Input Redundancy Research Articles

How does lead selection impact diagnosis through AI? Implications for continuous monitoring systems using convolutional neural networks

Abstract Background and Objectives Recently, there has been a surge in non-invasive diagnosing methods leveraging the dipolar 12-lead ECG information using Convolutional Neural Networks (CNNs). However, the traditional ECG contains 12 projections of the cardiac dipole in a three-dimensional space can result in redundancy. Furthermore, in continuous monitoring systems such as Holter and wearables, not all 12 leads are consistently available. This study aims to quantify redundancy and determine the best lead configuration for improved classification results using a CNN. It evaluates the level of redundancy in ECG leads and its impact on CNN classification. Methods The degree of redundancy was quantified by means of lead entropies (H) as depicted in Figure 1.A. The standard 12-lead ECG was chosen as the baseline input. From it, various subsets of leads were selected (6, 3, 1 leads) with the objective of attaining maximal orthogonality between leads while minimizing redundancy (Figure 1.B). A 2D-CNN model was trained for multiclass classification: Hypertension (HYP), ST-T interval Changes (STTC), Conduction Disturbances (CD), Myocardial Infarction (MI) and Normal (NORM). The designed inputs were employed to evaluate how redundancy impacts the performance of the CNN (see Figure 1.C). Results Reducing redundancy in input leads led to notable improvements in model prediction for all pathological conditions in terms of Area Under the Curve (AUC). Reducing to 6 and 8 leads were the most suitable input for the CNN (Table 1) increasing by 1.18% in HYP, 0.23% in STTC, 0.52% in CD, and 0.33% in MI. However, a significant reduction in redundancy may result in the loss of essential clinical information for classification, as observed in scenarios involving only 3 or 1 leads. Conclusions When diagnosing pathologies with systems featuring fewer leads, its combinations should aim for maximum orthogonality to reduce redundancy while preserving unique information. By strategically selecting a set of leads with reduced input redundancy, the effectiveness of the standard 12-lead ECG can be improved, thereby enhancing the utility of such continuous monitoring systems for automated diagnosis and also decreasing training and prediction times.

Measurement and coupling analysis of the efficiency of resource‐based treatment of municipal solid waste in Chengdu–Chongqing area

AbstractMunicipal solid waste (MSW) is crucial for carbon cycle, residents' lives, and green circular economy development, but quantitative research is limited in efficiency and regional synergy. Considering the regional characteristics of Chengdu and Chongqing, this study establishes the input–output indicator system of MSW treatment in 16 cities in the Chengdu–Chongqing area, constructs the Data Envelopment Analysis model and the coupling coordination degree model, and makes an in‐depth study on the efficiency and environmental benefits of MSW resource treatment from 2012 to 2021. The research conclusion is as follows: first, the improvement of MSW treatment efficiency can be enhanced through reasonable policies and measures to promote sustainable urban development and socioeconomic benefits. The input and output levels of MSW treatment in 16 cities all show an upward trend. Second, the 16 MSW treatment systems have good average pure technical efficiency (Chongqing 0.9879, Chengdu 0.9805), average scale efficiency (Nanchong 0.9396), and average comprehensive efficiency (Nanchong 0.9148), but the overall comprehensive efficiency needs improvement. Third, in 2021, Chengdu's ecological and environmental benefits are better than Chongqing's, while Chongqing has a certain degree of input redundancy and output deficiency. Fourth, in the coupling analysis of resource treatment efficiency and environmental improvement benefits in Chengdu and Chongqing between 2012 and 2021, the coordination between resource treatment and environmental improvement in Chengdu lags behind that in Chongqing, but overall, the coupling is improving. Finally, suggestions for improving the efficiency of MSW resource treatment and promoting environmental improvement are presented from the front, middle, and back ends, respectively, to provide a reference for the policy‐making of city managers.

Reduction in Optimal Time in Systems with Input Redundancy

This paper discusses a reduction in the optimal time due to the presence of input redundancy in time-optimal control problems. By introducing a non-idle channel to represent an active input channel, we establish the necessary and sufficient conditions that ensure a strict reduction in the optimal time for affine nonlinear systems. In cases of identical input redundancy, its impact varies according to the type of input constraint, and certain types may not lead to a reduction in the optimal time. Ultimately, in linear time-invariant (LTI) systems, the extent of the optimal time reduction depends on the system’s controllability.

