Second-order Markov Model Research Articles

A large-alphabet-oriented scheme for Chinese and English text compression

In this paper, a large-alphabet-oriented scheme is proposed for both Chinese and English text compression. Our scheme parses Chinese text with the alphabet defined by Big-5 code, and parses English text with some rules designed here. Thus, the alphabet used for English is not a word alphabet. After a token is parsed out from the input text, zero-, first-, and second-order Markov models are used to estimate the occurrence probabilities of this token. Then, the probabilities estimated are blended and accumulated in order to perform arithmetic coding. To implement arithmetic coding under a large alphabet and probability-blending condition, a way to partition count-value range is studied. Our scheme has been programmed and can be executed as a software package. Then, typical Chinese and English text files are compressed to study the influences of alphabet size and prediction order. On average, our compression scheme can reduce a text file's size to 33.9% for Chinese and to 23.3% for English text. These rates are comparable with or better than those obtained by popular data compression packages. Copyright © 2005 John Wiley & Sons, Ltd.

A TIED-MIXTURE 2D HMM FACIAL IMAGE RETRIEVAL SYSTEM

In this paper, the effect of mixture tying on a second-order 2D Hidden Markov Model (HMM) is studied as applied to the face recognition problem. While tying HMM parameters is a well-known solution in the case of insufficient training data that leads to nonrobust estimation, it is used here to improve the overall performance in the small model case where the resolution in the observation space is the main problem. The fully-tied-mixture 2D HMM-based face recognition system is applied to the facial database of AT&T and the facial database of Georgia Institute of Technology. The performance of the proposed 2D HMM tied-mixture system is studied and the expected improvement is confirmed.

Tailoring polyolefins by metallocene catalysis: kinetic and mechanistic aspects

Abstract The C s -symmetric complex [Ph 2 C(2,7-di tert BuFlu)(Cp)]ZrCl 2 is beside the constrained geometry compounds a very active catalyst for the copolymerisation of ethene and 1-octene. Activities up to 200,000 kg polymer /(mol Zr h c monomer ) were reached at 60 °C. The activity shows a maximum at 10 mol% 1-octene in the feed and decreases with higher amounts of comonomer. The molecular weights of the obtained copolymers are between 670 and 900 kg/mol. The melting points can be varied between 140 and 60 °C. There are no octene-diblocks observed in the microstructure. The insertion mechanism can be described by a second-order Markov model. The activity decreases with time because of β-H-transfer reaction and elimination of methane.

Simulating Climate over Western North America Using Stochastic Weather Generators

The climatologies of daily precipitation and of maximum and minimum temperatures over western North America are simulated using stochastic weather generators. Two types of generator, differentiated only by their method of modeling precipitation occurrence, are investigated. A second-order Markov model, in which the probability of the occurrence of precipitation is modeled as contingent upon its occurrence on the previous two days, is compared with a spell-length model, in which mass functions of wet- and dry-spell lengths are modeled. Both models are able to reproduce the observed annual and monthly climatology in the region to a high degree of accuracy. However, there is considerable over-dispersion in annual precipitation, resulting primarily from an underestimation in the interannual variability of precipitation intensity. The interannual variability of temperatures is similarly underestimated, and is most severe for minimum temperatures. There is a severe problem in estimating minimum temperature extremes, which can be attributed to the negatively skewed distribution of daily minimum temperatures. Non-normality in the distribution of daily temperatures is shown to be a problem in simulating extreme temperature maxima as well as of minima. It is suggested that the normal distribution used in the generation of daily temperatures in the widely used Richardson (1981) generator, and its derivations, be supplanted by a more appropriate distribution that permits skewness in either direction.

Estimation of operating characteristics for dependent diagnostic tests based on latent Markov models.

We describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test. Log-linear models are adopted for the classification distributions conditional on the latent state, where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests. A marginal likelihood is constructed by marginalizing over a latent two-state Markov process. Specific latent processes we consider include a first-order Markov model, a second-order Markov model, and a time-nonhomogeneous Markov model, although the method is described in full generality. Adaptations to handle missing data are described. Model diagnostics are considered based on the bootstrap distribution of conditional residuals. The methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement.

Second-order H ∞ optimal LMS and NLMS algorithms based on a second-order Markov model

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models.

