Complexity-invariant Distance Research Articles

Quantitative Methods for Analyzing Second Language Lexical Tone Production

The production of L2 lexical tone has proven difficult for learners of tonal languages, leading to the testing of different tone training techniques. To test the validity of these techniques, it is first necessary to capture the differences between L1 and L2 tone datasets. The current study explores three analyses designed to compare L1 and L2 tone: (1) using a single deviation score, (2) using deviation score calculations for specific regions of tone productions, and (3) applying a complexity-invariant distance measure to the two time series datasets. These three analyses were tested using datasets sampled from a previous study testing the effects of a visual feedback paradigm on the production of L2 Mandarin tone. Results suggest the first two analyses, although useful for providing an overall evaluation of how L2 speakers’ pretest versus posttest productions compare to L1 speakers, lose critical information about tone, namely pitch height, contour, and the timing of the production. The third analysis, applying the complexity-invariant distance measure to the datasets, can provide the pertinent information lost from the first two analyses in a more robust manner.

An analytical framework based on the recency, frequency, and monetary model and time series clustering techniques for dynamic segmentation

Nowadays, banks use data mining and business intelligence tools and techniques to analyze their customers’ behavior. Customer segmentation is a widely adopted analytical tool to identify distinct groups of customers. Most studies have adopted a static segmentation approach, leading to missing important trends and patterns. In this study, we propose a framework that represents each customer behavior as a time-series sequence of the Recency, Frequency, and Monetary variables, and then exploits time-series clustering algorithms to carry out customer segmentation. The framework consists of state-of-the-art clustering algorithms, including hierarchical, spectral, and k-shape algorithms to divide customers into homogeneous groups and implement point of sale devices transaction data of grocery and appliance retailers. We divide customers into four segments, analyze the behavioral trends, and provide marketing suggestions for each segment. Our results show that, in terms of the computed validity indices, the best clustering model for grocery retailers is reached using hierarchical clustering with the Complexity-Invariant Distance measure, and for appliance retailers, the best segmentation is achieved by applying the spectral clustering with the Complexity-Invariant Distance measure.

A New Hybrid Forecasting Model Based on SW-LSTM and Wavelet Packet Decomposition: A Case Study of Oil Futures Prices.

The crude oil futures prices forecasting is a significant research topic for the management of the energy futures market. In order to optimize the accuracy of energy futures prices prediction, a new hybrid model is established in this paper which combines wavelet packet decomposition (WPD) based on long short-term memory network (LSTM) with stochastic time effective weight (SW) function method (WPD-SW-LSTM). In the proposed framework, WPD is a signal processing method employed to decompose the original series into subseries with different frequencies and the SW-LSTM model is constructed based on random theory and the principle of LSTM network. To investigate the prediction performance of the new forecasting approach, SVM, BPNN, LSTM, WPD-BPNN, WPD-LSTM, CEEMDAN-LSTM, VMD-LSTM, and ST-GRU are considered as comparison models. Moreover, a new error measurement method (multiorder multiscale complexity invariant distance, MMCID) is improved to evaluate the forecasting results from different models, and the numerical results demonstrate that the high-accuracy forecast of oil futures prices is realized.

Forecasting wavelet neural hybrid network with financial ensemble empirical mode decomposition and MCID evaluation

By considering the properties of nonlinear data and the impact of historical data, this paper combines ensemble empirical mode decomposition (EEMD) into wavelet neural network with random time effective (WNNRT) to establish a hybrid neural network prediction model to improve the prediction accuracy of energy prices The EEMD is a noise-aided data analyze method, since it can effectively suppress pattern confusion and restore signal essence. Different from traditional models, the random time effective function that considers the timeliness of historical data and the random change of market environment is applied to the wavelet neural network to establish the WNNRT model. Moreover, multiscale complexity invariant distance (MCID) is utilized to evaluate the predicting performance of EEMD-WNNRT model. Further, the proposed model which is tested in predicting the impact on the global energy prices has carried on the empirical research, and it has also proved the corresponding superiority.