MIMTracking: Masked image modeling enhanced vision transformer for visual object tracking

Recently, one-stage trackers achieve state-of-the-art tracking results due to more sufficient integration of search and template representations. These methods usually adopt an encoder for synchronous feature generation and interaction. Despite their high performance, the one-stage approaches tend to feed the encoder full input representations that are highly redundant and dense during training. With a focus on tackling this problem, a novel algorithm termed MIMTracking is developed for visual target tracking. MIMTracking exploits an encoder and a decoder for masked image modeling during training. Randomly sampled discrete search embeddings and template embeddings serve as input of the encoder. The lightweight decoder takes full representations as input and progressively highlights the target region. This design alleviates input redundancy and reduces the computational cost of the training process, thereby allowing for more efficient learning of useful representations. The proposed MIMTracking achieves state-of-the-art tracking results on numerous tracking datasets, e.g., 51.5 % area under curve (AUC) on LaSOText, outperforming the previous top tracker OSTrack by 2 %. Especially, our large model MIMTracking-L further improves the AUC to 53.4 % on LaSOText.

Evaluation of Urban–Rural Total Factor Flow Efficiency Based on Multiple Symbiosis: Insights from 27 Provinces in China

The rational flow of production factors is crucial for promoting benign interactions between urban and rural areas. To unveil the intrinsic mechanisms of factor flow pathways promoting mutual symbiosis between urban and rural areas, this study, based on symbiosis theory, takes total factor flow including land, technology, capital, and labor as inputs and urban–rural symbiosis level as output. Utilizing the Super-Efficiency Slack-Based Measure (SBM) model, this study calculates the urban–rural total factor flow efficiency of 27 provinces in China from 2011 to 2021 and explores specific improvement directions of urban–rural factor flow based on projection analysis. This study revealed the following findings: (1) The overall efficiency of urban–rural total factor flow in China shows a fluctuating upward trend but has not yet reached an effective state. There are significant regional disparities, with 8 provinces such as Guangdong and Fujian reaching Pareto optimality, while the remaining 19 provinces exhibit varying degrees of inefficiency. (2) Provinces with insufficient symbiotic production are mainly concentrated in the central and western regions and the northeast region, with 14 provinces including Inner Mongolia showing the inadequate transformation of urban–rural symbiosis. However, except for Hainan, the situation is gradually improving in other regions annually. (3) There is input redundancy in total factor, where land, labor, and capital redundancy are the main reasons for the inefficiency of urban–rural total factor flow in China. However, trends show that the redundancy of land, labor, and capital elements is improving annually, while technology redundancy is worsening. (4) Through a comprehensive analysis of input redundancy, output deficiency, symbiosis coefficient, and efficiency, this study categorizes the impact of factor flow on urban–rural symbiosis level into basic matching, redundancy, and comprehensive scarcity types. The research provides scientific guidance for promoting sustainable development through the rational flow of total factors and offers valuable insights for similar countries.

A novel hybrid model based on multiple influencing factors and temporal convolutional network coupling ReOSELM for wind power prediction

Highly accurate wind power prediction is important for the operation and management of wind farms, energy utilization and power supply. In recent years, in order to further improve prediction accuracy, some researchers have considered utilizing factors such as wind speed and wind direction to establish prediction models. However, this often results in input redundancy due to a lack of technical means. In this paper, a multivariate prediction model for wind power based on variational mode decomposition (VMD), fuzzy entropy (FE), partial auto-correlation function and cross-correlation function (PACF&CCF, abbreviated as PC), improved artificial hummingbird algorithm (IAHA), temporal convolutional network (TCN), and regularized online sequential extreme learning machine (ReOSELM) is proposed. To address the nonlinearity and non-stationarity of the original wind power time series and decrease computational costs, the VMD combined with FE data preprocessing technique is employed. Considering the information redundancy in the multivariate data, the PC technique is utilized to conduct correlation analysis on the input data and select highly correlated features as inputs. When the input is multivariate and high-dimensional, the ReOSELM model struggles to achieve satisfactory prediction performance. Therefore, a new model based on TCN-ReOSELM is constructed. Additionally, to overcome the drawbacks of manual parameter adjustment, an IAHA algorithm is proposed, which integrates Latin hypercube sampling and chaotic local search strategies, to optimize the crucial parameters of TCN-ReOSELM. The experimental results demonstrate that the multivariate method proposed in this paper reduces the RMSE by 31% compared to the univariate method. Specifically, the proposed VMD-FE-PC-TCN-ReOSELM model reduces the RMSE, MAE, and SMAPE by 60–64%, 55–58%, and 10–36%, respectively, compared to the PC-TCN-ReOSELM model.

