15769711
Combining Clustering with Moving Sequential Pattern Mining: A Novel and Efficient Technique
Sequential pattern mining is a well-studied problem. In the context of mobile computing, moving sequential patterns that reflects the moving behavior of mobile users attracted researchers’ interests recently. In this paper a novel and efficient technique is proposed to mine moving sequential patterns. Firstly the idea of clustering is introduced to process the original moving histories into moving sequences as a preprocessing step. Then an efficient algorithm called PrefixTree is presented to mine the moving sequences. Performance study shows that PrefixTree outperforms LM algorithm, which is revised to mine moving sequences, in mining large moving sequence databases.
15257131
Incremental Maintenance of Discovered Mobile User Maximal Moving Sequential Patterns
In the context of mobile computing, a special sequential pattern, moving sequential pattern that reflects the moving behavior of mobile users attracted researchers' interests recently. While there have been a number of efficient moving sequential pattern mining algorithms reported, this paper concentrates on the maintenance of mined maximal moving sequential patterns. In particular, we developed an incremental approach, where maximal moving sequential patterns are stored in prefix trees, and new moving sequences can be easily combined with the existing patterns. A performance study indicated that the proposed approach performs significantly faster than straightforward approaches that mine from the whole updated database.
6066243
Extending Dependencies with Conditions
This paper introduces a class of conditional inclusion dependencies (CINDs), which extends traditional inclusion dependencies (INDs) by enforcing bindings of semantically related data values. We show that CINDs are useful not only in data cleaning, but are also in contextual schema matching [7]. To make effective use of CINDs in practice, it is often necessary to reason about them. The most important static analysis issue concerns consistency, to determine whether or not a given set of CINDs has conflicts. Another issue concerns implication, i.e., deciding whether a set of CINDs entails another CIND. We give a full treatment of the static analyses of CINDs, and show that CINDs retain most nice properties of traditional INDs: (a) CINDs are always consistent; (b) CINDs are finitely axiomatizable, i.e., there exists a sound and complete inference system for implication of CINDs; and (c) the implication problem for CINDs has the same complexity as its traditional counterpart, namely, PSPACE-complete, in the absence of attributes with a finite domain; but it is EXPTIME-complete in the general setting. In addition, we investigate the interaction between CINDs and conditional functional dependencies (CFDs), an extension of functional dependencies proposed in [9]. We show that the consistency problem for the combination of CINDs and CFDs becomes undecidable. In light of the undecidability, we provide heuristic algorithms for the consistency analysis of CFDs and CINDs, and experimentally verify the effectiveness and efficiency of our algorithms.
17213172
A New Fast Clustering Algorithm Based on Reference and Density
Density-based clustering is a sort of clustering analysis methods, which can discover clusters with arbitrary shape and is insensitive to noise data. The efficiency of data mining algorithms is strongly needed with data becoming larger and larger. In this paper, we present a new fast clustering algorithm called CURD, which means Clustering Using References and Density. Its creativity is capturing the shape and extent of a cluster with references, and then it analyzes the data based on the references. CURD preserves the ability of density based clustering method’s good advantages, and it is much efficient because of its nearly linear time complexity, so it can be used in mining very large databases. Both our theoretic analysis and experimental results confirm that CURD can discover clusters with arbitrary shape and is insensitive to noise data; In the meanwhile, its executing efficiency is much higher than R*-tree based DBSCAN algorithm.
3081148
The Existence and Nonexistence of Perfect Addition Sets
Abstract A (v, k, λ, μ)-perfect addition set is a subset A of Z υZ with k elements such that the expression ai + aj, for ai ≠ aj in A, represents 0 exactly μ times and each nonzero element exactly λ times. Several infinite classes of such sets using quadratic residues of primes, a few isolated examples using cubic residues, and a construction in certain cases when υ is twice an odd integer, are give. There is an efficient method, based on the Chinese remainder theorem, which decides the existence or nonexistence of a perfect addition set. Some further results on nonexistence are given. In particular, two previously unsolved cases of Isbell (Discrete Math. 24 (1978), 13–18) are settled. The article ends with a list of nontrivial perfect addition sets with k ⩽ 20.
44609559
Cyclic Relative Difference Sets with Classical Parameters
We investigate the existence of cyclic relative difference sets with parameters ((qd?1)/(q?1), n, qd?1, qd?2(q?1)/n), q any prime power. One can think of these as “liftings” or “extensions” of the complements of Singer difference sets. When q is odd or d is even, we find that relative difference sets with these parameters exist if and only if n is a divisor of q?1. In case q is even and d is odd, relative difference sets with these parameters exist if and only if n is a divisor of 2(q?1).
32200257
Partial difference sets
A (?,k,?,β)-partial difference set in a finite group G of order ? is a subset D of G with k distinct elements such that expressions dnd?12 for d1 and d2 in D, represent each non-identity element not contained in D exactly ? times and each non-identity element contained in D exactly ?+β times. Such a set is closely related to association schemes of PBIB designs with two associate classes.