Interval Data Processing Using Probabilistic Model

As the rapid development of computer and internet technology, people are collecting and processing more and more kinds of different format data. There are a lot work of the common real data, while relatively less research on interval data. Interval data has a wide application in many fields like:Multivariate analysis, pattern recognition, data mining and controls. Comparing to real data, interval data is represented by intervals while not precise values. This decides that itself contains uncertainty. Therefore, interval data need special handling.Random events are widely arising in real world. And a major source of interval data is de-rived from unobservable random variables. In addition, probability theory is a mature discipline. There are a lot of theoretical and technical works and also fit to be applied to model uncertainty. Therefore, based on the uncertainty characteristic of interval data itself, this paper tries using a probabilistic model for interval data processing, explains the realistic basis of the corresponding probability model and reforms and puts forward some dissimilar measure and regression, clustering algorithms.The main work is as follows:1).Two examples are given on the realistic basis of probability model of interval data. Intervals are seen as random variables and mapped to certain distributions. Three dissimilar measures are defined on the basis of probability model. And some properties of them are proved; 2).On the basis of probabilistic model, combining the characteristics of uncer-tainty of interval data, this paper puts forward the application of regression algorithm for interval data, including:multivariable linear regression and kernel Regression algorithm; 3). Based on a new objective function, a new clustering algorithm for interval data is proposed. The algorithm also can be applied to real data, and the convergence of the algorithm are proved.