K2 Algorithm Research Articles

Identifying vital nodes for yeast network by dynamic network entropy

BackgroundThe progress of the cell cycle of yeast involves the regulatory relationships between genes and the interactions proteins. However, it is still obscure which type of protein plays a decisive role in regulation and how to identify the vital nodes in the regulatory network. To elucidate the sensitive node or gene in the progression of yeast, here, we select 8 crucial regulatory factors from the yeast cell cycle to decipher a specific network and propose a simple mixed K2 algorithm to identify effectively the sensitive nodes and genes in the evolution of yeast.ResultsConsidering the multivariate of cell cycle data, we first utilize the K2 algorithm limited to the stationary interval for the time series segmentation to measure the scores for refining the specific network. After that, we employ the network entropy to effectively screen the obtained specific network, and simulate the gene expression data by a normal distribution approximation and the screened specific network by the partial least squares method. We can conclude that the robustness of the specific network screened by network entropy is better than that of the specific network with the determined relationship by comparing the obtained specific network with the determined relationship. Finally, we can determine that the node CDH1 has the highest score in the specific network through a sensitivity score calculated by network entropy implying the gene CDH1 is the most sensitive regulatory factor.ConclusionsIt is clearly of great potential value to reconstruct and visualize gene regulatory networks according to gene databases for life activities. Here, we present an available algorithm to achieve the network reconstruction by measuring the network entropy and identifying the vital nodes in the specific nodes. The results indicate that inhibiting or enhancing the expression of CDH1 can maximize the inhibition or enhancement of the yeast cell cycle. Although our algorithm is simple, it is also the first step in deciphering the profound mystery of gene regulation.

VertiBayes: learning Bayesian network parameters from vertically partitioned data with missing values

Federated learning makes it possible to train a machine learning model on decentralized data. Bayesian networks are widely used probabilistic graphical models. While some research has been published on the federated learning of Bayesian networks, publications on Bayesian networks in a vertically partitioned data setting are limited, with important omissions, such as handling missing data. We propose a novel method called VertiBayes to train Bayesian networks (structure and parameters) on vertically partitioned data, which can handle missing values as well as an arbitrary number of parties. For structure learning we adapted the K2 algorithm with a privacy-preserving scalar product protocol. For parameter learning, we use a two-step approach: first, we learn an intermediate model using maximum likelihood, treating missing values as a special value, then we train a model on synthetic data generated by the intermediate model using the EM algorithm. The privacy guarantees of VertiBayes are equivalent to those provided by the privacy preserving scalar product protocol used. We experimentally show VertiBayes produces models comparable to those learnt using traditional algorithms. Finally, we propose two alternative approaches to estimate the performance of the model using vertically partitioned data and we show in experiments that these give accurate estimates.

Implementation of K-Means, K-Medoid and DBSCAN Algorithms In Obesity Data Clustering

Obesity is an excessive accumulation of body fat and can be harmful to health. This study aims to understand the patterns and relationships between obesity data that have been obtained, so a data clustering step will be carried out using the K-Means, K-Medoid and DBSCAN algorithms. This study utilizes the Davies Bouldin Index (DBI) to determine the best cluster value comparison and validated. So the results of the best cluster value in processing obesity data are using the K-Means K2 algorithm with a value of 0.604. The K-Medoid algorithm obtained the best cluster k2, with a DBI value of around 0.614. and the DBSCAN algorithm clustering trial K3, with a value of 1.040. Thus in this study the comparison results of the application of 3 clustering algorithms, the results obtained are the K-Means algorithm shows the value of the resulting cluster is the best of other algorithms in clustering obesity data with a value of 0.604.

Data and knowledge collaborative-driven fault identification and self-healing control action inference framework for blast furnace

The blast furnace reactor has a large volume, and smelting occurs at high temperatures and high-pressure environments. The blast furnace reactor has a large volume, and smelting occurs at high temperatures and high-pressure environments. Considering the small samples of fault data and non-stationarity of the production process with a considerable time lag, it is difficult to diagnose and eliminate the faults timely. This paper proposes for the first time a data and knowledge collaborative-driven framework to identify fault and perform self-healing control. Following the adaptive two-scale sequence division method, the prior knowledge matrix refined K2 algorithm is used to construct Bayesian networks to model the control process. When a new abnormal condition arises, the most similar historical sequence will be found, and inference on the corresponding Bayesian network can lead to fault identification results and self-healing control action. The proposed framework has achieved satisfactory results in simulation experiments and real data experiments. In the simulation data, the Bayesian network (BN) modeling achieved an accuracy of 98.75%, and the time required for structure learning of the BN was reduced by over 75.69%. In real data, the accuracy of identifying blast furnace faults reached 97.1%, and the results of self-healing control reasoning surpassed those of traditional BN reasoning methods in terms of correctness, order, completeness, and necessity.