A hybrid stock price index forecasting model based on variational mode decomposition and LSTM network

Changes in the composite stock price index are a barometer of social and economic development. To improve the accuracy of stock price index prediction, this paper introduces a new hybrid model, VMD-LSTM, that combines variational mode decomposition (VMD) and a long short-term memory (LSTM) network. The proposed model is based on decomposition-and-ensemble framework. VMD is a data-processing technique through which the original complex series can be decomposed into a limited number of subseries with relatively simple modes of fluctuations. It can effectively overcome the shortcomings of mode mixing that sometimes exist in the empirical mode decomposition (EMD) method. LSTM is an improved version of recurrent neural networks (RNNs) that introduces a “gate” mechanism, and can effectively filter out the critical previous information, making it suitable for the financial time series forecasting. The capability of VMD-LSTM in stock price index forecasting is verified comprehensively by comparing with some single models and the EMD-based and other VMD-based hybrid models. Evaluated by level and directional prediction criteria, as well as a newly introduced statistic called the complexity-invariant distance (CID), the VMD-LSTM model shows an outstanding performance in stock price index forecasting. The hybrid models perform significantly better than the single models, and the forecasting accuracy of the VMD-based models is generally higher than that of the EMD-based models.

Energy futures and spots prices forecasting by hybrid SW-GRU with EMD and error evaluation

Abstract Forecasting energy market volatility by artificial neural network has long been a focus of economic research. Based on the discriminatory attitude to the historical price information, a novel hybrid forecasting model of gated recurrent unit with stochastic time effective weights (SW-GRU) is proposed and applied to global energy prices forecasting with empirical mode decomposition (EMD). Since crude oil and gasoline count much in global energy markets, the futures and spots prices of them are adopted in the present research. After real energy price series is decomposed into intrinsic mode functions (IMFs) and a residual, the forecasting IMFs and residual in the test set can be performed by SW-GRU and utilized to calculate the prediction prices. With several error criteria and double-scale complexity invariant distance, the forecasting errors of proposed model SW-GRU with EMD and other models are evaluated and compared. According to the empirical study in energy markets, the forecasting model of SW-GRU with EMD is distinguished from other models by its best performances.

Stochastic recurrent wavelet neural network with EEMD method on energy price prediction

Novel hybrid neural network prediction model (denoted by E-SRWNN) is formed by combining ensemble empirical mode decomposition (EEMD) and stochastic recurrent wavelet neural network (SRWNN), in order to improve the precision of energy indexes price forecasting. Energy index price series are non-stationary, nonlinear and random. EEMD method is utilized to decompose the closing prices of four energy indexes into subsequences with different frequencies, and the SRWNN model is composed by adding stochastic time effective function and recurrent layer to the wavelet neural network (WNN). Stochastic time effective function makes the model assign different weights to the historical data at different times, and the introduction of recurrent layer structure will enhance the data learning. In this paper, E-SRWNN model is compared with other WNN-based models and the deep learning network GRU. In the error evaluation, the general standards, such as linear regression analysis, mean absolute error and theil inequality coefficient, are utilized to compare the predicted effects of different models, and then multiscale complexity-invariant distance is applied for further analysis. Empirical research illustrates that the proposed E-SRWNN model displays strong forecasting ability and accurate forecasting results in energy price series forecasting.

Forecasting hybrid neural network with variational learning rate and q-DSCID synchronization evaluation for energy market

Because of the nonlinearity, uncertainty, and dynamics of crude oil price, its price forecasting has continuously been a burdensome international research issue. To better implement the prediction of the energy market by machine learning algorithms, premeditating the influence factors of historical data in different periods on prediction consequence, random inheritance formula error correction algorithm is proposed in this work. The empirical wavelet transform and reconstruction are applied to extract data features simultaneously. A novel hybrid neural network model is constructed, which integrates empirical wavelet transform, Elman recurrent neural network, and random inheritance formula. Variational learning rate is proposed and used to ameliorate the selection of parameters for the network training procedure. In this paper, the proposed model is applied in crude oil futures price forecasting. Further, a variety of evaluation indicators are introduced to contrast and evaluate the predictions. An original representative synchronization evaluation arithmetic q-order dyadic scales complexity invariant distance is put forward and utilized. Demonstration results suggest that the proposed model has superior preciseness among comparison models.

