Dimensionality Of High-dimensional Data Research Articles

Research on the Passenger Flow Distribution Mining of Urban Rail Transit Based on Clustering Algorithm: Taking Beijing as an Instance

Based on the principal component analysis and k-means cluster analysis, the paper classified and analyzed the 310 stations of the Beijing subway. According to data such as the number of people entering and leaving each station of the Beijing Metro, the line to which the station belongs, and whether it is a transfer station by period. We selected a total of 52-time variables to participate in the PCA analysis and finally got two principal components and named them principal component 1 and principal component 2. Subsequently, we clustered the Principal Component 1 and Principal Component 2 scores of 310 sites and the latitude and longitude of the sites in k-means clustering. According to the elbow method and the contour coefficient, the final clustering results into five clusters are classified. The five clusters of stations have strong regional characteristics, and the stations of each type are more concentrated. The results of principal component analysis and cluster analysis have passed the test and have good convincing power. Finally, we conduct an in-depth analysis of the two categories with the most stations. Cluster 4 contains the largest number of stations, located in the core area of Beijing's urban area, and the passenger flow is significantly higher than other areas. Cluster 1 contains the second largest number of stations, mainly including Fengtai District. The region's economy is underdeveloped, the passenger flow is small, and there are peak and trough periods. This paper performs cluster analysis on high-dimensional data. The principal component analysis is used to reduce the dimension of high-dimensional data and retain the time and space dimensions required for clustering. The final result was in line with expectations. It is improved the shortcomings of k-means clustering for high-dimensional data. This article analyzes the daily passenger flow in Beijing, and the analysis results may be random. In the subsequent analysis, more data can be added to make the analysis more accurate.

The study on systemic risk of rural finance based on macro–micro big data and machine learning

It’s the basic premise of promoting the healthy development of rural finance and strengthening macro-prudential supervision to measure the systemic risk of rural finance accurately. We establish the dynamic factor CAPM and make an all-round and multi-angle quantitative study on the systemic risk of rural finance in China by constructing macro–micro index system and using machine learning to reduce the dimension of high-dimensional data. Our results show that the dynamic factor CAPM of using macro–micro big data can evaluate systemic risk of rural finance more comprehensively and systematically, and machine learning performs well in processing high-dimensional data. In addition, China's rural financial systemic risk is stable compared with the Shanghai and Shenzhen main markets, but it is also susceptible to macro and micro influenced factors. Finally, it is pointed out that the early warning system of rural financial systemic risk could be constructed at macro and micro level, respectively.

Research on Type 2 Diabetes Risk based on Lifestyle Factors

Diabetes is a global chronic disease, and the number of patients and medical expenses are increasing. It is predicted that by 2045, the number of adult diabetics in the world will reach 693 million, and the expenditure on health care will increase to 958 billion US dollars. Diabetes can be divided into two types: type 1 and type 2, of which type 2 diabetes accounts for 95% of all diabetes cases. In this study, principal component analysis and stochastic forest algorithm are used to evaluate the performance of the model by using large-scale survey data and ROC curve, which provides a new idea for diabetes prediction research. The results show that the stochastic forest algorithm performs well in dealing with high-dimensional data, while the principal component analysis method can reduce the dimension of high-dimensional data, reduce redundant features and improve the prediction ability of the model. Therefore, the method proposed in this paper can help medical researchers to make better use of diabetes data for research, and provide a new method for diabetes risk prediction.

Study on EEG signal of epileptic patients based on NLSOMAP algorithm

Epilepsy is a chronic disease with sudden abnormal discharge of brain neurons, leading to transient brain dysfunction, which has a great impact on the physical and mental health of patients. In this paper, we use the NISOMAP manifold algorithm to reduce the dimension of high-dimensional data randomly selected from the public epilepsy data set, aiming at the disadvantage that the traditional supervised model is nonlinear in feature extraction. The experimental results show that, compared with other dimension reduction algorithms, NISOMAP has a better dimension reduction effect. The visualized shape is oval, with certain regularity, and it is convenient to observe the attack point. It is superior to other algorithms in different sample data, and provides great help for the diagnosis of epilepsy patients.

