Data Mining Methods and Models

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xvi PREFACE express my eternal gratitude to my dear wife, Debra J. Larose, for her patience and love and “for everlasting bond of fellowship.” Live hand in hand, and together we’ll stand, on the threshold of a dream. . . . —The Moody Blues Daniel T. Larose, Ph.D. Director, Data Mining@CCSU www.math.ccsu.edu/larose
CHAPTER1 DIMENSION REDUCTION METHODS NEED FOR DIMENSION REDUCTION IN DATA MINING PRINCIPAL COMPONENTS ANALYSIS FACTOR ANALYSIS USER-DEFINED COMPOSITES NEED FOR DIMENSION REDUCTION IN DATA MINING The databases typically used in data mining may have millions of records and thousands of variables. It is unlikely that all of the variables are independent, with no correlation structure among them. As mentioned in Discovering Knowledge in Data: An Introduction to Data Mining [1], data analysts need to guard against multicollinearity, a condition where some of the predictor variables are correlated with each other. Multicollinearity leads to instability in the solution space, leading to possible incoherent results, such as in multiple regression, where a multicollinear set of predictors can result in a regression that is significant overall, even when none of the individual variables are significant. Even if such instability is avoided, inclusion of variables that are highly correlated tends to overemphasize a particular component of the model, since the component is essentially being double counted. Bellman [2] noted that the sample size needed to fit a multivariate function grows exponentially with the number of variables. In other words, higher-dimension spaces are inherently sparse. For example, the empirical rule tells us that in one dimension, about 68% of normally distributed variates lie between 1 and −1, whereas for a 10-dimensional multivariate normal distribution, only 0.02% of the data lie within the analogous hypersphere. The use of too many predictor variables to model a relationship with a response variable can unnecessarily complicate the interpretation of the analysis and violates the principle of parsimony: that one should consider keeping the number of predictors Data Mining Methods and Models By Daniel T. Larose Copyright C○ 2006 John Wiley & Sons, Inc. 1
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CHAPTER5 NAIVE BAYES ESTIMATION AND
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