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Two symmetrical fractional factorial designs are said to be combinatorially equivalent if one design can be obtained from another by reordering the runs, relabeling the factors and relabeling the levels of one or more factors. This article presents concepts of ordered distance frequency matrix, distance frequency vector, and reduced distance frequency vector for a design. Necessary conditions for two designs to be combinatorial equivalent based on these concepts are presented. A new algorithm based on the results obtained is proposed to check combinatorial non-equivalence of two factorial designs and several illustrating examples are provided. [ABSTRACT FROM AUTHOR]

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some essential geometric concepts/properties such as the minimum bounding region and the area of a region in a CDS are no longer valid in an NDDS.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. [ABSTRACT FROM AUTHOR]

We introduce a novel statistical procedure for clustering categorical data based on Hamming distance (HD) vectors. The proposed method is conceptually simple and computationally straightforward, because it does not require any specific statistical models or any convergence criteria. Moreover, unlike most currently existing algorithms that compute the class membership or membership probability for every data point at each iteration, our algorithm sequentially extracts clusters from the given dataset. That is, at each iteration our algorithm strives to identify only one cluster, which will then be deleted from the dataset at the next iteration; this procedure repeats until there are no more significant clusters in the remaining data. Consequently, the number of clusters can be determined automatically by the algorithm. As for the identification and extraction of a cluster, we first locate the cluster center by using a Pearson chi-squared-type statistic on the basis of HD vectors. The partition of the dataset produced by our algorithm is unique and insensitive to the input order of data points. The performance of the proposed algorithm is examined using both simulated and real world datasets. Comparisons with two well-known clustering algorithms, K-modes and AutoClass, show that the proposed algorithm substantially outperforms these competitors, with the classification rate or the information gain typically improved by several orders of magnitude. Computational complexity and run time comparisons are also provided. [ABSTRACT FROM AUTHOR]

The problem of approximate string searching comprises two classes of problems: string searching with k mismatches and string searching with k differences. In this paper we present a short survey and experimental results for well known sequential approximate string searching algorithms. We consider algorithms based on different approaches including dynamic programming, deterministic finite automata, filtering, counting and bit parallelism. We compare these algorithms in terms of running time against pattern length and for several values of k for four different kinds of text: binary alphabet, alphabet of size 8, English alphabet and DNA alphabet. Finally, we compare the experimental results of the algorithms with their theoretical complexities. [ABSTRACT FROM AUTHOR]