Locally generalized preserving projection and flexible grey wolf optimizer-based ELM for fault diagnosis of rolling bearing

It is a challenge for bearing fault diagnosis to effectively reduce the dimension of high dimensional data and improve the accuracy of fault identification. To address this issue, a novel fault diagnosis method based on locally generalized preserving projection (LGPP) and flexible grey wolf optimizer-based extreme learning machine (FGWO-ELM) is proposed in this paper. Firstly, the high dimensional features are obtained from the time–frequency domain of the signal. Secondly, a novel LGPP algorithm is proposed to reduce the dimension of high dimensional features more effectively. The algorithm uses a generalized discriminant matrix to calculate the degree similarity between data, rather than a simple Euclidean distance, so as to obtain sensitive features with better discrimination. Thirdly, a FGWO algorithm is proposed and used to optimize the parameters of ELM to improve the fault recognition rate. Finally, the effectiveness of the proposed fault diagnosis method is verified by two bearing experiments. Experimental results show that compared with other methods, the proposed method not only has the better dimension reduction ability, but also has higher diagnostic accuracy.

Research on Learner Modeling and Curriculum Recommendation Based on Emotional Factors

With the increasing with the number of courses, learners cannot find the courses they need quickly. Therefore, the primary problem to change the efficiency of online courses is to recommend corresponding courses for a certain group of people according to their needs. Learner characteristics are an important aspect of reflecting learner preferences, and learner models are abstract representations and descriptions of learner characteristics. It is necessary to enhance the use of online courses among students; we must build a relatively comprehensive curriculum model. At present, the construction of learner model is mostly based on cognitive level and learning style, ignoring the emotion expressed by learners to the curriculum, and emotion is a very important characteristic of learners. In order to establish a perfect learner model, it is necessary to incorporate learners’ aspect emotion into the learner model to make the course recommendation process more accurate. Firstly, based on the attention mechanism long-term and short-term memory network, this paper extracts the learner’s aspect emotion to the curriculum from the learner’s curriculum review. At the same time, it studies various characteristics, such as demography, cognitive level, motor behavior, and learning style. By establishing a perfect model integrating researchers’ emotional state, finally, the complex interaction between learner characteristics and curriculum characteristics is modeled by using deep factor natural decomposition, so as to achieve accurate curriculum recommendation. In this study, the learner’s aspect emotion is included in the construction of learner model and enriched and perfected the learner model. It provides a reference for the theoretical research and applied research of learner model and has reference significance. At the same time, combining Deep learning can improve the accuracy of course recommendation, help learners’ learning efficiency and personalized learning quality, and also contribute to the long-term development of online platform. The mathematical modeling in this paper uses learning analysis technology and general factor model based on matrix factorization to calculate and uses factorization machine to reduce the dimension of high-dimensional data, which is efficient and accurate.

Optimize classification testing of apple juice combining derivative fluorescence spectroscopy with PCA

Cluster analysis of apple juice is an important method in the quality identification of fruit juice. However, the traditional principal component analysis (PCA) is to reduce the dimension of high dimensional data and to achieve clustering by way of score value. Experiments have found that this clustering method is not suitable for real samples with fluorescence overlap. In this paper, we propose a processing mechanism to optimize the derivative of the fluorescence spectrum. When the derivative is calculated, we can amplify the spectral difference of the similar matter and improve the ability of the PCA to achieve the best effect of clustering. Experiments show that the optimized method for the actual sample classification accuracy rate of 100%, which can fully realize the type of commercially available apple juice beverage distinction and achieve the practical application of quality testing.

Social e-commerce consumer behaviour prediction model based on hierarchical polarisation characteristics

In this paper, a social e-commerce consumer behaviour prediction model based on layered polarisation characteristics is constructed. Consumer characteristics, product characteristics and interaction features are the three aspects used to construct the social electricity consumer behaviour prediction index system; with the improved locally linear embedding method for social electricity consumer behaviour predictors of high-dimensional data dimension used to reduce processing. According to the hierarchical polarisation characteristics, social electricity consumer behaviour prediction index weight calculation was based on the weight coefficient to construct the complete prediction model of social e-commerce consumer behaviour based on the characteristics of stratified polarisation. The simulation results show that the established model can predict the consumer behaviour of social e-commerce with high accuracy and short prediction time.