Analysis of air pollution time series using complexity-invariant distance and information measures

Air pollution is known to be a major threat to human and ecosystem health. A proper understanding of the factors generating pollution and of the behavior of air pollution in time is crucial to support the development of effective policies aiming at the reduction of pollutant concentration. This paper considers the hourly time series of three pollutants, namely NO2, O3 and PM2.5, collected on sixteen measurement stations in Switzerland. The air pollution patterns due to the location of measurement stations and their relationship with anthropogenic activities, and specifically land use, are studied using two approaches: Fisher–Shannon information plane and complexity-invariant distance between time series. Clustering analysis is used to recognize within the measurements of same pollutant groups of stations behaving in a similar way. The results clearly demonstrate the relationship between air pollution probability densities and land use activities.

Fluctuation behavior analysis of stochastic exclusion financial dynamics with random jump

A novel financial price model combining stochastic exclusion system and compound Poisson process with lattice fractal Sierpinski carpet percolation jumps is established to reflect fluctuation behaviors of energy markets. The exclusion system (one of statistical physics systems) is applied in implementing interaction behaviors of traders, and the percolation theory is used to implement gusty jumps of price volatilities. Further, the actual market data and the simulation data are combined to analyze statistical properties and complex characteristics by applying autocorrelation analysis, detrended fluctuation analysis method and fractional fuzzy entropy. Moreover, a new synchronization measurement method named the cross CID FuzzyEn, which is composed of cross-fuzzy entropy and complexity-invariant distance, is firstly proposed in this work. Empirical results show that the analog returns and the actual returns have parallel characteristics and strong synchronicity, which displays that the proposed model is rational and can effectively reflect the internal mechanism of real energy markets to some extent.

Complexity Synchronization of Energy Volatility Monotonous Persistence Duration Dynamics

A new concept named volatility monotonous persistence duration (VMPD) dynamics is introduced into the research of energy markets, in an attempt to describe nonlinear fluctuation behaviors from a new perspective. The VMPD sequence unites the maximum fluctuation difference and the continuous variation length, which is regarded as a novel indicator to evaluate risks and optimize portfolios. Further, two main aspects of statistical and nonlinear empirical research on the energy VMPD sequence are observed: probability distribution and autocorrelation behavior. Moreover, a new nonlinear method named the cross complexity-invariant distance (CID) FuzzyEn (CCF) which is composed of cross-fuzzy entropy and complexity-invariant distance is firstly proposed to study the complexity synchronization properties of returns and VMPD series for seven representative energy items. We also apply the ensemble empirical mode decomposition (EEMD) to resolve returns and VMPD sequence into the intrinsic mode functions, and the degree that they follow the synchronization features of the initial sequence is investigated.

CLUSTERING OF RAINFALL DISTRIBUTION PATTERNS IN PENINSULAR MALAYSIA USING TIME SERIES CLUSTERING METHOD

Time series clustering technique was used in this study to categorize the locations in Peninsular Malaysia according to the similarity of rainfall distribution patterns. Daily rainfall time series data from 12 meteorological observation stations across Peninsular Malaysia have been considered for this study. Four dissimilarity measure methods were examined and compared in terms of accuracy and suitability, namely Euclidean distance (ED), complexity-invariant distance (CID), correlation-based distance (COR) and integrated periodogram-based distance (IP). The average silhouette width (ASW) was used to determine the optimal group number for the rainfall time series data. Using Ward’s hierarchical clustering method, this study found that the rainfall time series in Peninsular Malaysia can be divided into four regions of homogeneous climate zones. Based on the results, the IP was the most suitable dissimilarity measures for clustering rainfall time series data in Peninsular Malaysia, except during the Southwest Monsoon where the COR performed better.

