Due to the rapid growth of the volume of data that are available, it is of importance and challenge to develop scalable methodologies and frameworks that can be used to perform efficient and effective data mining on large data sets. Vertical data mining strategy aims at addressing the scalability issues by organizing data in vertical layouts and conducting logical operations on vertical partitioned data instead of scanning the entire database horizontally in order to perform various data mining tasks.

Association rule mining, originally proposed for market basket data, has potential applications in many areas. Spatial data, such as remote sensed imagery (RSI) data, is one of the promising application areas. Extracting interesting patterns and rules from spatial data sets, composed of images and associated ground data, can be of importance in precision agriculture, resource discovery, and other areas. However, in most cases, the sizes of the spatial data sets are too large to be mined in a reasonable amount of time using existing algorithms. In this paper, we propose an efficient approach to derive association rules from spatial data using Peano Count Tree (P-tree) structure. P-tree structure provides a lossless and compressed representation of spatial data. Based on P-trees, an efficient association rule mining algorithm PARM with fast support calculation and significant pruning techniques is introduced to improve the efficiency of the rule mining process. The P-tree based Association Rule Mining (PARM) algorithm is implemented and compared with FP-growth and Apriori algorithms. Experimental results showed that our algorithm is superior for association rule mining on RSI spatial data.

For several decades and especially with the preeminence of relational database systems, data is almost always formed into horizontal record structures and then processed vertically (vertical scans of files of horizontal records). This makes good sense when the requested result is a set of horizontal records. In knowledge discovery and data mining, however, researchers are typically interested in collective properties or predictions that can be expressed very briefly. Therefore, the approaches for scan-based processing of horizontal records are known to be inadequate for data mining in very large data repositories (Han & Kamber, 2001; Han, Pei, & Yin, 2000; Shafer, Agrawal, & Mehta, 1996).

The k-nearest neighbour (KNN) technique is a simple yet effective method for classification. In this paper, we propose an efficient weighted nearest neighbour classification algorithm, called PINE, using vertical data representation. A metric called HOBBit is used as the distance metric. The PINE algorithm applies a Gaussian podium function to set weights to different neighbours. We compare PINE with classical KNN methods using horizontal and vertical representation with different distance metrics. The experimental results show that PINE outperforms other KNN methods in terms of classification accuracy and running time.

The volume of data keeps increasing. There are many data sets that have become extremely large. It is of importance and a challenge to develop scalable methodologies that can be used to perform efficient and effective data mining on large data sets. Vertical data mining strategy aims at addressing the scalability issues by organizing data in vertical layouts and conducting logical operations on vertical partitioned data instead of scanning the entire database horizontally.

Data-mining algorithms look for patterns in data. Most data-mining algorithms look for patterns in a single relation or table, while most real-world databases store information in multiple tables [HK01]. Multi-relational data mining (MRDM) has gained more and more interest recently and will continue to be significantly important in the future. MRDM approaches have been successfully applied to a number of problems in a variety of areas, e.g., in the area of bioinformatics. In this dissertation, we use the breakthrough vertical database and data-mining predicate-tree (P-tree)1 technology to solve the non-scalability problem which exists for MRDM in standard horizontal databases. We develop methods to generate data-mining-ready vertical materialized views to facilitate fast vertical mining. We store the vertical materialized views into P-tree format. P-trees are lossless and compressed representations of the original data that record count information in order to facilitate efficient data mining. Our vertical method of MRDM offers these advantages. First, we can generate vertical materialized views directly by replication or Boolean operations. Second, by fully vertical partitioning (to the bit position level), we only need to read what is needed; therefore, I/O is minimized. Third, we encode attribute values into bit vector format in a highly compressed manner. Finally, data mining can be formulated as highly parallelizable, logical operations facilitating fast implementations, and index is totally eliminated. 1P-tree technology is patent pending at North Dakota State University.

