Interval analysis: theory and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Interval arithmetic: From principles to implementation
Journal of the ACM (JACM)
New algorithms for statistical analysis of interval data
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Descriptive statistics of non-uniform interval symbolic data
Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation
Standardization of interval symbolic data based on the empirical descriptive statistics
Computational Statistics & Data Analysis
| Hi-index | 0.11 |
Interval data are generally defined by the upper and the lower value assumed by a unit for a continuous variable. In our approach we introduce a special type of interval description depending on time. Each observation is characterized by an oriented interval of values with a starting and an ending value for each period of observation: for example, the opening and the closing price of a stock in a financial market in a day or a week, the initial and the final expression of a gene at the beginning and at the ending of an experiment. Several factorial techniques have been developed in order to treat interval data, but not yet for oriented intervals. In this paper we present an extension of principal component analysis to time dependent interval data, or, in general, to oriented intervals. From a geometrical point of view, the proposed approach can be considered as an analysis of oriented segments (nicely called ''spaghetti'') defined in a multidimensional space identified by periods. We introduce the formulas for the standardization of data, the calculation of matrices and the interpretation of the results.