Modified multifractal large deviation spectrum based on CID for financial market system

We modify the basic roughness grain exponent, only available for application of one single series, to complexity-invariant distance (CID) for studying multifractal features between two time series. CID is taken into consideration as a new roughness grain exponent with the large deviation spectrum to detect the similarity and correlation between different stock markets in this work.The new method is firstly applied to artificial series in order to test the scale invariance hypothesis with both the Legendre spectrum and large deviation spectrum. Results show that the large deviation spectrum is better in the detection of multifractal analysis between two time series as it exhibit plentiful scaling structures. Then we investigate the scaling behavior between financial time series so as to test whether there is scale invariance of stock markets in China and the US. Besides, from the α values responding to the maximal fα in the 5 pair series and the widths of the spectrum, a new way of measurement of the similarity and correlation has been found. To overcome the limitation of q, we then compute the surface area of the large deviation spectrum under each scale and further detect the evolution of the slope by a scaling/non-scaling criterion which helps in the measurement of scaling behavior. Moreover, the proposed method can give us more information between different markets and distinguish them from different angles.

A Feature Extraction Method Based on Sparse Filtering With Local Structure Preserved and Its Applications to Bearing Fault Diagnosis

Unsupervised feature learning, as a promising tool for extracting features automatically, overcomes shortcomings of traditional feature extraction methods which generally take plenty of effort on designing features. Among various unsupervised feature learning methods, sparse filtering is an efficient and popular one owing to its simplicity with fewer hyper-parameters. However, the standard sparse filtering fails to consider the local structure of input samples, which may affect and restrict its feature learning ability. To address this deficiency, a new feature extraction approach named sparse filtering with local structure preserved (SF-Local) is proposed. The objective function of SF-Local is composed by the standard sparse filtering and a local structural regularization (LSR) which is formulated to preserve the local structure of the input samples. To design LSR, we adopt complexity-invariant distance to select neighbors for each sample rather than the widely used Euclidean distance, which is beneficial to establishing a reliable K-nearest graph. Based on SF-Local, an intelligent fault diagnosis method is developed by leveraging a supervised classifier. The developed diagnostic approach is applied to diagnose the bearing faults as well as its performance is evaluated on a bearing data set with a constant operating condition and a data set with variable operating conditions. Experimental results demonstrate the effectiveness and superiority of the proposed SF-Local.

Multidimensional scaling method for complex time series feature classification based on generalized complexity-invariant distance

In this paper, we propose a multidimensional scaling (MDS) method based on complexity-invariant distance (CID) and generalized complexity-invariant distance (GCID) to analyze and classify complex time series like traffic signals and financial stock indexes. Three types of simulation time series from the $$\upalpha $$ -map model, the 2D Henon map model and the Lozi map model as well as two real-world time series are used to illustrate the practicability of the proposed MDS method. Results from two traditional MDS and the MDS based on the mutual information are compared with the MDS based on CID and GCID, which demonstrate the proposed method is more effective and reasonable.

Forecasting neural network model with novel CID learning rate and EEMD algorithms on energy market

Abstract In view of the applications of artificial neural networks in economic and financial forecasting, it is vital to improve the prediction methods and the forecasting accuracy for the neural networks. In this paper, a neural network architecture with novel learning rate which is controlled by the complexity invariant distance (CID) is developed for energy market forecasting, where the CID is generally utilized to measure the complexity differences between two time series by employing the Euclidean distance. Moreover, stochastic time strength neural network (STNN) is a kind of supervised neural network which is introduced to forecast the time series. Based on the above theories, a new neural network model called CID-STNN is proposed in this work, in an attempt to improve the forecasting accuracy. For comparing the forecasting performance of CID-STNN and STNN deeply, the ensemble empirical mode decomposition (EEMD) is applied to decompose time series into several intrinsic mode functions (IMFs), and these IMFs are utilized to train the models. Further, the empirical research is performed in testing the prediction effect of WTI and Brent by evaluating predicting ability of the proposed model, and the corresponding superiority is also demonstrated.