Development of a CFD model to simulate the dispersion of atmospheric NH3 in a semi-open barn

The dispersion of atmospheric NH3 constitutes the most common passive polluting system in cattle stables. Although the studies carried out through computational fluid dynamics (CFD) are focused on improving the environmental conditions in situ to increase the productivity of stables, they do not refer to determining the environmental impact of NH3 emissions into the atmosphere. This work evaluated the distribution of the NH3 flux inside a barn using CFD and its relationship with environmental conditions through probabilistic analysis by the K2 algorithm. The initial data on environmental conditions were wind speed and direction, maximum temperature, and humidity from the nearest weather station in a region characterized by hot weather conditions during summer. The vertical trajectory was used to analyze the impact of long-range transport on the spatial distribution, where 75% is between 0 and 5 m in height, and 25% is between 10 and 20 m outside the eaves. The work concluded that temperature is the main parameter of influence.

PSO-K2PC: Bayesian structure learning using optimized K2 algorithm for parents-children detection

Bayesian networks, revered for their adeptness in modeling uncertainty and predicting outcomes, encounter a formidable hurdle during the structure learning phase – an NP-hard problem, posing insurmountable computational challenges for large networks. To surmount this barrier and advance the field, we propose an innovative optimization of the K2PC algorithm for Bayesian network structure learning. Derived from the popular K2 algorithm, our novel optimization ingeniously tackles K2PC's vulnerability to predetermined node order. Leveraging the power of a particle swarm optimization algorithm, we adeptly seek the optimal node ordering, yielding exceptional results. Through rigorous evaluations on benchmark networks, our proposed method surpasses prior approaches in structure difference and accuracy, affirming its potential as a promising avenue for Bayesian network structure learning in large, complex networks. We posit that our novel approach constitutes an important advance in the field of Bayesian network structure learning, with the potential to stimulate additional progress through further scientific investigation.

Research on the prediction model of hazardous chemical road transportation accidents

In recent years, hazardous chemicals road transport accidents have occurred frequently, causing huge casualties and property losses, and accident risk assessment has become the focus of researchers' research. To predict the risk probability value of hazardous chemical road transport accidents, first, we compiled data on road transportation accidents of hazardous chemicals in China in the past five years. And the nine nodes in the Bayesian network (BN) structure were defined in combination with relevant classification standards. The optimal Bayesian network structure for hazardous chemical road transport accidents was determined based on the K2 algorithm and the causalities between the nodes. Second, the node conditional probabilities were derived by parameter learning of the model using Netica, and the validity of the model was verified using the 5-fold cross-validation method. Last, the Bayesian network model of hazardous chemical road transport accidents is used to analyze accident examples, and the accident chain of “rear-end-leakage” is predicted, and the accident is most likely to be disposed of within 3–9 h. The study shows that the derived accident prediction model for hazardous chemical road transportation can reason reasonably about the evolution of accident scenarios and determine the probability values of accident risks under different parameter conditions.

Multi-objective optimal allocation of distributed generation considering the spatiotemporal correlation of wind-photovoltaic-load

• A multi-objective DG planning model is developed from the perspective of multi-dimensional data mining. • The model is used to solve the correlation analysis for wind speed, light intensity, and load demand of adjacent regions. • The spatiotemporal correlation, economic and system safety and environmental benefits are considered. • The effects of the seasonal difference on the favorable level of the DG's grid connection have been investigated. Aiming at the problem of the distributed generation (DG) planning caused by the strong spatiotemporal coupling between DG output and load demand in adjacent areas, a multi-objective planning model is proposed to describe the spatiotemporal correlation of sources. By combining the most weight supported tree (MWST) and depth first search (DFS), the method achieves the a priori requirement for constructing bayesian network (BN) structure using the K2 algorithm. Then, the MDK2-BN model is established through the measured data, which can describe the correlation between multi-dimensional wind-photovoltaic-load. A DG multi-objective programming model with maximum annual profit rate and minimum comprehensive operation risk is constructed. The results has three main advantages: (1) the MDK2-BN structure can achieve satisfactory results when dealing with small networks. (2) the MDK2-BN model conforms to the spatiotemporal correlation of the DG output, and the proposed configuration can improve the access capacity of DG. (3) the favorable level of the DG's grid connection can be effectively improved by considering the seasonal difference in performance and providing the planners with the decision-making references that balance the economic benefits, system operational safety, and environmental benefits.

