Equiprobable Symbolization Pattern Entropy for Time Series Complexity Measurement

In order to more effectively mine the structural features in time series, while simplifying the complexity of time series analysis, equiprobable symbolization pattern entropy (EPSPE) based on time series symbolization combined with sliding window technology is proposed in this paper. Firstly, time series are implemented symbolic procession according to the equal probability distribution of the original data, which greatly simplifies the difficulty of analyzing the signal on the premise of small loss of precision to the original signal. Then, sliding window technique is used to obtain a finite number of different symbolic patterns, and the pattern pairs are determined by calculating the conversion between the symbolic patterns. Next, the conversion frequency between symbolized patterns is counted to calculate the probability of the pattern pairs, thus estimating the complexity measurement of complex signals. The results of test using the Logistic system with different parameters show that compared with multiscale sample entropy(MSE), EPSPE can more concisely and intuitively reflect the structural characteristics of time series. Finally, EPSPE is used to investigate the natural wind field signals collected at an outdoor space in which nine high precision two-dimensional (2D) ultrasonic anemometers are deployed in line with 1m interval. The values of EPSPE show consistent increase or decrease trend with the spatial regular arrangement of the nine anemometers. While the results of MSE are irregular, and cannot accurately predict the spatial deployment relationship of nine 2D ultrasonic anemometers.

A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task

Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

Modeling Software Development Process Complexity

Modern software systems are growing increasingly complex, requiring increased complexity of software and software development process (SDP). Most software complexity measurement approaches focus on software features such as code size, code defects, number of control paths, etc. However, software complexity measurement should not only focus on code features but on features that cover several aspects of SDP in order to have a more complete approach to software complexity. To implement this approach, an extensive literature review for identifying factors that contribute to the complexity of SDP was performed and seventeen complexity factors were identified. As there were indications that the identified factors were not independent from each other but there were interrelations between them, statistical methods for identifying the underlined relations and refining them were applied, resulting to the final set of measures used in the proposed model. Finally, the proposed model has been tested in five software projects and the results were evaluated.

Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal

The complexity of a heart rate variability (HRV) signal is considered an important nonlinear feature to detect cardiac abnormalities. This work aims at explaining the physiological meaning of a recently developed complexity measurement method, namely, distribution entropy (DistEn), in the context of HRV signal analysis. We thereby propose modified distribution entropy (mDistEn) to remove the physiological discrepancy involved in the computation of DistEn. The proposed method generates a distance matrix that is devoid of over-exerted multi-lag signal changes. Restricted element selection in the distance matrix makes “mDistEn” a computationally inexpensive and physiologically more relevant complexity measure in comparison to DistEn.

BAYESIAN BELIEF NETWORK-BASED PROJECT COMPLEXITY MEASUREMENT CONSIDERING CAUSAL RELATIONSHIPS

This research proposes a Bayesian belief network-based approach to measure the project complexity in the construction industry. Firstly, project complexity nodes are identified for model development based on the literature review. Secondly, the project complexity measurement model is developed with 225 training samples and validated with 20 test samples. Thirdly, the developed measurement model is utilized to conduct model analytics for sequential decision making, which includes predictive, diagnostic, sensitivity, and influence chain analysis. Finally, EXPO 2010 is used to testify the effectiveness and applicability of the proposed approach. Results indicate that (1) more attention should be paid on technological complexity, information complexity, and task complexity in the process of complexity management; (2) the proposed measurement model can be applied into practice to predict the complexity level for a specific project. The uniqueness of this study lies in developing project complexity measurement model (PCMM) with the cause-effect relationships taken into account. This research contributes to (a) the state of knowledge by proposing a method that is capable of measuring the complexity level under what-if scenarios for complexity management, and (b) the state of practice by providing insights into a better understanding of causal relationships among influencing factors of complexity in construction projects.