Research on total factor energy efficiency in western China based on the three-stage DEA-Tobit model.

As an essential material basis and power source for economic and social development, Western China's low energy use efficiency has hindered its sustainable economic development. This study aims to evaluate the total factor energy efficiency of the region and identify its influencing factors. A three-stage DEA model was used to measure the efficiency of 11 provinces from 2006 to 2021, and the Tobit model was employed to investigate internal factors. The findings show that (i) external environmental factors and stochastic perturbations have a significant impact on TFEE in the western region, overestimating integrated efficiency and scale efficiency and underestimating pure technical efficiency. (ii) the study of external influencing factors finds that the level of economic development increases input redundancy; the industrial structure increases capital input and labor input redundancy while decreasing energy input redundancy; and the energy consumption structure increases capital input and energy input redundancy while decreasing labor input redundancy. (iii) the study of internal influencing factors finds that the level of scientific and technological innovation, the level of openness to the outside world, and the TFEE have a positive correlation. In contrast, the intensity of environmental regulation has a negative correlation.

Performance Test, Index System Establishment, and Comprehensive Evaluation of Earthquake Rescue Robots

To effectively enhance the adaptability of earthquake rescue robots in dynamic environments and complex tasks, there is an urgent need for a comprehensive evaluation method that encompasses establishing an evaluation index system, testing performance indexes, and conducting performance evaluation. Firstly, four main criterion and twenty-three sub-criterion indexes are established by conducting a comprehensive review of existing assessment measures for rescue robots across diverse domains. These indexes are validated through test modules developed by the National Earthquake Response Support Service to obtain corresponding values for each criterion. Moreover, a method for establishing the index system is proposed based on the fuzzy clustering analysis and grey correlation analysis methods. This method effectively addresses issues related to excessive subjectivity, redundancy, and ambiguous stratification of indexes. Subsequently, the DEMATEL is employed to scrutinize the interrelationships and causal connections among each index within the established index system, leading to the identification of input and output indexes based on the analysis outcomes. Finally, as an empirical example, three earthquake rescue robots are comprehensively evaluated and ranked using the super efficiency DEA model. Alongside analyzing results regarding input redundancy and output deficiency, targeted improvement suggestions are provided for each earthquake rescue robot. Additionally, comparison analysis with the entropy weight method and VIKOR method verifies the effectiveness of our proposed method.

High-performance LQR control for continuous time systems with redundant control inputs

This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance.

What types of business environment fosters the emergence of more specialized and sophisticated “little giant” enterprises?—An empirical study based on the TOE framework and configuration adaptation theory

AbstractNurturing specialized and sophisticated enterprises is a vital strategic initiative to mitigate the dependency on crucial technologies and to promote the competitiveness of Chinese manufacturing industry. Basing on a technology, organization, and environment (TOE) framework, combined with geographic concentration, qualitative comparative analysis (QCA), and data envelopment analysis (DEA) methods, this article analyzes the conducive business environment for the growth of specialized and sophisticated “little giant” enterprises (LGEs) from configurational perspective. It takes the quantity and density of LGEs in different regions of China as the consequence event. The findings show that: (1) the spatial distribution of LGEs is highly uneven with a geographic concentration index (CR5) of 0.436 and a Herfindahl–Hirschman Index of 0.0599. (2) The presence of numerous technology‐oriented SMEs and a “favorable” business environment are not necessarily the regions where a larger number of LGEs are fostered. Indeed, the harmonious interplay of TOE is more important for achieving optimal outcomes. The differential configurations contributing to the regional output variations of LGEs can be classified with three patterns: technology‐organization‐environment synergistic promotion type (H1), innovation stimulation through effective financial support type (H2a), and compensatory type for inadequate innovation resources (H2b). While these configurations may lead to similar outcomes, they do not yield the same effectiveness. (3) The DEA reveals a tendency for “over‐optimization” in improving regional business environment under the TOE framework, indicating the presence of “input redundancy” and corresponding “output loss” issues in TOE factors. Local governments must adhere to the “barrel principle” and optimize the business environment that aligns with development of LGEs through the concept of dynamic adaptation. Adopting an organizational mindset of “stringing beads into chains” can help construct regional industrial chains with distinctive features.

