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A distance measure between two histograms has applications in feature selection, image indexing and retrieval, pattern classiÿcation and clustering, etc. We propose a distance between sets of measurement values as a measure of dissimilarity of two histograms. The proposed measure has the advantage over the traditional distance measures regarding the overlap between two distributions; it takes the similarity of the non-overlapping parts into account as well as that of overlapping parts. We consider three versions of the univariate histogram, corresponding to whether the type of measurement is nominal, ordinal, and modulo and their computational time complexities are (b), (b) and O(b 2 ) for each type of measurements, respectively, where b is the number of levels in histograms. ?

Motivated by several rulings in United States courts concerning expert testimony in general and handwriting testimony in particular, we undertook a study to objectively validate the hypothesis that handwriting is individualistic. Handwriting samples of one thousand five hundred individuals, representative of the US population with respect to gender, age, ethnic groups, etc., were obtained. Analyzing differences in handwriting was done by using computer algorithms for extracting features from scanned images of handwriting. Attributes characteristic of the handwriting were obtained, e.g., line s e p aration, slant, character shapes, etc. These attributes, which are a subset of attributes used by expert document examiners, were used to quantitatively establish individuality by using machine learning approaches. Using global attributes of handwriting and very few characters in the writing, the ability to determine the writer with a high degree of confidence was established. The work is a step towards providing scientific support for admitting handwriting evidence in court. The mathematical approach and the resulting software also have the promise of aiding the expert document examiner.

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