Measuring the Similarity of Metro Stations Based on the Passenger Visit Distribution

The distribution of passengers reflects the characteristics of urban rail stations. The automatic fare collection system of rail transit collects a large amount of passenger trajectory data tracking the entry and exit continuously, which provides a basis for detailed passenger distributions. We first exploit the Automatic Fare Collection (AFC) data to construct the passenger visit pattern distribution for stations. Then we measure the similarity of all stations using Wasserstein distance. Different from other similarity metrics, Wasserstein distance takes the similarity between values of quantitative variables in the one-dimensional distribution into consideration and can reflect the correlation between different dimensions of high-dimensional data. Even though the computational complexity grows, it is applicable in the metro stations since the scale of urban rail transit stations is limited to tens to hundreds and detailed modeling of the stations can be performed offline. Therefore, this paper proposes an integrated method that can cluster multi-dimensional joint distribution considering similarity and correlation. Then this method is applied to cluster the rail transit stations by the passenger visit distribution, which provides some valuable insight into the flow management and the station replanning of urban rail transit in the future.

Adaptive graph-based generalized regression model for unsupervised feature selection

Unsupervised feature selection is an important method to reduce dimensions of high-dimensional data without labels, which is beneficial to avoid “curse of dimensionality” and improve the performance of subsequent machine learning tasks, like clustering and retrieval. A lot of methods have been developed in recent years. However, most of them only focus on selecting discriminative features but ignore the redundancy of features. Besides, these methods construct the similarity structure of data in the original input space and remain fixed during feature selection. The similarity structure is easily affected by the noises and outliers. Then the reliability of the similarity structure will be reduced in the procedure of feature selection. In order to address these issues, we present a novel generalized regression model equipped with an uncorrelated constraint and the ℓ2,1-norm regularization. It can simultaneously select the uncorrelated and discriminative features as well as reduce the variance of these data points belonging to the same neighborhood, which is helpful for the clustering task. Furthermore, to obtain the similarity structure of data and alleviate the influence of noises and outliers, we propose to adaptively learn a similarity-induced graph matrix in the reduced space and integrate it into the generalized regression model. An alternative iterative optimization algorithm is developed to solve the final objective function. A series of experiments are carried out on nine real-world data sets to demonstrate the effectiveness of the proposed method in comparison with other competing approaches.

Non-invasive load identification based on LSTM-BP neural network

Smart power consumption is an important part of ubiquitous power Internet of things. Load identification, as an important part of smart power consumption, is of great significance to users and power grid. Aiming at the problems of long training time and low recognition accuracy in existing algorithms, this paper proposes a non-invasive load identification algorithm based on LSTM-BP. Firstly, the data is normalized, and then the dimension of high-dimensional data is reduced by PCA. Then, LSTM-BP neural network is built for load identification. Finally, Redd data set is used to test and analyze the algorithm. Compared with the existing load identification algorithm based on event detection, this method has higher stability and accuracy.

Towards an efficient real-time kernel function stream clustering method via shared nearest-neighbor density for the IIoT

The rapid development of 5G communication technology will considerably help the expansion and gth Industrial Internet of things (IIoT). Indeed, both the data scale and dimension will significantly increase, leading to a challenging problem of the effective real-time stream clustering in the field of IIoT streaming mining. This paper proposes an efficient and novel real-time kernel function stream clustering method based on shared nearest-neighbor density for IIoT. In the proposed method, the projection technology is used to select the dimensions of high-dimensional data, while the Euler kernel function is used as the similarity measure. Furthermore, the micro-clusters are divided by the shared nearest-neighbor density, and the outliers are relearned. The main innovation lies in using the Euler kernel function to measure the similarity, reduce the sensitivity of outliers, and use the relearning strategy to improve the clustering quality of the data stream. The theoretical analysis and experimental comparisons on the simulated data sets show that the proposed method is very effective and represents a good solution for clustering real-time data streams of IIoT.

