COMPOSITIONAL GEOMETRY AND MASS CONSERVATION

Abstract

A geometrical structure is imposed on compositional data by physical and chemical laws, principally mass conservation. Therefore, statistical or mathematical investigation of possible relations between data values and such laws must be consistent with this structure. This demands that geometrical concepts, such as points that specify both mass and composition in linear space, and lines in projective space that specify composition only, be clearly defined and consistent with mass conservation. Mass thus becomes the norm in composition space in place of the Euclidean norm of ordinary space. Coordinate transformations inconsistent with this geometry are accordingly unnatural and misleading. They are also unnecessary because correlation arising from the constant mass presents no unusual difficulty in the analysis of the underlying quadratic form.