6659460
Generalized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to c"n is an infinite, lower triangular array determined by the pair (g(t),f(t)) and has the generic element d"n","k=[t^n/c"n]g(t)(f(t))^k/c"k, where c"n is a fixed sequence of non-zero constants with c"0=1. We demonstrate that the generalized Riordan arrays have similar properties to those of the classical Riordan arrays. Based on the definition, the iteration matrices related to the Bell polynomials are special cases of the generalized Riordan arrays and the set of iteration matrices is a subgroup of the Riordan group. We also study the relationships between the generalized Riordan arrays and the Sheffer sequences and show that the Riordan group and the group of Sheffer sequences are isomorphic. From the Sheffer sequences, many special Riordan arrays are obtained. Additionally, we investigate the recurrence relations satisfied by the elements of the Riordan arrays. Based on one of the recurrences, some matrix factorizations satisfied by the Riordan arrays are presented. Finally, we give two applications of the Riordan arrays, including the inverse relations problem and the connection constants problem.
17247210
Identities on Bell polynomials and Sheffer sequences
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.
9921122
Probabilistic Skyline Operator over Sliding Windows
Skyline computation has many applications including multi-criteria decision making. In this paper, we study the problem of efficient processing of continuous skyline queries over sliding windows on uncertain data elements regarding given probability thresholds. We first characterize what kind of elements we need to keep in our query computation. Then we show the size of dynamically maintained candidate set and the size of skyline. We develop novel, efficient techniques to process a continuous, probabilistic skyline query. Finally, we extend our techniques to the applications where multiple probability thresholds are given or we want to retrieve "top-k" skyline data objects. Our extensive experiments demonstrate that the proposed techniques are very efficient and handle a high-speed data stream in real time.
16343248
iRANK: an interactive ranking framework and its application in query-focused summarization
We address the problem of unsupervised ensemble ranking in this paper. Traditional approaches either combine multiple ranking criteria into a unified representation to obtain an overall ranking score or to utilize certain rank fusion or aggregation techniques to combine the ranking results. Beyond the aforementioned combine-then-rank and rank-then-combine approaches, we propose a novel rank-learn-combine ranking framework, called Interactive Ranking (iRANK), which allows two base rankers to "teach" each other before combination during the ranking process by providing their own ranking results as feedback to the others so as to boost the ranking performance. This mutual ranking refinement process continues until the two base rankers cannot learn from each other any more. The overall performance is improved by the enhancement of the base rankers through the mutual learning mechanism. We apply this framework to the sentence ranking problem in query-focused summarization and evaluate its effectiveness on the DUC 2005 data set. The results are encouraging with consistent and promising improvements.
5447146
Mining long sequential patterns in a noisy environment
Pattern discovery in long sequences is of great importance in many applications including computational biology study, consumer behavior analysis, system performance analysis, etc. In a noisy environment, an observed sequence may not accurately reflect the underlying behavior. For example, in a protein sequence, the amino acid N is likely to mutate to D with little impact to the biological function of the protein. It would be desirable if the occurrence of D in the observation can be related to a possible mutation from N in an appropriate manner. Unfortunately, the support measure (i.e., the number of occurrences) of a pattern does not serve this purpose. In this paper, we introduce the concept of compatibility matrix as the means to provide a probabilistic connection from the observation to the underlying true value. A new metric match is also proposed to capture the "real support" of a pattern which would be expected if a noise-free environment is assumed. In addition, in the context we address, a pattern could be very long. The standard pruning technique developed for the market basket problem may not work efficiently. As a result, a novel algorithm that combines statistical sampling and a new technique (namely border collapsing) is devised to discover long patterns in a minimal number of scans of the sequence database with sufficiently high confidence. Empirical results demonstrate the robustness of the match model (with respect to the noise) and the efficiency of the probabilistic algorithm.
10324009
A Low-Granularity Classifier for Data Streams with Concept Drifts and Biased Class Distribution
Many applications track streaming data for actionable alerts, which may include, for example, network intrusions, transaction frauds, bio-surveilence abnormalities, and so forth. Some stream classification models are built for this purpose. Due to concept drifts, maintaining a model's up-to-dateness has become one of the most challenging tasks in mining data streams. State-of-the-art approaches, including both the incrementally updated classifiers and the ensemble classifiers, have proved that model update is a very costly process. In this paper, we show that reducing model granularity reduces the update cost, as models of fine granularity enable us to efficiently pinpoint local components in the model that are affected by the concept drift. It also enables us to derive new model components to reflect the current data distribution, thus avoiding expensive updates on a global scale. Furthermore, those actionable alerts being monitored are usually rare occurrences. The existing stream classifiers cannot handle this problem. We address this problem and show that the low-granularity classifier handles rare events on stream data with ease. Experiments on real and synthetic data show that our approach is able to maintain good prediction accuracy at a fraction of the model updating cost of state-of-the-art approaches.
13632117
A Novel Intrusion Detection Method Based on Principle Component Analysis in Computer Security
Intrusion detection is an important technique in the defense-in-depth network security framework and a hot topic in computer security in recent years. In this paper, a new intrusion detection method based on Principle Component Analysis (PCA) with low overhead and high efficiency is presented. System call data and command sequences data are used as information sources to validate the proposed method. The frequencies of individual system calls in a trace and individual commands in a data block are computed and then data column vectors which represent the traces and blocks of the data are formed as data input. PCA is applied to reduce the high dimensional data vectors and distance between a vector and its projection onto the subspace reduced is used for anomaly detection. Experimental results show that the proposed method is promising in terms of detection accuracy, computational expense and implementation for real-time intrusion detection.