An optimized approach for community detection of Uttar Pradesh state, India (Census 1991, 2001 & 2011)

Abstract

The study on the gender ratio of overall population and of children in 0-6 age group for different districts of Uttar Pradesh state concentrates on the following: The data collected is evaluated for any pattern of sex ratio’s in terms of urban, rural segregation and to find whether the indices are different from district to district of Uttar Pradesh state so that precautionary measures can be taken care of to tackle this alarming situation in the state. For comparing sex ratios between pair of districts, it is tempting to arrange these (districts) in an increasing or decreasing order of sex ratio. But the reported sex ratios are not directly comparable since their “reliability” depends on the size of the population of the districts. Hence, a more reasonable index of dissimilarity between districts is the Chi-square measure computed under the hypothesis that the districts have the same sex ratio. The sex ratios/Chi-square values cannot be arranged on a linear interval scale and hence one has to think of an alternative more complex partial ordering among the districts to reflect a more meaningful structure that may be present in the data. Any ordering based on the results to be meaningful should be such that in the sequence, the difference between neighboring districts possible and the “effective difference” may be defined as the largest of these differences between successive pairs along the ordered set. Hence, ordering between every pair of districts must be such that this largest “gap” between consecutive pairs along the ordering should be as small as possible, that is among all possible sequences one can introduce between any specified district pairs. Hence, Minmaxion, an operation which enables one to find such “optimal approach distance” between every district pair, based on the Chi-square as an index or dissimilarity with respect to the sex ratios.