## Improved Heterogeneous Distance Functions (1997)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 229 - 10 self |

### BibTeX

@ARTICLE{Wilson97improvedheterogeneous,

author = {D. Randall Wilson and Tony R. Martinez},

title = {Improved Heterogeneous Distance Functions},

journal = {Journal of Artificial Intelligence Research},

year = {1997},

volume = {6},

pages = {1--34}

}

### Years of Citing Articles

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### Abstract

Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values between nominal attribute values, but it largely ignores continuous attributes, requiring discretization to map continuous values into nominal values. This paper proposes three new heterogeneous distance functions, called the Heterogeneous Value Difference Metric (HVDM), the Interpolated Value Difference Metric (IVDM), and the Windowed Value Difference Metric (WVDM). These new distance functions are designed to handle applications with nominal attributes, continuous attributes, or both. In experiments on 48 applications the new distance metrics achieve higher classification accuracy on average than three previous distance functions on those datasets that have both nominal and continuous attributes. 1. Introduction Instance-Based Learning (IBL) (Aha, ...

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Citation Context ...cy (Ventura & Martinez, 1995). Many real-world applications have both nominal and linear attributes, including, for example, over half of the datasets in the UCI Machine Learning Database Repository (=-=Merz & Murphy, 1996-=-). This paper introduces three new distance functions that are more appropriate than previous functions for applications with both nominal and continuous attributes. These new distance functions can b... |

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Citation Context ...1972), the selective nearest neighbor rule (Rittler et al., 1975), typical instance based learning algorithm (Zhang, 1992), prototype methods (Chang, 1974), hyperrectangle techniques (Salzberg, 1991; =-=Wettschereck & Dietterich, 1995-=-), rule-based techniques (Domingos, 1995), random mutation hill climbing (Skalak, 1994; Cameron-Jones, 1995) and others (Kibler & Aha, 1987; Tomek, 1976; Wilson, 1972). 8. Conclusions & Future Researc... |

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Citation Context ...HVDM as the distance metric. The system was tested on the heterogeneous datasets appearing in Table 1 using the three different normalization schemes discussed above, using ten-fold cross-validation (=-=Schaffer, 1993-=-), and the results are summarized in Table 2. All the normalization schemes used the same training sets and test sets for each trial. Bold entries indicate which scheme had the highest accuracy. An as... |

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Citation Context ...techniques (Salzberg, 1991; Wettschereck & Dietterich, 1995), rule-based techniques (Domingos, 1995), random mutation hill climbing (Skalak, 1994; Cameron-Jones, 1995) and others (Kibler & Aha, 1987; =-=Tomek, 1976-=-; Wilson, 1972). 8. Conclusions & Future Research Areas There are many learning systems that depend on a reliable distance function to achieve accurate generalization. The Euclidean distance function ... |

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Citation Context ...nC) time. Though m and C are typically fairly small, the generalization process can require a significant amount of time and/or computational resources as n grows large. Techniques such as k-d trees (=-=Deng & Moore, 1995-=-; Wess, Althoff & Derwand, 1993; Sproull, 1991) and projection (Papadimitriou & Bentley, 1980) can reduce the time required to locate nearest neighbors from the training set, though such algorithms ma... |

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Citation Context ... on a wide variety of applications (real-world classification tasks). Many neural network models also make use of distance functions, including radial basis function networks (Broomhead & Lowe, 1988; =-=Renals & Rohwer, 1989-=-; Wasserman, 1993), counterpropagation networks (Hecht-Nielsen, 1987), ART (Carpenter & Grossberg, 1987), selforganizing maps (Kohonen, 1990) and competitive learning (Rumelhart & McClelland, 1986). D... |

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Citation Context ... 1978), Mahalanobis (Nadler & Smith, 1993), Camberra, Chebychev, Quadratic, Correlation, and Chi-square distance metrics (Michalski, Stepp & Diday, 1981; Diday, 1974); the Context-Similarity measure (=-=Biberman, 1994-=-); the Contrast Model (Tversky, 1977); hyperrectangle distance functions (Salzberg, 1991; Domingos, 1995) and others. Several of these functions are defined in Figure 1. Although there have been many ... |

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Categorizing Numeric Information for Generalization
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- 1985
(Show Context)
Citation Context ...(Cost & Salzberg, 1993; Rachlin et al., 1994). These distance metrics work well in many nominal domains, but they do not handle continuous attributes directly. Instead, they rely upon discretization (=-=Lebowitz, 1985-=-; Schlimmer, 1987), which can degrade generalization accuracy (Ventura & Martinez, 1995). Many real-world applications have both nominal and linear attributes, including, for example, over half of the... |

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