Stable ant‐antlion optimiser for feature selection on high‐dimensional data

High-dimensional data exists widely in the real world, such as gene, magnetic resonance imaging (MRI), text, web data and so on. Feature selection is an effective and powerful method that is often adopted to reduce dimensions of high-dimensional data for promoting learning algorithm's ability to obtain useful information from them. However, feature selection stability lacks attention for a long time, which plays an important role in getting compelling results. This study proposes a stable feature selection approach called stable ant-antlion optimiser (SALO) that is a modified hybrid evolutionary method combining ant colony optimisation and antlion optimiser. Several relative stable filter methods are employed to rank features as guide information, fisher discriminant rate is used to evaluate features as heuristic information, and F1 indicator and the similarity between feature subset and stable ranked feature list are taken as optimisation objects. Comprehensive experiments show the fantasy stability and excellent classification performance of our proposed sophisticated method.

Application of Neural Network Algorithm Based on Principal Component Image Analysis in Band Expansion of College English Listening.

With the development of information technology, band expansion technology is gradually applied to college English listening teaching. This technology aims to recover broadband speech signals from narrowband speech signals with a limited frequency band. However, due to the limitations of current voice equipment and channel conditions, the existing voice band expansion technology often ignores the high-frequency and low-frequency correlation of the audio, resulting in excessive smoothing of the recovered high-frequency spectrum, too dull subjective hearing, and insufficient expression ability. In order to solve this problem, a neural network model PCA-NN (principal components analysis-neural network) based on principal component image analysis is proposed. Based on the nonlinear characteristics of the audio image signal, the model reduces the dimension of high-dimensional data and realizes the effective recovery of the high-frequency detailed spectrum of audio signal in phase space. The results show that the PCA-NN, i.e., neural network based on principal component analysis, is superior to other audio expansion algorithms in subjective and objective evaluation; in log spectrum distortion evaluation, PCA-NN algorithm obtains smaller LSD. Compared with EHBE, Le, and La, the average LSD decreased by 2.286 dB, 0.51 dB, and 0.15 dB, respectively. The above results show that in the image frequency band expansion of college English listening, the neural network algorithm based on principal component analysis (PCA-NN) can obtain better high-frequency reconstruction accuracy and effectively improve the audio quality.

A hybrid feature selection algorithm combining ReliefF and Particle swarm optimization for high-dimensional medical data

Due to high-dimensional feature and strong correlation of features, the classification accuracy of medical data is not as good enough as expected. feature selection is a common algorithm to solve this problem, and selects effective features by reducing the dimensionality of high-dimensional data. However, traditional feature selection algorithms have the blindness of threshold setting and the search algorithms are liable to fall into a local optimal solution. Based on it, this paper proposes a hybrid feature selection algorithm combining ReliefF and Particle swarm optimization. The algorithm is mainly divided into three parts: Firstly, the ReliefF is used to calculate the feature weight, and the features are ranked by the weight. Then ranking feature is grouped according to the density equalization, where the density of features in each group is the same. Finally, the Particle Swarm Optimization algorithm is used to search the ranking feature groups, and the feature selection is performed according to a new fitness function. Experimental results show that the random forest has the highest classification accuracy on the features selected. More importantly, it has the least number of features. In addition, experimental results on 2 medical datasets show that the average accuracy of random forest reaches 90.20%, which proves that the hybrid algorithm has a certain application value.

Half-Quadratic Minimization for Unsupervised Feature Selection on Incomplete Data.

Unsupervised feature selection (UFS) is a popular technique of reducing the dimensions of high-dimensional data. Previous UFS methods were often designed with the assumption that the whole information in the data set is observed. However, incomplete data sets that contain unobserved information can be often found in real applications, especially in industry. Thus, these existing UFS methods have a limitation on conducting feature selection on incomplete data. On the other hand, most existing UFS methods did not consider the sample importance for feature selection, i.e., different samples have various importance. As a result, the constructed UFS models easily suffer from the influence of outliers. This article investigates a new UFS method for conducting UFS on incomplete data sets to investigate the abovementioned issues. Specifically, the proposed method deals with unobserved information by using an indicator matrix to filter it out the process of feature selection and reduces the influence of outliers by employing the half-quadratic minimization technique to automatically assigning outliers with small or even zero weights and important samples with large weights. This article further designs an alternative optimization strategy to optimize the proposed objective function as well as theoretically and experimentally prove the convergence of the proposed optimization strategy. Experimental results on both real and synthetic incomplete data sets verified the effectiveness of the proposed method compared with previous methods, in terms of clustering performance on the low-dimensional space of the high-dimensional data.