Asphalt pavement classification using smartphone accelerometer and Complexity Invariant Distance

Most modern smartphones have a variety of built-in sensors, as an accelerometer, gyroscope, GPS, proximity and a magnetic sensor. The large variety of sensors makes these devices powerful measurement tools, allowing the emergence of new systems and applications. In this paper, is presented a real data stream application related to asphalt pavement evaluation using acceleration data gathered by the accelerometer sensor of smartphones. The quality of the pavement has a significant influence on the final price of goods and services, the safety of drivers, pedestrians and passengers, and driver’s comfort. Thus, it is essential the use of tools, as proposed in this work, that allows the constant monitoring of pavement conditions by the Government authorities or private entities for more precise interventions in the maintenance planning with fewer expenses. This task is mainly important in developing countries where there is a lack of technology and a reduced budget for maintenance. Due to the popularity of smartphones, this tool can make possible that different users help to monitor the pavement quality ubiquitously during driving periods without effort. The application of asphalt evaluation is modeled in this work as a multi-dimensional time series classification problem, where the time series are the data from the three-axis accelerometer sensor. Given the characteristics of the data, we discuss and propose the combination of some classical distance measure for time series as Dynamic Time Warping or Longest Common Subsequence Similarity with the Complexity Invariant Distance. A comprehensive experimental evaluation was performed on three datasets that represent different scenarios of asphalt pavement classification. The proposed approach reaches a classification accuracy of 80% to 98% in the three evaluated problems and we experimentally show that the complexity invariance substantially improves the results achieved by classical distance measures given our classification tasks.

Forecasting stochastic neural network based on financial empirical mode decomposition

In an attempt to improve the forecasting accuracy of stock price fluctuations, a new one-step-ahead model is developed in this paper which combines empirical mode decomposition (EMD) with stochastic time strength neural network (STNN). The EMD is a processing technique introduced to extract all the oscillatory modes embedded in a series, and the STNN model is established for considering the weight of occurrence time of the historical data. The linear regression performs the predictive availability of the proposed model, and the effectiveness of EMD–STNN is revealed clearly through comparing the predicted results with the traditional models. Moreover, a new evaluated method (q-order multiscale complexity invariant distance) is applied to measure the predicted results of real stock index series, and the empirical results show that the proposed model indeed displays a good performance in forecasting stock market fluctuations.

Nonlinear multiscale coupling analysis of financial time series based on composite complexity synchronization

In the paper, based on the combination of sample entropy and complexity-invariant distance, a new synchrony-measured method, called the composite complexity synchronization (CCS), is proposed to measure the degree of synchrony of two time series with same data length. Implementing the multiscale cross-sample entropy and multiscale composite complexity synchronization (MCCS) analysis for seven representative stock market indexes, multiscale coupling behaviors of logarithmic returns are compared. Furthermore, the selective data of different sampling frequency within the same time period are applied to analyze the effect of sampling rate in the data on the MCCS behaviors. And we apply the ensemble empirical mode decomposition to decompose the stock logarithmic returns into the intrinsic mode functions and investigate the extent that they have inherited the coupling behaviors of original returns. Empirical results demonstrate the feasibility and effectiveness of the proposed method, and exhibit its superiority in distinguishing the very subtle synchrony behaviors among the time series.

Forecasting energy market indices with recurrent neural networks: Case study of crude oil price fluctuations

In an attempt to improve the forecasting accuracy of crude oil price fluctuations, a new neural network architecture is established in this work which combines Multilayer perception and ERNN (Elman recurrent neural networks) with stochastic time effective function. ERNN is a time-varying predictive control system and is developed with the ability to keep memory of recent events in order to predict future output. The stochastic time effective function represents that the recent information has a stronger effect for the investors than the old information. With the established model the empirical research has a good performance in testing the predictive effects on four different time series indices. Compared to other models, the present model is possible to evaluate data from 1990s to today with extreme accuracy and speedy. The applied CID (complexity invariant distance) analysis and multiscale CID analysis, are provided as the new useful measures to evaluate a better predicting ability of the proposed model than other traditional models.