Non-ordered Discrete Data Space Research Articles

The BINDS-Tree: A Space-Partitioning Based Indexing Scheme for Box Queries in Non-Ordered Discrete Data Spaces

The BINDS-Tree: A Space-Partitioning Based Indexing Scheme for Box Queries in Non-Ordered Discrete Data Spaces

The BoND-Tree: An Efficient Indexing Method for Box Queries in Nonordered Discrete Data Spaces

Box queries (or window queries) are a type of query which specifies a set of allowed values in each dimension. Indexing feature vectors in the multidimensional Nonordered Discrete Data Spaces (NDDS) for efficient box queries are becoming increasingly important in many application domains such as genome sequence databases. Most of the existing work in this field targets the similarity queries (range queries and k-NN queries). Box queries, however, are fundamentally different from similarity queries. Hence, the same indexing schemes designed for similarity queries may not be efficient for box queries. In this paper, we present a new indexing structure specifically designed for box queries in the NDDS. Unique characteristics of the NDDS are exploited to develop new node splitting heuristics. For the BoND-tree, we also provide theoretical analysis to show the optimality of the proposed heuristics. Extensive experiments with synthetic data demonstrate that the proposed scheme is significantly more efficient than the existing ones when applied to support box queries in NDDSs. We also show effectiveness of the proposed scheme in a real-world application of primer design for genome sequence databases.

Efficient k-nearest neighbor searching in nonordered discrete data spaces

Numerous techniques have been proposed in the past for supporting efficient k -nearest neighbor ( k -NN) queries in continuous data spaces. Limited work has been reported in the literature for k -NN queries in a nonordered discrete data space (NDDS). Performing k -NN queries in an NDDS raises new challenges. The Hamming distance is usually used to measure the distance between two vectors (objects) in an NDDS. Due to the coarse granularity of the Hamming distance, a k -NN query in an NDDS may lead to a high degree of nondeterminism for the query result. We propose a new distance measure, called Granularity-Enhanced Hamming (GEH) distance, which effectively reduces the number of candidate solutions for a query. We have also implemented k -NN queries using multidimensional database indexing in NDDSs. Further, we use the properties of our multidimensional NDDS index to derive the probability of encountering valid neighbors within specific regions of the index. This probability is used to develop a new search ordering heuristic. Our experiments on synthetic and genomic data sets demonstrate that our index-based k -NN algorithm is efficient in finding k -NNs in both uniform and nonuniform data sets in NDDSs and that our heuristics are effective in improving the performance of such queries.

Reducing non-determinism of k-NN searching in non-ordered discrete data spaces

We propose a generalized version of the Granularity-Enhanced Hamming (GEH) distance for use in k-NN queries in non-ordered discrete data spaces (NDDS). The use of the GEH distance metric improves search semantics by reducing the degree of non-determinism of k-NN queries in NDDSs. The generalized form presented here enables the GEH distance to be used for a much greater variety of scenarios than was possible with the original form.

CNODE: clustering of set-valued non-ordered discrete data

This paper introduces a clustering technique named 'Clustering of set-valued Non-Ordered DiscretE data' (CNODE), in which each data item is a vector having a set of non-ordered discrete values per dimension. Since usual definitions of distance like Euclidean and Manhattan do not hold for 'non-ordered discrete data space' (NDDS), other measures like Hamming distance are often used to define distance between vectors having single-valued discrete dimensions. Such type of distance is not meaningful for set-valued dimensions and hence, we propose a similarity measure based on set intersection for clustering set-valued vectors. We also suggest a new measure for determining quality of clustering named 'lines of clustroids' (LOC) for this type of data. In contrast to other existing clustering techniques in NDDS, CNODE does not rely on any kind of pre-processing of dataset. Experiments with synthetic and real datasets show that CNODE is robust to data variations, scalable to large dataset size and efficient for high dimensions.

Dynamic indexing for multidimensional non-ordered discrete data spaces using a data-partitioning approach

Similarity searches in multidimensional Non-ordered Discrete Data Spaces (NDDS) are becoming increasingly important for application areas such as bioinformatics, biometrics, data mining and E-commerce. Efficient similarity searches require robust indexing techniques. Unfortunately, existing indexing methods developed for multidimensional (ordered) Continuous Data Spaces (CDS) such as the R-tree cannot be directly applied to an NDDS. This is because some essential geometric concepts/properties such as the minimum bounding region and the area of a region in a CDS are no longer valid in an NDDS. Other indexing methods based on metric spaces such as the M-tree and the Slim-trees are too general to effectively utilize the special characteristics of NDDSs, resulting in nonoptimized performance. In this article, we propose a new dynamic data-partitioning-based indexing technique, called the ND-tree, to support efficient similarity searches in an NDDS. The key idea is to extend the relevant geometric concepts as well as some indexing strategies used in CDSs to NDDSs. Efficient algorithms for ND-tree construction and techniques to solve relevant issues such as handling dimensions with different alphabets in an NDDS are presented. Our experimental results on synthetic data and real genome sequence data demonstrate that the ND-tree outperforms the linear scan, the M-tree and the Slim-trees for similarity searches in multidimensional NDDSs. A theoretical model is also developed to predict the performance of the ND-tree for random data.

A space-partitioning-based indexing method for multidimensional non-ordered discrete data spaces

There is an increasing demand for similarity searches in a multidimensional non-ordered discrete data space (NDDS) from application areas such as bioinformatics and data mining. The non-ordered and discrete nature of an NDDS raises new challenges for developing efficient indexing methods for similarity searches. In this article, we propose a new indexing technique, called the NSP-tree , to support efficient similarity searches in an NDDS. As we know, overlap causes a performance degradation for indexing methods (e.g., the R-tree) for a continuous data space. In an NDDS, this problem is even worse due to the limited number of elements available on each dimension of an NDDS. The key idea of the NSP-tree is to use a novel discrete space-partitioning (SP) scheme to ensure no overlap at each level in the tree. A number of heuristics and strategies are incorporated into the tree construction algorithms to deal with the challenges for developing an SP-based index tree for an NDDS. Our experiments demonstrate that the NSP-tree is quite promising in supporting efficient similarity searches in NDDSs. We have compared the NSP-tree with the ND-tree, a data-partitioning-based indexing technique for NDDSs that was proposed recently, and the linear scan using different NDDSs. It was found that the search performance of the NSP-tree was better than those of both methods.