Mental Health and Safety Assessment Methods of Bus Drivers

To explore the influence of the health psychology characteristics of bus driver on the probability of traffic accidents, such as the severity of unhealthy psychology and negative and impulsive personality. Combined with the demographic questionnaire, SCL-90 scale, and Y-G scale, the psychological factors of drivers causing traffic accidents were evaluated. The key factors selected by binary logistic regression analysis are used as node variables, and the Bayesian network structure was established by combining the K2 algorithm and expert knowledge. The EM algorithm was used for parameter learning. The work identified seven key factors that made bus drivers prone to accidents. The most likely factors were moderate depression, mild anxiety, and mild somatization. Bus drivers in the accident group were significantly more anxious, depressed, and more hypersensitive and emotionally unstable than drivers in the non-accident group. The psychological scale and a Bayesian network model were used to evaluate the mental health and traffic safety of bus drivers. It shows that different degrees of depression, anxiety, and different degrees of subjective and cyclical personality of bus drivers had different effects on traffic safety.

Risk Assessment and Prediction of Underground Utility Tunnels Based on Bayesian Network: A Case Study in Beijing, China

The underground utility tunnels accommodate various types of urban lifelines, which are of great significance for improving the living standards of the citizens. With the rapid development of underground utility tunnels, the large-scale underground utility tunnel systems are gradually becoming the operational lifeblood of China’s large cities. Currently, most of the underground utility tunnels’ risks are estimated and analyzed from a static perspective, and the analysis results are one-sided. This study proposes a dynamic risk evaluation framework. A risk assessment and sensitivity analysis framework based on Bayesian network is established in this study. Combined with the groundwater and electric tunnel risk accident case study, the operation and maintenance data of Beijing Future Science and Technology City from 2010 to 2018 are collected for learning to obtain the conditional probability of the Bayesian network node by using the K2 algorithm. The overall evolution process from the beginning to the end of groundwater tunnel accidents is clearly described and displayed. Through sensitivity analysis and critical path analysis, the critical points of an accident and the probabilities of risk occurrence are identified and predicted. This proposed framework could facilitate the underground utility tunnel management for controlling risk resources, mitigating risk damage and reducing risk losses.

A Bayesian network structural learning algorithm for calculating the failure probabilities of complex engineering systems with limited data

The failure of complex engineering systems is easy to lead to disastrous consequences. To prevent the failure, it is necessary to model complex engineering systems using probabilistic techniques with limited data which is a major feature of complex engineering systems. It is a good choice to perform such modeling using Bayesian network because of its advantages in probabilistic modeling. However, few Bayesian network structural learning algorithms are designed for complex engineering systems with limited data. Therefore, an algorithm for learning the Bayesian network structure of them should be developed. Based on the process of self-purification of water, a complex engineering system is segmented into three components according to the degree of difficulty in solving them. And then a Bayesian network learning algorithm with three components (TC), including PC algorithm, MIK algorithm which is originated by the paper through combining Mutual Information and K2 algorithm, and the Hill-Climbing method, is developed, i.e. TC algorithm. To verify its effectiveness, TC algorithm, K2 algorithm, and Max-Min Hill-Climbing are respectively used to learn Alarm network with different sizes of samples. The results imply that TC algorithm has the best performance. Finally, TC algorithm is applied to study tank spill accidents with 220 samples.

