesets stored at the node is correspondent to maxsize, then the leaf node is converted into an inner node. New leaf nodes are created as offshootren of the old leaf node. Applicant acesets previously stored in the old leaf node are reserved to the offshootren domiciled on their hash appreciates. The new applicant is besides hashed to its after a whilehold leaf node.

How multifarious leaf nodes are there in the applicant hash tree? How multifarious inner nodes are there?

Consider a proceeding that contains the subjoined aces: {1, 2, 3, 5, 6}. Using the hash tree contrived in keep-akeep-apart (a), which leaf nodes get be checked over the proceeding? What are the applicant 3-itemsets contained in the proceeding?

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