Minimum Description Length Method Research Articles

Two dimensional automatic active shape model of degenerative disc repaired by low-intensity laser.

Intervertebral disc degeneration is the main factor causing low back pain, and the related long-term treatment can improve the situation of degeneration. This study aimed to investigate the effect of low-intensity laser irradiation on the repair of degenerative intervertebral disc by two dimensional automatic active shape model (2D-AASM). Nine Bama miniature pigs were randomly divided into three groups: control group (Con), model group (Mod) and laser treatment group (Las). After one month, the discs were treated with low-energy laser for another month. MRI was performed for one month, and the statistical shape model and 2D-AASM of intervertebral disc were established based on the minimum description length method. The model established by the proposed method is more accurate and the segmentation result is more accurate. From the segmented T2-weighted image, the signal intensity of the Mod group decreased significantly, and the signal intensity in the Las group was moderate and high compared with the Mod group. The HE staining display the structure of Con group was damaged, and the construction of Las group was restored compared with Mod group. The 2D-AASM method effectively improves the accuracy of intervertebral disc segmentation. The low-intensity laser has a protective effect on the repair of the degenerative intervertebral disc.

Novel trajectory privacy-preserving method based on prefix tree using differential privacy

Location-based services, such as DiDi and bike sharing, are becoming increasingly popular. However, the use of these services raises privacy concerns. In the past few years, differential privacy technology has been applied to location information protection. However, most existing models largely fail to resist complex background-knowledge attacks. This paper proposes a novel privacy preservation method for trajectory data. It is based on a prefix tree and uses differential privacy. It should be noted that existing methods only consider either a certain location point or the entire trajectory. In the proposed prefix tree structure, the nodes of the tree store the trajectory segments. The parameter minimum description length method is combined with the Dijkstra method to select feature trajectory points that represent the entire trajectory, thus further reducing the (computational) complexity of data processing. To protect privacy, Laplacian noise is added to the location data of trajectory segments by using differential privacy. In addition, a background and contextual information attack model is proposed, and the corresponding protection method is provided. Finally, a Markov chain is used to limit the size of the noise added to the data. The proposed algorithm is compared with related state-of-the-art algorithms on a public dataset. The results demonstrate that our algorithm can ensure not only privacy but also data availability.

Source number estimation based on a novel multi-view meta-hierarchical classification framework

Accurately measuring the direction of arrival (DOA) is one of the most important issues in multiple sensor/antenna array monitoring scenarios. However, as a necessary parameter of almost all state-of-the-art DOA estimation methods, the source number is normally hard to determine using the traditional Akaike information criterion or minimum description length methods, especially in low or very low signal-to-noise ratio (SNR) conditions. In this paper, we propose to estimate the source number in a data-driven manner by employing a novel multi-view meta-hierarchical classification framework. Specifically, there are two collaborative views and two hierarchical classification layers employed for generating meta-features. Then, the obtained meta-features are re-learned by the final meta-classification layer to estimate the final prediction of the source number. Experimental results illustrated that the proposed method can estimate the source number accurately and reliably even in low SNR conditions.

Model-Aided Deep Neural Network for Source Number Detection

Source number detection is a critical problem in array signal processing. Conventional model-driven methods e.g., Akaikes information criterion (AIC) and minimum description length (MDL), suffer from severe performance degradation when the number of snapshots is small or the signal-to-noise ratio (SNR) is low. In this paper, we exploit the model-aided based deep neural network (DNN) to estimate the source number. Specifically, we first propose the eigenvalue based regression network (ERNet) and classification network (ECNet) to estimate the number of non-coherent sources, where the eigenvalues of the received signal covariance matrix and the source number are used as the input and the supervise label of the networks, respectively. Then, we extend the ERNet and ECNet for estimating the number of coherent sources, where the forward-backward spatial smoothing (FBSS) scheme is adopted to improve the performance of ERNet and ECNet. Numerical results demonstrate the outstanding performance of ERNet and ECNet over the conventional AIC and MDL methods as well as their excellent generalization capability, which also shows their great potentials for practical applications.