A new hybrid copula‐based nonparametric Bayesian model for risk assessments of water inrush

AbstractBayesian networks (BNs) can be automatically constructed with field data when the data can sufficiently support the objectivity of the model. However, in most risk assessments, field data cannot effectively support learning with BNs. In this paper, a new hybrid method is proposed to construct BNs and estimate the corresponding parameters considering the objectivity of field data and the accessibility of expert knowledge. This method is combined with the ISM‐K2 (interpretive structural model) algorithm, copula theory, and the nonparametric method. First, the ISM is used to identify the relationships among the directly and indirectly related variables (i.e., obtain the parent variable set). Second, based on the parent variable set, the K2 algorithm is used to construct BNs with the search volume reduced from an exponential to a quadratic form. Third, copula theory is introduced to consider several marginal distributions of variables, and a copula parameter is used to replace the multivariate joint cumulative distribution. The Gumbel copula function is first introduced to replace the often‐used normal copula function. Fourth, four types of distributions are utilized to fit the characteristics of the variables as the marginal distribution by using a nonparametric method. Finally, the proposed method was used to construct BNs for water inrush and estimate the risk of water inrush for a tunnel.

Bayesian Network Structure Learning Approach Based on Searching Local Structure of Strongly Connected Components

Learning the structure of Bayesian networks is a challenging problem because it is a NP-Hard problem. As an excellent search & score based method, the K2 algorithm strongly depends on the input of global order of all nodes to ensure the result is a directed acyclic graph. And the K2 algorithm searches parents for each node from the nodes before it in the global order. Incorrect node order is likely to result in a wrong structure. In this paper, we propose a new method to avoid the global order by Local structure Searching for Strongly Connected Components with hill climbing method Twice. Firstly, we search the best parent nodes for each node from all the remaining nodes except itself, and form a global directed graph by concatenating the arcs between nodes and their parents. Then, the directed acyclic structure of all the strongly connected components are determined by hill climbing algorithm twice. Finally, we adopt local search method further to get the final result by taking the previous result as start point. The proposed algorithm is evaluated on some standard benchmark networks with sampled data. Experimental results show that our algorithm outperforms the four compared algorithms in terms of structural Hamming distance, Bayesian information criterion score and their average ranking.

A Mobile Bayesian Network Structure Learning Method Using Genetic Incremental K2 Algorithm and Random Attribute Order Technology

The application of existing datasets to construct a probabilistic network has always been the primary research focus for mobile Bayesian networks, particularly when the dataset size is large. In this study, we improve the K2 algorithm. First, we relax the K2 algorithm requirements for node order and generate the node order randomly to obtain the best result in multiple random node order. Second, a genetic incremental K2 learning method is used to learn the Bayesian network structure. The training dataset is divided into two groups, and the standard K2 algorithm is used to find the optimal value for the first set of training data; simultaneously, three similar suboptimal values are recorded. To avoid falling into the local optimum, these four optimal values are mutated into a new genetic optimal value. When the second set of training data is used, only the best Bayesian network structure within the five abovementioned optimal values is identified. The experimental results indicate that the genetic incremental K2 algorithm based on random attribute order achieves higher computational efficiency and accuracy than the standard algorithm. The new algorithm is especially suitable for building Bayesian network structures in cases where the dataset and number of nodes are large.

A method for detecting causal relationships between industrial alarm variables using Transfer Entropy and K2 algorithm

Advances in technology allowed the fast and easy creation and configuration of industrial alarms. The growth in the number of alarms, however, brought some problems to the alarm management systems, for example, alarm flooding. In this paper, it is propose a new method to detect the causal relationships between industrial alarm variables using Transfer Entropy theory and the structural learning of the Bayesian networks K2 Algorithm as its fundamental basis. This work argues that the detection of these relationships can help to reduce the number of alarms in the alarm management systems, avoiding the overloading of operators in case of plant failures. To validate the proposal, a case study using the well-known plant-wide simulator Tennessee Eastman Process was performed. In this study case the graph of the causal relationships obtained by the proposed method was compatible with the system functioning.

Constructing the Electronic Countermeasures System Architecture Based on Case-Based Reasoning and Bayesian Inference

In order to promote the quality of electronic countermeasures system architecture, this paper present a methodology for constructing the electronic countermeasures system architecture based on case-based reasoning and Bayesian inference. The methodology described history cases by CPN model, established the largest similarity case and feasibility space by combining the CPN color set and k-means algorithm, and then proposed the optimizing orderings of variables of Bayesian by the LFS (Legal Firing Sequence) of CPN model and maximum information entropy, learned the Bayesian networks structure by K2 algorithm using the result of orderings of variables. At last, this paper concluded the electronic countermeasures system architecture tactics and discussed the way of reasoning for constructing the electronic countermeasures system architecture.

