By Evangelos Triantaphyllou

The significance of getting ef cient and potent tools for info mining and kn- ledge discovery (DM&KD), to which the current publication is dedicated, grows on a daily basis and diverse such tools were constructed in fresh many years. There exists a superb number of various settings for the most challenge studied by way of facts mining and information discovery, and it sounds as if a really renowned one is formulated when it comes to binary attributes. during this environment, states of nature of the applying zone into account are defined via Boolean vectors de ned on a few attributes. that's, via facts issues de ned within the Boolean area of the attributes. it truly is postulated that there exists a partition of this house into sessions, which will be inferred as styles at the attributes whilst in simple terms numerous facts issues are identified, the so-called confident and unfavourable education examples. the most challenge in DM&KD is de ned as nding ideas for spotting (cl- sifying) new information issues of unknown category, i. e. , figuring out which ones are confident and that are destructive. In different phrases, to deduce the binary price of 1 extra characteristic, referred to as the target or category characteristic. to unravel this challenge, a few equipment were recommended which build a Boolean functionality isolating the 2 given units of confident and damaging education information issues.

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Extra resources for Data Mining and Knowledge Discovery via Logic-Based Methods: Theory, Algorithms, and Applications

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1 Comparison of Sample and Class Sizes for Biopsy and Cancer (from Woman’s Hospital in Baton Rouge, Louisiana, Unpublished Data, 1995). . . . . . . . . . . . . . . . . . . . . . . . 5 History of Monotone Boolean Function Enumeration. . . . . . . A Sample Data Set for Problem 3. . . . . . . . . . . . . . . Example Likelihood Values for All Functions in M3 . . . . . . . Updated Likelihood Ratios for m z (001) = m z (001) + 1.

1a Attributes for the Breast Cancer Data Set from Woman’s Hospital in Baton Rouge, LA (Part (a); Attributes 1 to 16). . . . . . . . . 1b Attributes for the Breast Cancer Data Set from Woman’s Hospital in Baton Rouge, LA (Part (b); Attributes 17 to 26). . . . . . . . 2a Interpretation of the Breast Cancer Diagnostic Classes (Part (a); Malignant Classes Only). . . . . . . . . . . . . . . . . . . 2b Interpretation of the Breast Cancer Diagnostic Classes (Part (b); Benign Classes Only).

In the general case this number is too high. Apparently, even for a small value of n, this task may be practically impossible to realize. Fortunately, many real-life applications are governed by the behavior of a monotone system or they can be described by a combination of a small number of monotone systems. In data mining the property of monotonicity offers some unique computational advantages. By knowing the value of certain examples, one can easily infer the values of more examples. This, in turn, can significantly expedite the learning process.

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