Reservoir water level forecasting using group method of data handling

Accurately forecasted reservoir water level is among the most vital data for efficient reservoir structure design and management. In this study, the group method of data handling is combined with the minimum description length method to develop a very practical and functional model for predicting reservoir water levels. The models’ performance is evaluated using two groups of input combinations based on recent days and recent weeks. Four different input combinations are considered in total. The data collected from Chahnimeh#1 Reservoir in eastern Iran are used for model training and validation. To assess the models’ applicability in practical situations, the models are made to predict a non-observed dataset for the nearby Chahnimeh#4 Reservoir. According to the results, input combinations (L, L−1) and (L, L−1, L−12) for recent days with root-mean-squared error (RMSE) of 0.3478 and 0.3767, respectively, outperform input combinations (L, L−7) and (L, L−7, L−14) for recent weeks with RMSE of 0.3866 and 0.4378, respectively, with the dataset from https://www.typingclub.com/st . Accordingly, (L, L−1) is selected as the best input combination for making 7-day ahead predictions of reservoir water levels.

Improvement of Source Number Estimation Method for Single Channel Signal.

Source number estimation methods for single channel signal have been investigated and the improvements for each method are suggested in this work. Firstly, the single channel data is converted to multi-channel form by delay process. Then, algorithms used in the array signal processing, such as Gerschgorin’s disk estimation (GDE) and minimum description length (MDL), are introduced to estimate the source number of the received signal. The previous results have shown that the MDL based on information theoretic criteria (ITC) obtains a superior performance than GDE at low SNR. However it has no ability to handle the signals containing colored noise. On the contrary, the GDE method can eliminate the influence of colored noise. Nevertheless, its performance at low SNR is not satisfactory. In order to solve these problems and contradictions, the work makes remarkable improvements on these two methods on account of the above consideration. A diagonal loading technique is employed to ameliorate the MDL method and a jackknife technique is referenced to optimize the data covariance matrix in order to improve the performance of the GDE method. The results of simulation have illustrated that the performance of original methods have been promoted largely.

Source Enumeration Based on the Singular Vector of Hankel Matrix for Low Signal-to-Noise Ratio

Most existing source enumeration techniques in sensor-based studies have a satisfactory performance in high or middle signal-to-noise ratio (SNR), but lose effectiveness at low SNR. After Hankel matrices with different referenced signals and changeable dimensions are constructed, a source enumeration method is proposed based on the squared Euclidean norm of the product vector of the steering matrix and left singular vectors of Hankel matrix for low SNR. The proposed method employs the blind beamforming technique to estimate the steering matrix and the spatial smoothing scheme to dispose the dimension mismatched problem. Simulations are performed to display the validation for the non-coherent and coherent source signals and better enumeration performance at low SNR, in comparison with the conventional Akaike information criterion and minimum description length methods.

Improved MDL method for estimation of source number at subarray level

The eigenvalue-based minimum description length (MDL) method for source number estimation is widely applied in practical scenarios. However, the performance of the MDL method degrades significantly when it is applied to an asymmetrical subarray situation due to the inequality of the noise power of each channel. Therefore, an improved MDL method for subarray level is proposed by normalising noise power to reconstruct the received signal covariance matrix. Simulation results show that the proposed method outperforms the conventional source number estimation methods for a subarray situation.

Improvement of Statistical Shape Models for Soft Tissues Using Modified-Coherent Point Drift

In this paper, we present a method to build statistical shape models for soft tissues. The efficiency of the model is close to the models built by the MDL (Minimum Description Length) algorithm; however, our method is much faster. The core of our method is based on finding corresponding points by a modified Coherent Point Drift method. The conventional CPD algorithm is modified to prepare a robust methods to find corresponding points of soft tissues. Our method achieved the Compactness, Generality, and Specificity of 18, 3.64(±0.85) mm, and 0.21(±0.06) respectively. Our results are close to the MDL results. The run-time of our method is 68 seconds which is faster than the MDL (3600 seconds) and TPS-RPM (390 seconds) methods.

Segmentation algorithm of intervertebral disc magnetic resonance images based on two-dimensional automatic active shape model

In response to the issue that the intervertebral disk manual modeling was time-consuming and subjective, and the existing segmentation method was not accurate enough, a new method named two-diememsional Automatic Active Shape Model( 2D-AASM) was proposed. It included three parts: automatic statistical shape modeling of intervertebral disk based on minimum description length, 2D local gradient modeling and segmentation. Adopting the manual segmentation results of 25sets of spinal MR images as the training set, the study used minimum description length method to determine the point correspondence, built statistical shape model and 2D local gradient model for intervertebral disk T4-5. The generated shape model had lower variance and the objective function value than the manual and arc length parameter method. After the model was built, three sets of Magnetic Resonance Image( MRI) images were used to test the proposed method. Compared with the traditional ASM and 1D-ASM, the segmentation result of the proposed method had a higher Dice coefficient and lower oversegmentation and under-segmentation rate. The experiment results indicate that the proposed method generates a better model and more accurate segmentation result.