Optimal use of Markov models for DPCM picture transmission over noisy channels

Joint source/channel decoders that use the residual redundancy in the source are investigated for differential pulse code modulation (DPCM) picture transmission over a binary symmetric channel. Markov sequence decoders employing the Viterbi algorithm that use first-order source statistics are reviewed, and generalized for decoders that use second-order source statistics. To make optimal use of the source correlation in both horizontal and vertical directions, it is necessary to generalize the conventional Viterbi decoding algorithm for a one higher-dimensional trellis. The paths through the trellis become two-dimensional "sheets", thus, the technique is coined "sheet decoding". By objective [reconstruction signal-to-noise ratio (SNR)] and subjective measure, it is found that the sheet decoders outperform the Markov sequence decoders that use a first-order Markov model, and outperform two other known decoders (modified maximum a posteriori probability and maximal SNR) that use a second-order Markov model. Moreover, it is found that the use of a simple rate-2/3 block code in conjunction with Markov model-aided decoding (MMAD) offers significant performance improvement for a 2-bit DPCM system. For the example Lenna image, it is observed that the rate-2/3 block code is superior to a rate-2/3 convolutional code for channel-error rates higher than 0.035. The block code is easily incorporated into any of the MMAD DPCM systems and results in a 2-bit MMAD DPCM system that significantly outperforms the noncoded 3-bit MMAD DPCM systems for channel-error rates higher than 0.04.

A Markov chain model for longitudinal categorical data when there may be non-ignorable non-response

Longitudinal data with non-response occur in studies where the same subject is followed over time but data for each subject may not be available at every time point. When the response is categorical and the response at time t depends on the response at the previous time points, it may be appropriate to model the response using a Markov model. We generalize a second-order Markov model to include a non-ignorable non-response mechanism. Simulation is used to study the properties of the estimators. Large sample sizes are necessary to ensure that the algorithm converges and that the asymptotic properties of the estimators can be used.

Automatic word recognition based on second-order hidden Markov models

We propose an extension of the Viterbi algorithm that makes second-order hidden Markov models computationally efficient. A comparative study between first-order (HMM1s) and second-order Markov models (HMM2s) is carried out. Experimental results show that HMM2s provide a better state occupancy modeling and, alone, have performances comparable with HMM1s plus postprocessing.

Markov models of search state patterns in a hypertext information retrieval system

The objective of this research is to discover the search state patterns through which users retrieve information in hypertext systems. The Markov model is used to describe users' search behavior. As determined by the log-linear model test, the second-order Markov model is the best model. Search patterns of different user groups were studied by comparing the corresponding transition probability matrices. The comparisons were made based on the following factors: gender, search experience, search task, and the user's academic background. The statistical tests revealed that there were significant differences between all the groups being compared. © 1993 John Wiley & Sons, Inc.

Computer improvisation of blues melodies.

A computer program has been written that generates blues melodies to fit input chord progressions. The program uses a combination of stochastic methods and high-level rules. Second-order Markov models govern the generation of pitches and rhythms, with fall back procedures (to first- and zero-order models) used to deal with zero-frequency problems. Pitches and rhythms are generated by independent processes; an experimental goal is to determine the degree to which these processes may be linked. The rhythm model uses rhythmic patterns of varying lengths, thus incorporating a moderately variable time scale. Long-term time scale factors are controlled by rules operating at the phrase level. Output from the program will be judged by listeners to determine the degree to which the program captures the structure of blues melodies. Results of these listening experiments will be presented at the conference.

Highly efficient coding schemes for contour lines based on chain code representations

The encoding schemes utilize the first- and second-order Markov models to describe the source structure. Two coding techniques, Huffman encoding and arithmetic encoding, are used to achieve a high coding efficiency. Universal code tables which match the statistics of contour line drawings obtained from 64 contour maps are presented and can be applied to encode all contour line drawings with chain code representations. Experiments have shown about a 50% improvement on the code amount over the conventional chain encoding scheme with arithmetic coding schemes, and also have shown a compression rate comparable to that obtained by T. Kaneko and M. Okudaira (1985) with Huffman coding schemes, while this implementation is substantially simpler. >

A statistical analysis system (SAS) computer program for Markov chain analysis

A computer program for Markov chain analysis is presented and discussed. The program is written in the language of the Statistical Analysis System (SAS) but detailed knowledge of SAS is not required for its use. The program tests hypotheses about the goodness of fit of first- and second-order Markov models. It also tests if transition probabilities are homogeneous between the first and the second half of each sequence.

