Decision Trees for Uncertain Data

Traditional decision tree classifiers work with data whose values are known and precise. We extend such classifiers to handle data with uncertain information. Value uncertainty arises in many applications during the data collection process. Example sources of uncertainty include measurement/quantization errors, data staleness, and multiple repeated measurements. With uncertainty, the value of a data item is often represented not by one single value, but by multiple values forming a probability distribution. Rather than abstracting uncertain data by statistical derivatives (such as mean and median), we discover that the accuracy of a decision tree classifier can be much improved if the “complete information” of a data item (taking into account the probability density function (pdf)) is utilized.

                      

                 We extend classical decision tree building algorithms to handle data tuples with uncertain values. Extensive experiments have been conducted that show that the resulting classifiers are more accurate than those using value averages. Since processing pdf’s is computationally more costly than processing single values (e.g., averages), decision tree construction on uncertain data is more CPU demanding than that for certain data. To tackle this problem, we propose a series of pruning techniques that can greatly improve construction efficiency.

EXISTING SYSTEM

             In traditional decision-tree classification, a feature (an attribute) of a tuple is either categorical or numerical. For the latter, a precise and definite point value is usually assumed. In many applications, however, data uncertainty is common. The value of a feature/attribute is thus best captured not by a single point value, but by a range of values giving rise to a probability distribution. Although the previous techniques can improve the efficiency of means, they do not consider the spatial relationship among cluster representatives, nor make use of the proximity between groups of uncertain objects to perform pruning in batch. A simple way to handle data uncertainty is to abstract probability distributions by summary statistics such as means and variances. We call this approach Averaging. Another approach is to consider the complete information carried by the probability distributions to build a decision tree. We call this approach Distribution-based.

PROPOSED SYSTEM

           We study the problem of constructing decision tree classifiers on data with uncertain numerical attributes. Our goals are (1) to devise an algorithm for building decision trees from uncertain data using the Distribution-based approach; (2) to investigate whether the Distribution-based approach could lead to a higher classification accuracy compared with the Averaging approach; and (3) to establish a theoretical foundation on which pruning techniques are derived that can significantly improve the

computational efficiency of the Distribution-based algorithms.

MODULES

Data Insertion

                  

               In many applications, however, data uncertainty is common. The value of a feature/attribute is thus best captured not by a single point value, but by a range of values giving rise to a probability distribution.  With uncertainty, the value of a data item is often represented not by one single value, but by multiple values forming a probability distribution. This uncertain data is inserted by user.

               

Generate Tree

                Building a decision tree on tuples with numerical, point valued data is computationally demanding. A numerical attribute usually has a possibly infinite domain of real or integral numbers, inducing a large search space for the best “split point”. Given a set of n training tuples with a numerical attribute, there are as many as n-1 binary split points or ways to partition the set of tuples into two non-empty groups. Finding the best split point is thus computationally expensive. To improve efficiency, many techniques have been proposed to reduce the number of candidate split points

Averaging

                A simple way to handle data uncertainty is to abstract probability distributions by summary statistics such as means and variances. We call this approach Averaging. A straight-forward way to deal with the uncertain information is to replace each pdf with its expected value, thus effectively converting the data tuples to point-valued tuples. This reduces the problem back to that for point-valued data. AVG is a greedy algorithm that builds a tree top-down. When processing a node, we examine a set of tuples S. The algorithm starts with the root node and with S being the set of all training tuples. At each node n, we first check if all the tuples in S have the same class label.

Distribution Based

         An approach is to consider the complete information carried by the probability distributions to build a decision tree. We call this approach Distribution-based. Our goals are,

 (1) To devise an algorithm for building decision trees from uncertain data using the Distribution-based approach;

 (2) To investigate whether the Distribution-based approach could lead to a higher classification accuracy compared with the Averaging approach;

 (3) To establish a theoretical foundation on which pruning techniques are derived that can significantly improve the computational efficiency of the Distribution-based algorithms.