Particle System Based Adaptive Sampling on Spherical Parameter Space to Improve the MDL Method for Construction of Statistical Shape Models

Minimum description length (MDL) based group-wise registration was a state-of-the-art method to determine the corresponding points of 3D shapes for the construction of statistical shape models (SSMs). However, it suffered from the problem that determined corresponding points did not uniformly spread on original shapes, since corresponding points were obtained by uniformly sampling the aligned shape on the parameterized space of unit sphere. We proposed a particle-system based method to obtain adaptive sampling positions on the unit sphere to resolve this problem. Here, a set of particles was placed on the unit sphere to construct a particle system whose energy was related to the distortions of parameterized meshes. By minimizing this energy, each particle was moved on the unit sphere. When the system became steady, particles were treated as vertices to build a spherical mesh, which was then relaxed to slightly adjust vertices to obtain optimal sampling-positions. We used 47 cases of (left and right) lungs and 50 cases of livers, (left and right) kidneys, and spleens for evaluations. Experiments showed that the proposed method was able to resolve the problem of the original MDL method, and the proposed method performed better in the generalization and specificity tests.

Minimum Description Length Methods in Bayesian Model Selection: Some Applications

Computations involved in Bayesian approach to practical model selection problems are usually very difficult. Computational simplifications are sometimes possible, but are not generally applicable. There is a large literature available on a methodology based on information theory called Minimum Description Length (MDL). It is described here how many of these techniques are either directly Bayesian in nature, or are very good objective approximations to Bayesian solutions. First, connections between the Bayesian approach and MDL are theoretically explored; thereafter a few illustrations are provided to describe how MDL can give useful computational simplifications.

PRESEE: An MDL/MML Algorithm to Time-Series Stream Segmenting

Time-series stream is one of the most common data types in data mining field. It is prevalent in fields such as stock market, ecology, and medical care. Segmentation is a key step to accelerate the processing speed of time-series stream mining. Previous algorithms for segmenting mainly focused on the issue of ameliorating precision instead of paying much attention to the efficiency. Moreover, the performance of these algorithms depends heavily on parameters, which are hard for the users to set. In this paper, we propose PRESEE (parameter-free, real-time, and scalable time-series stream segmenting algorithm), which greatly improves the efficiency of time-series stream segmenting. PRESEE is based on both MDL (minimum description length) and MML (minimum message length) methods, which could segment the data automatically. To evaluate the performance of PRESEE, we conduct several experiments on time-series streams of different types and compare it with the state-of-art algorithm. The empirical results show that PRESEE is very efficient for real-time stream datasets by improving segmenting speed nearly ten times. The novelty of this algorithm is further demonstrated by the application of PRESEE in segmenting real-time stream datasets from ChinaFLUX sensor networks data stream.

A demand forecast model using a combination of surrogate data analysis and optimal neural network approach

As rough or inaccurate estimation of demands is one of the main causes of the bullwhip effect harming the entire supply chain, we have developed a mathematical approach, the minimum description length (MDL), to determine the optimal artificial neural network (ANN) that can provide accurate demand forecasts. Two types of simulated customer and one practical demand are employed to validate the capability of the MDL method. Since stochastic factors hidden in the demand data disturb the prediction, the surrogate data method is proposed for identifying the characteristics of the demand data. This method excludes demands that are totally stochastic when forecasting. We demonstrate how optimal models estimated by MDL are consistent with the dynamics of demand data identified by the surrogate data method. The complementary approach of the surrogate data method and neural network constitutes a comprehensive framework for making various demand predictions. This framework is applicable to a wide variety of real-world data.

Flexible scan statistic test to detect disease clusters in hierarchical trees

This paper presents a flexible scan test statistic to detect disease clusters in data sets represented as a hierarchical tree. The algorithm searches through the branches of the tree and it is able to aggregate leaves located in different branches. The test statistic combines two terms, the log-likelihood of the data and the amount of information necessary to computationally code each potential cluster. This second term penalizes the search algorithm avoiding the detection of oddly shaped clusters and it is based on the Minimum Description Length (MDL) principle. Our MDL method reaches an automatic compromise between bias and variance. We present simulated results showing that its power performance as compared to the usual scan statistic and the high accuracy of the MDL to identify clusters that are scattered on the tree. The MDL method is illustrated with a large database looking at the relationship between occupation and death from silicosis.

