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Download Combinatorial Machine Learning: A Rough Set Approach by Mikhail Moshkov, Beata Zielosko (auth.) PDF

Posted On March 3, 2017 at 6:47 pm by / Comments Off on Download Combinatorial Machine Learning: A Rough Set Approach by Mikhail Moshkov, Beata Zielosko (auth.) PDF

By Mikhail Moshkov, Beata Zielosko (auth.)

Decision timber and choice rule structures are commonplace in several applications

as algorithms for challenge fixing, as predictors, and as a fashion for

knowledge illustration. Reducts play key function within the challenge of attribute

(feature) choice. The goals of this ebook are (i) the honor of the sets

of choice timber, principles and reducts; (ii) examine of relationships between these

objects; (iii) layout of algorithms for building of bushes, ideas and reducts;

and (iv) acquiring bounds on their complexity. purposes for supervised

machine studying, discrete optimization, research of acyclic courses, fault

diagnosis, and development popularity are thought of additionally. it is a combination of

research monograph and lecture notes. It includes many unpublished results.

However, proofs are rigorously chosen to be comprehensible for students.

The effects thought of during this ebook should be worthy for researchers in machine

learning, info mining and information discovery, specially in the event you are

working in tough set conception, try out idea and logical research of information. The book

can be utilized in the production of classes for graduate students.

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Extra resources for Combinatorial Machine Learning: A Rough Set Approach

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Let T be a decision table with n columns labeled with attributes f1 , . . , fn. 1. If S is a complete system of decision rules for T then the set of attributes from rules in S is a test for T . 2. If F = {fi1 , . . , fim } is a test for T then there exists a complete system S of decision rules for T which uses only attributes from F and for which L(S) = m. Proof. 1. Let S be a complete system of decision rules for T , and r1 , r2 be two rows of T with different decisions. Then there exists a rule from S which is realizable for r1 and is not realizable for r2 .

N, the i-th row has 1 only at the intersection with the column fi . This row is labeled with the decision 1. The last (n + 1)-th row is filled by 0 only and is labeled with the decision 2. One can show that N (Tn ) = n + 1 and R(Tn ) = n. 14 is unimprovable in the general case. 16. Let T be the table depicted in Fig. 1. 3) that R(T ) = 2. 14 gives us the upper bound R(T ) ≤ 4. Now, we consider an upper bound on the value h(T ). It will be also an upper bound on the value L(T ). Let our decision table T have a column fi in which the number of 0 is equal to the number of 1.

We can find efficiently sets of upper zeros for these functions (it can be useful for design of lazy learning algorithms). However, there are no polynomial algorithms for construction of the set of lower units for characteristic functions (in the case of tests, lower units correspond to reducts, and in the case of rules—to irreducible decision rules). We can compare efficiently sets of decision trees for decision tables with the same names of attributes. We studied relationships among decision trees, rules and tests which allow us to work effectively with bounds on complexity and algorithms for construction of rules, tests and trees.

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