Researchers face many class prediction challenges stemming from a small size of training data vis-a-vis a large number of unlabeled samples to be predicted. Transductive learning is proposed to utilize information abo...Researchers face many class prediction challenges stemming from a small size of training data vis-a-vis a large number of unlabeled samples to be predicted. Transductive learning is proposed to utilize information about unlabeled data to estimate labels of the unlabeled data for this condition. This work presents a new transductive learning method called two-way Markov random walk(TMRW) algorithm. The algorithm uses information about labeled and unlabeled data to predict the labels of the unlabeled data by taking random walks between the labeled and unlabeled data where data points are viewed as nodes of a graph. The labeled points correlate to unlabeled points and vice versa according to a transition probability matrix. We can get the predicted labels of unlabeled samples by combining the results of the two-way walks. Finally, ensemble learning is combined with transductive learning, and Adboost.MH is taken as the study framework to improve the performance of TMRW, which is the basic learner. Experiments show that this algorithm can predict labels of unlabeled data well.展开更多
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTR...In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...展开更多
A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical c...A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given. At the end, a typical example is provided to show the recurrence and transience. Key words random environment - random walk in timerandom environment - skew product Markov chain CLC number O 211.6 Foudation item: Supported by the National Natural Science Foundation of China (10371092) and Foundation of Wuhan University.Biography: Zhang Xiao-min (1977-), male, Ph. D candidate, research direction: stochastic processes and random fractal.展开更多
The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared...The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.展开更多
In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v1 and v2. We consider a special type of b...In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v1 and v2. We consider a special type of boundary which can trap the particle for a random time. We found closed-form expressions for the stationary distribution of the position of the particle not only for the alternating Markov process but also for a broad class of semi-Markov processes.展开更多
基金Project(61232001) supported by National Natural Science Foundation of ChinaProject supported by the Construct Program of the Key Discipline in Hunan Province,China
文摘Researchers face many class prediction challenges stemming from a small size of training data vis-a-vis a large number of unlabeled samples to be predicted. Transductive learning is proposed to utilize information about unlabeled data to estimate labels of the unlabeled data for this condition. This work presents a new transductive learning method called two-way Markov random walk(TMRW) algorithm. The algorithm uses information about labeled and unlabeled data to predict the labels of the unlabeled data by taking random walks between the labeled and unlabeled data where data points are viewed as nodes of a graph. The labeled points correlate to unlabeled points and vice versa according to a transition probability matrix. We can get the predicted labels of unlabeled samples by combining the results of the two-way walks. Finally, ensemble learning is combined with transductive learning, and Adboost.MH is taken as the study framework to improve the performance of TMRW, which is the basic learner. Experiments show that this algorithm can predict labels of unlabeled data well.
基金Supported by the National Natural Science Foundation of China (10771185 and 10871200)
文摘In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...
文摘A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given. At the end, a typical example is provided to show the recurrence and transience. Key words random environment - random walk in timerandom environment - skew product Markov chain CLC number O 211.6 Foudation item: Supported by the National Natural Science Foundation of China (10371092) and Foundation of Wuhan University.Biography: Zhang Xiao-min (1977-), male, Ph. D candidate, research direction: stochastic processes and random fractal.
基金supported by the National Natural Science Foundation of China(No.10702050)
文摘The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.
文摘In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v1 and v2. We consider a special type of boundary which can trap the particle for a random time. We found closed-form expressions for the stationary distribution of the position of the particle not only for the alternating Markov process but also for a broad class of semi-Markov processes.