False Alarm Rate Estimation for Information-Theoretic-Based Source Enumeration Methods

The Tracy-Widom distribution is used to determine the false alarm rate of information theoretic methods that statistically estimate the number of sources in a multichannel receiver input. The Tracy-Widom distribution is the limiting distribution for the largest eigenvalue of a covariancematrix having a central whiteWishart distribution. Such covariance matrices are produced by the output of multi-channel receivers whose signals can be characterized as zero-mean Gaussian processes. The Tracy-Widom distribution is used to estimate the false alarm rate of the Akaike Information Criterion and Minimum Description Length methods when no external sources are present. The Tracy-Widom distribution along with the eigenvalue inclusion principle is used to obtain an upper bound on the false alarm rate of the Akaike Information Criterion and Minimum Description Length when one external source is present. Monte-Carlo simulations were performed to demonstrate the effectiveness of both methods for cases where both the array and data sample sizes are small.

MDL Constrained 3-D Grayscale Skeletonization Algorithm for Automated Extraction of Dendrites and Spines from Fluorescence Confocal Images

This paper presents a method for improved automatic delineation of dendrites and spines from three-dimensional (3-D) images of neurons acquired by confocal or multi-photon fluorescence microscopy. The core advance presented here is a direct grayscale skeletonization algorithm that is constrained by a structural complexity penalty using the minimum description length (MDL) principle, and additional neuroanatomy-specific constraints. The 3-D skeleton is extracted directly from the grayscale image data, avoiding errors introduced by image binarization. The MDL method achieves a practical tradeoff between the complexity of the skeleton and its coverage of the fluorescence signal. Additional advances include the use of 3-D spline smoothing of dendrites to improve spine detection, and graph-theoretic algorithms to explore and extract the dendritic structure from the grayscale skeleton using an intensity-weighted minimum spanning tree (IW-MST) algorithm. This algorithm was evaluated on 30 datasets organized in 8 groups from multiple laboratories. Spines were detected with false negative rates less than 10% on most datasets (the average is 7.1%), and the average false positive rate was 11.8%. The software is available in open source form.

Minimum description length modelling of musical structure

This article presents a method of inductive inference whose aim is to build formal quantitative models of musical structure. The models are constructed by statistical extraction of significant patterns from a musical corpus. The minimum description length (MDL) principle is used to select the best model from among the members of a non-parametric model family characterized by an unbounded parameter set. The chosen model achieves optimal compromise between goodness-of-fit and model complexity, thereby avoiding the over-fitting normally associated with such a family of models. The MDL method is illustrated through its application to the Hidden Markov Model (HMM) framework. We derive an original mathematical expression for the MDL complexity of HMMs that employ a finite alphabet of symbols; these models are particularly suited to the symbolic modelling of musical structure. As an illustration, we use the proposed HMM complexity expression to construct a model for a common melodic formula in Greek church chant. Such formulas are characterized by text–tune association that is governed by complex rules. We show that MDL-guided model construction gradually ‘learns’ important aspects of the melodic formula's structure, and that the MDL principle terminates the process when nothing significant is left to learn. We outline how the musical applications of MDL can be extended beyond the HMM framework, and how they address general methodological concerns in empirical music research.

MMSE-Based MDL Method for Robust Estimation of Number of Sources Without Eigendecomposition

It is well known that the conventional eigenvalue-based minimum description length (MDL) approach for source number estimation suffers from high computational load and performs optimally only in the presence of spatially and temporally white noise. To improve the robustness of the MDL methodology, we propose to utilize the minimum mean square error (MMSE) of the multistage Wiener filter to calculate the required description length for encoding the observed data, instead of relying on the eigenvalues of the data covariance matrix. As there is no need to calculate the covariance matrix and its eigenvalue decomposition, our derived MMSE-based MDL (mMDL) method is also more computationally efficient than the traditional counterparts. Numerical examples are included to demonstrate the robustness of the mMDL detector in nonuniform noise.

MMSE-Based MDL Method for Accurate Source Number Estimation

In civilian communication systems, the signature sequence of the desired signal in training phase is known to the receiver. In this letter, using the mutual information, we bridge the probability density function and minimum mean-square error (MMSE) between the observed data and training sequence of the desired signal, and then employ the MMSE to construct a minimum description length (MDL) criterion for accurate source enumeration. Numerical results demonstrate that the proposed method is superior to existing MDL methods in terms of detection performance particularly for small number of snapshots and/or source angular separation.