Mass customization: 2-D projection of high dimensional data

The paper makes three observations: 1) that preference is a partial ordering in one-dimension; 2) that a product, or a service, may be high-dimensional; consequently, and 3) transitivity, or its lack, results from choice of the direction for projection from high to low dimensions. The mass customization of cellular telephone designs gives the paper a context. The dimensions of the product space are: function, size, styling, color, etc. The medium for presentation (i.e., screen or paper), however, is necessarily two-dimensional (2-D). A criterion for projection is to preserve the information (such as, the similarity between the products, manifested as clusters, and the market opportunities, manifested as voids) from the high dimension. Drawing upon an analogy from the deformation mechanics of materials, the equilibrium conditions are formulated as distance and curvature. Distances give the clustering information; curvature gives the shape information. Projection is then seen as the process that minimizes the deformation in the projected geometry. The findings then become apparent. There are infinitely many ways to project. In most projections, intransitivity of preference results.