Semi-supervised elastic manifold embedding with deep learning architecture

Graph-based embedding aims to reduce the dimension of high dimensional data and to extract relevant features for learning tasks. In this letter, we propose an Elastic graph-based embedding with deep architecture which deeply explores the structural information of the data. We introduce a flexible deep learning that can overcome the limitations and weaknesses of single-layer learning models. The proposed deep architecture incorporates the geometrical manifold structure of the data. The resulting framework can be used for semi-supervised and supervised settings. Besides, the resulting optimization problems can be solved efficiently. We apply the algorithm on five public image datasets including scene, face and object datasets. These experiments demonstrate the effectiveness of the proposed embedding method, and also show that the proposed method compares favorably with many competing state-of-the-art graph-based methods.

Unsupervised discriminative feature representation via adversarial auto-encoder

Feature representation is generally applied to reducing the dimensions of high-dimensional data to accelerate the process of data handling and enhance the performance of pattern recognition. However, the dimensionality of data nowadays appears to be a rapidly increasing trend. Existing unsupervised feature representation methods are susceptible to the rapidly increasing dimensionality of data, which may result in learning a meaningless feature that in turn affect their performance in other applications. In this paper, an unsupervised adversarial auto-encoder network is studied. This network is a probability model that combines generative adversarial networks and variational auto-encoder to perform variational inference and aims to generate reconstructed data similar to original data as much as possible. Due to its adversarial training, this model is relatively robust in feature learning compared with other methods. First, the architecture and training strategy of adversarial auto-encoder are presented. We attempt to learn a discriminative feature representation for high-dimensional image data via adversarial auto-encoder and take its advantage into image clustering, which has become a difficult computer vision task recently. Then amounts of comparative experiments are carried out. The comparison contains eight feature representation methods and two recently proposed deep clustering methods performed on eight different publicly available image data sets. Finally, to evaluate their performance, we utilize a K-means clustering on the low-dimensional feature learned from each feature representation algorithm, and select three evaluation metrics including clustering accuracy, adjusted rand index and normalized mutual information, to provide a comparison. Comprehensive experiments prove the usefulness of the learned discriminative feature via adversarial auto-encoder in the tested data sets.

A Dimension Reduction Method Based on Adaptive RBF Neural Network in Supervised Machine Learning

For the purpose of high dimensional data reduction in supervised machine learning, an adaptive RBF (Radial Basis Function) neural network algorithm was proposed. According to the relationship between the total error of this training and last training, the learning rate and momentum factor in the algorithm were adjusted dynamically and adaptively. So, the learning direction of RBF neural network was enhanced and the learning speed was improved. This algorithm was used to reduce the dimension of high dimensional data. The data set auto-mpg in UCI machine learning database was taken as an example to carry out dimension reduction experiments. The experimental results show that the learning performance of RBF neural network was improved and its general error was reduced after reducing the dimensionality of high dimensional data set by this algorithm. This reduction method is of great significance to solve the “dimensionality disaster” and “cost disaster” in machine learning.

Learning a discriminant graph-based embedding with feature selection for image categorization

Graph-based embedding methods are very useful for reducing the dimension of high-dimensional data and for extracting their relevant features. In this paper, we introduce a novel nonlinear method called Flexible Discriminant graph-based Embedding with feature selection (FDEFS). The proposed algorithm aims to classify image sample data in supervised learning and semi-supervised learning settings. Specifically, our method incorporates the Manifold Smoothness, Margin Discriminant Embedding and the Sparse Regression for feature selection. The weights add ℓ2,1-norm regularization for local linear approximation. The sparse regression implicitly performs feature selection on the original features of data matrix and of the linear transform. We also provide an effective solution method to optimize the objective function. We apply the algorithm on six public image datasets including scene, face and object datasets. These experiments demonstrate the effectiveness of the proposed embedding method. They also show that proposed the method compares favorably with many competing embedding methods.