Multivariate cross-sectional data (i.e. not time-series or repeated measure) are indicated by rectangular data in which each column is a variable (feature), and each row is a case or record.
First procedure of representing rectangle data is to map it onto a higher-dimensional point data and use point-based data structure procedures such as the grid file, PR quadtree, point quadtree, and k-d-tree. Procedure mapping of the rectangular data to a four-dimensional point can be performed in number techniques such as x and y coordinates of the opposite corners, or x and y coordinates of one corner and the width and height, etc. Drawback of point-based representations of rectangular data have the is that they lack to benefit from the locality of data for the efficiency of both storage and spatial operations.
Second procedure of representing rectangle data is in terms of the lines it is composed of and line-based data structure procedures such as PM quadtree, PMR quadtree, etc. Drawback of line-based representations of rectangular data was that a spatial operation specified in terms of its line segments may not satisfy the conditions of the operation yet the rectangle they are composed of satisfies them.
Third procedure of representing rectangle data is in terms of the area it occupies. Procedures such as MX-CIF quadtrees and R-Trees organize rectangle data in hierarchical groupings of lowest bounding boxes. In case of MX-CIF quadtree implements space-based
quadtree partitioning where each rectangle is associated with its lowest enclosing quadtree block. In R-Trees rectangle data is partitioned into hierarchically nested lowest bounded boxes. Drawback of R-Trees is that, there locality of data is not implemented.