Online Analytical Processing (OLAP) is an important application of data warehouses. With more and more spatial data being collected, such as remotely sensed images, geographical information, digital sky survey data, efficient OLAP for spatial data is in great demand. In this paper, we build up a new data warehouse structure -- PD-cube, With PD-cube, OLAP operations and queries can be efficiently implemented. All these are accomplished based on the fast logical operations of Peano Trees (P-Trees*). One of the P-tree variations, Predicate P-tree, is used to efficiently reduce data accesses by filtering out "bit holes" consisting of consecutive 0's. Experiments show that OLAP operations can be executed much faster than with traditional OLAP methods.

Given a set of training data, nearest neighbor classification predicts the class value for an unknown tuple X by searching the training set for the k nearest neighbors to X and then classifying X according to the most frequent class among the k neighbors. Each of the k nearest neighbors casts an equal vote for the class of X. In this paper, we propose a new algorithm, Podium Incremental Neighbor Evaluator (PINE), in which nearest neighbors are weighted for voting. A metric called HOBBit is used as the distance metric, and a data structure, the P-tree, is used for efficient implementation of the PINE algorithm on spatial data. Our experiments show that by using a Gaussian podium function, PINE outperforms the k-nearest neighbor (KNN) method in terms of classification accuracy for spatial data. In addition, in the PINE algorithm, all the instances are potential neighbors so that the value of k need not be pre-specified as in KNN methods. By assigning high weights to the nearest neighbors and low (even zero) weights to other neighbors, high classification accuracy can be achieved.

Association Rule Mining, originally proposed for market basket data, has potential applications in many areas. Remote Sensed Imagery (RSI) data is one of the promising application areas. Extracting interesting patterns and rules from datasets composed of images and associated ground data, can be of importance in precision agriculture, community planning, resource discovery and other areas. However, in most cases the image data sizes are too large to be mined in a reasonable amount of time using existing algorithms. In this paper, we propose an approach to derive association rules on RSI data using Peano Count Tree (P-tree) structure. P-tree structure, proposed in our previous work, provides a lossless and compressed representation of image data. Based on P-trees, an efficient association rule mining algorithm P-ARM with fast support calculation and significant pruning techniques are introduced to improve the efficiency of the rule mining process. P-ARM algorithm is implemented and compared with FP-growth and Apriori algorithms. Experimental results showed that our algorithm is superior for association rule mining on RSI spatial data.

Many organizations have large quantities of spatial data collected in various application areas, including remote sensing, geographical information systems (GIS), astronomy, computer cartography, environmental assessment and planning, etc. These data collections are growing rapidly and can therefore be considered as spatial data streams. For data stream classification, time is a major issue. However, these spatial data sets are too large to be classified effectively in a reasonable amount of time using existing methods. In this paper, we developed a new method for decision tree classification on spatial data streams using a data structure called Peano Count Tree (P-tree). The Peano Count Tree is a spatial data organization that provides a lossless compressed representation of a spatial data set and facilitates efficient classification and other data mining techniques. Using P-tree structure, fast calculation of measurements, such as information gain, can be achieved. We compare P-tree based decision tree induction classification and a classical decision tree induction method with respect to the speed at which the classifier can be built (and rebuilt when substantial amounts of new data arrive). Experimental results show that the P-tree method is significantly faster than existing classification methods, making it the preferred method for mining on spatial data streams.

Advanced data mining technologies and the large quantities of Remotely Sensed Imagery provide a data mining opportunity with high potential for useful results. Extracting interesting patterns and rules from data sets composed of images and associated ground data, can be of importance in precision agriculture, community planning, resource discovery and other areas. However, in most cases the image data sizes are too large to be mined in a reasonable amount of time using standard methods. A new spatial data organization, bit Sequential organization (bSQ) and a new “data-mining ready” data structure, the Peano Count Tree (Ptree) provide a lossless and compressed representation of image data which facilitate association rule mining, classification and other data mining techniques markedly. In this paper we propose a new model for association rule mining and classification on spatial datasets using Ptrees. Experimental results show the new model applies well to data mining on Remotely Sensed Imagery data.