Time-series discord is widely used in data mining applications to characterize anomalous subsequences in time series. Compared to some other discord search algorithms, the direct search algorithm based on the recurren...Time-series discord is widely used in data mining applications to characterize anomalous subsequences in time series. Compared to some other discord search algorithms, the direct search algorithm based on the recurrence plot shows the advantage of being fast and parameter free. The direct search algorithm, however, relies on quasi-periodicity in input time series, an assumption that limits the algorithm＇s applicability. In this paper, we eliminate the periodicity assumption from the direct search algorithm by proposing a reference function for subsequences and a new sampling strategy based on the reference function. These measures result in a new algorithm with improved efficiency and robustness, as evidenced by our empirical evaluation.展开更多
We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in deta...We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.展开更多
基金Support by Australian Research Council Linkage Grant No. LP 0776417
文摘Time-series discord is widely used in data mining applications to characterize anomalous subsequences in time series. Compared to some other discord search algorithms, the direct search algorithm based on the recurrence plot shows the advantage of being fast and parameter free. The direct search algorithm, however, relies on quasi-periodicity in input time series, an assumption that limits the algorithm＇s applicability. In this paper, we eliminate the periodicity assumption from the direct search algorithm by proposing a reference function for subsequences and a new sampling strategy based on the reference function. These measures result in a new algorithm with improved efficiency and robustness, as evidenced by our empirical evaluation.
基金supported by National Natural Science Foundations of China (Grant Nos. 10771216 and 11071259)
文摘We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.