A Bayesian network model for fault diagnosis of a lock mechanism based on degradation data

This paper aims to build a diagnosis model of a lock mechanism system considering multiple joints wear. The lock mechanism is a complex mechanical system. Diagnosis is difficult because fault modes are not easy to identify. The diagnosis result is affected by the strong dependence of wear between each component. Besides, some lock mechanism’s wear detection data is challenging to acquire because of fewer sensors in some particular situations. For these problems, an improved Bayesian network-based fault diagnosis methodology considering component degradation is proposed to distinguish the fault types. An experiment of congeneric lock mechanisms is conducted, and wear data of the joints is obtained. The Bayesian networks model in which the dependence of components is not considered is established based on experimental data. Because the Bayesian network structure is affected by the strong dependence between components, the K2 algorithm is used to build the Bayesian network structure based on acquired wear data to obtain causality between components. The entire fault model is built by combining two established Bayesian networks. Three fault diagnosis cases are used to validate the accuracy and efficiency of the proposed model. A comparison is made between the improved diagnosis model and the model without considering dependence. Finally, the revolute joints are ranked by the established diagnostic model so that the weakest component can be identified.

A Bayesian approach for major European football league match prediction

This paper presents a Bayesian Approach for Major European Football League match prediction. In this study, four variants of Bayesian approaches are investigated to observe the impact of different structural learning algorithms within the family of Bayesian Network which are Naive Bayes (NB), Tree Augmented Naive Bayes (TAN) and two General Bayesian Networks (GBN); K2 algorithm with BDeu scoring function (GBN-K2) and Hill Climbing algorithm with MDL scoring function (GBNHC). The predictive performance of all Bayesian approaches is evaluated and compared based on football match results from five major European Football League consisting of three complete seasons of 1,140 matches. The results showed that GBN-HC gained 92.01% of accuracy while GBN-K2 and TAN produced comparable results with 91.86% and 91.94% accuracy, respectively. The lowest result was produced by NB, with only 72.78% accuracy. The results suggest that TAN requires further exploration in football prediction with its ability to cater the minimal dependency among attributes in a small-sized dataset.

Improved Key Recovery Attacks on Simplified Version of K2 Stream Cipher

Abstract The K2 stream cipher, designed for 32-bit words, is an ISO/IEC 18033 standard and is listed as a recommended algorithm used by the Japanese government in the CRYPTREC project. The main feature of the K2 algorithm is the use of a dynamic feedback control mechanism between the two linear feedback shift registers, which makes the analysis of the K2 algorithm more difficult. In this paper, for its simplified version algorithm, a key recovery attack is performed by using differential attacks. Firstly, for the unknown key, the same IV is fixed in two chosen IV differential attacks, and we use the input differences and the output differences of the S-box to recover the input of S-box; the internal state values can be uniquely determined by taking intersection of the input of S-box. This technology is used to improve the key recovery attack of seven-round algorithm proposed by Deike Priemuth-Schmid. Secondly, we find the constraint relationship between the keystream equations and the unknown differences by introducing the guess difference bit and eliminate the impossible differences by the constraint relationship. Thus, we expand the key recovery attack from seven to nine rounds. The time complexity of the attack is $\boldsymbol{O} \boldsymbol{(2^{113.93})}$, the data complexity is $\boldsymbol{O}\boldsymbol{(2^{8.71})}$ and the success rate is $\textbf{99.07\%}$.

Dynamic Knowledge Inference Based on Bayesian Network Learning

On the basis of studying datasets of students' course scores, we constructed a Bayesian network and undertook probabilistic inference analysis. We selected six requisite courses in computer science as Bayesian network nodes. We determined the order of the nodes based on expert knowledge. Using 356 datasets, the K2 algorithm learned the Bayesian network structure. Then, we used maximum a posteriori probability estimation to learn the parameters. After constructing the Bayesian network, we used the message-passing algorithm to predict and infer the results. Finally, the results of dynamic knowledge inference were presented through a detailed inference process. In the absence of any evidence node information, the probability of passing other courses was calculated. A mathematics course (a basic professional course) was chosen as the evidence node to dynamically infer the probability of passing other courses. Over time, the probability of passing other courses greatly improved, and the inference results were consistent with the actual values and can thus be visualized and applied to an actual school management system.