Short-Term Single-Station Forecasting of Precipitation

Forecast probabilities of rain were calculated up to 12 hours in advance using a Markov chain model applied to three-hourly observations from five major Australian cities. The four weather states chosen in this first study were three cloudiness states (0–2 oktas, 3–5 oktas and 6–8 oktas) and a rain state. Second-order Markov models with time-of-day dependent transition probabilities were fitted after appropriate statistical testing. Forecasts were made using transition probabilities for summer and winter seasons. The skill of the Markov chain forecast probabilities of rain was evaluated in terms of Brier scores using to years of independent data, and compared with forecasts based upon persistence and climatology. The skill of the Markov model forecasts appreciably exceeded that of persistence and climatology and a real time trial of the procedure is being planned.

Prediction of water levels in a tidal inlet

It is a very important and difficult problem to operate gates at the inlets of tidal lakes to control water quality and quantity, simultaneously. The main purpose of gate operation at the inlets of tidal lakes are flood control and irrigation. That is to say, the gate operation must sufficiently satisfy two purposes. As the first step to optimize the effect of gate control, the water levels downstream of the gate are predicted by a combined model between regression theory and control theory. The prediction model consists of two parts. The regression equation is used to predict the water levels downstream of the gate by the sea levels in the first part. The causality in this part is physically evident. The Kalman filtering algorithm is employed to identify parameters which construct the state equation in the second part. The prediction is made by joining the two parts. By applying this process to the prediction of water levels on the downstream side of the gate at the inlet of Lake Kahokugata, Kanazawa, Japan, it becomes possible to predict the fluctuations of the water levels under arbitrary gate operations before one or two hours. As the state equation in the Kalman filtering algorithm, first- and second-order Markov models are adopted for the prediction. The result of the latter is better than that of the former.

A second-order Markov Gravity Anomaly Model

A second-order Markov process is proposed as a statistical model for gravity anomalies in a local region. The method is applied to the analysis of errors in an inertial navigation system caused by unknown gravity phenomena. Statistical models of vertical deflection obtained from the anomaly model by means of the Vening Meinesz equations yield predictions of rms position and velocity errors for the navigation system. Actual vertical deflection data are used as simulated inputs to a computer model of an inertial navigator; resulting system errors are compared with errors predicted by the proposed model. The results demonstrate the validity of the second-order Markov model in analyzing errors in an inertial navigation system.

Statistical Properties of Dunes Generated by Undirectional Water Currents: ABSTRACT

Field and laboratory studies of ripples and dunes formed in sand by unidirectional water currents show for coarse and very fine sand that the ripple index is related to median particle size and to flow intensity as measured by a dimensionless shear stress parameter. However, for medium-grained sand (0.25-0.50 mm.) End_Page 476------------------------------ the ripple index is approximately constant and is independent of flow intensity. For medium-grained sand statistical properties of the ripples and dunes other than the ripple index are required to correlate the characteristics of the bed configurations with flow parameters. Two methods of analysis for medium sand have been developed. In the first, spectral analyses of profiles of the channel bed lead to a linear second-order Markov model which describes the essential statistical properties of the dunes. All the parameters of the model are simple linear functions of the water discharge per unit width of channel. One of the parameters, the standard deviation of the bed elevation about the mean, shows excellent correlation (correlation coefficient of 0.99) with unit water discharge for flows ranging from 0.7 to 10 cfs. per foot of width and for average dune lengths from 2-25 feet. The second method of analysis consists of defining distributions of dune lengths, amplitudes, ripple indices, and angles of downstream faces, and relating the moments of these distributions to flow characteristics. All the distributions are skewed, and the skewness correlates roughly with flow intensity. This analysis gives useful indications of the variations in the geometric properties of ripples and dunes, but it is time-consuming and requires extensive data. Moreover, the parameters describing the ripples and dunes show only a crude relation to flow characteristics. Of the two methods, the spectral analysis appears to be more useful. End_of_Article - Last_Page 477------------