1. A data analysis apparatus comprising: an index setting unit configured to set a different index for each of a plurality of grid sections of a grid coordinate system; a cluster generation unit configured to generate a cluster in a region of the grid coordinate system, the region having data values, and to set a representative value of the cluster using the data values existing in the generated cluster; an index determination unit configured to respond to new data input to any one of the grid sections by determining an index of the grid section to which the new data has been input; and a clustering unit configured to cluster the new data using the determined index; wherein at least one of the index setting unit, the cluster generation unit, the index determination unit, and the clustering unit is implemented by one or more hardware processors.