Adoption mode of agricultural machinery and food productivity: evidence from China

Many researchers argue that the adoption of agricultural mechanization services (AMSs) is an important way for smallholder farmers in China to engage in modern agricultural production. However, the impact of the adoption mode of agricultural machinery on food productivity remains under-analyzed. We investigate the links between the adoption mode of agricultural machinery and food productivity using data on 795 grain farmers collected from the North China Plain. The results indicate that, compared with service outsourcing (SO), self-purchase (SP) improves the technical efficiency of farms; however, it reduces the input efficiency of agricultural machinery. The channel of the effect is that, although SO can reduce the redundancy of agricultural machinery's input, the opportunistic behavior of AMS suppliers and labor supervision problems lead to a decline in agricultural machinery's operation quality. The impact of the adoption mode of agricultural machinery on food productivity is asymmetrical among different types of farmers. Large-scale and professional farmers benefit more from SP, whereas small-scale and part-time farmers benefit more from SO. The AMS is not perfect, and the Chinese government should pay close attention to the loss of technical efficiency in agricultural production caused by the opportunistic behavior of AMS suppliers. Therefore, it is necessary to adjust the agricultural machinery subsidy policy and reduce the transaction cost of AMS.

Online Active Fault Detection for Over-Actuated Systems With Prescribed Control Performance

In the field of fault detection, active fault detection for dynamic systems is an emerging research topic. By redesigning the control input, active fault detection can enhance fault detection performance. In this study, the online active fault detection problem is investigated for over-actuated systems, where the control input is designed by considering both the prescribed control performance and the fault detection performance. A two-stage input design architecture is constructed, where the first stage is a virtual controller design and the second stage is a control allocation design. In the first stage, the virtual control input is designed by utilizing a prescribed performance function to fulfill the control requirement. In the second stage, a differential evolution method is adopted to obtain an optimal control allocation algorithm for improving the fault detection performance. The designed control input can both improve fault detection performance and achieve the prescribed control performance. Two cases, including a numerical example and a manned submersible propulsion system, are studied to support theoretical results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In this study, the aim is to design a control input for over-actuated systems to obtain better fault detection performance while achieving prescribed control performance. To achieve it, a two-stage control input design architecture is constructed, where the first stage is a virtual controller design and the second stage is a control allocation design. In the first stage, choose a proper prescribed performance function and a sliding mode function to accomplish the transient and steady behavioral bounds on the tracking errors. In the second stage, design a special observer to generate the system residual signal, which is used for indicating system faults. Based on the residual signal, construct an index for the control allocation algorithm. Differential evolution algorithm is applied to obtain the optimal control allocation algorithm by maximizing the index. Thus the control allocation algorithm which can improve fault detection performance is designed. In this way, the input can improve fault detection performance without affecting system behavior. The proposed technique of this study can be applied to dynamic systems with input redundancy.

Exploration and efficiency assessment of the management model of higher vocational education with poa concepts

Abstract Current vocational high school management practices suffer from low efficiency, mainly due to inadequate backing from pertinent educational theories. In this study, the POA concept is first used as a guideline for the innovation of the management mode of higher vocational education, and 30 provinces, cities, and autonomous regions in China are taken as the research objects. Then, based on the output and input indicators, we constructed the efficiency assessment system of education management, used the DEA model to make static measurements of education management efficiency in 2020-2022, and further analyzed the dynamic evolution trend of the efficiency of higher vocational education management by using the Malmquist index. According to the results, less than 50% of higher vocational colleges and universities are classified as non-DEA practical situations. For these higher vocational colleges and universities, their input redundancy and output insufficiency are analyzed, in which the two input indicators of total public expenditure and the number of administrative personnel of decision-making unit 1 are insufficient. The input insufficiency rate is 13.43% and 73.01%, respectively. According to the input and output of each higher vocational college or university, the corresponding solution measures are proposed to improve the efficiency of educational management of higher vocational.

Análise da eficiência da produção de citros e da variabilidade interprovincial na China sob as restrições da poluição de fonte difusa

ABSTRACT: Globally, China is one of the primary citrus producers. This study provided a theoretical reference for sustainable production in the citrus industry in China by measuring citrus production efficiency under non-point source pollution and analyzing inter-provincial variability. In this study, non-radio logical and non-angled data envelopment analysis models were used in seven provinces during 2006-2018 based on non-desired outputs. The temporal and spatial characteristics were analyzed to determine the factors that cause efficiency losses. Results indicated that the citrus production efficiency had a general w-type trend with high inter-provincial variability, where the highest and lowest production efficiencies occurred in Hubei Province and Guangdong Province, respectively. In the past four years, a redundancy in labor and fertilizer inputs was also observed in Guangdong and Fujian, respectively. The shrinkable proportion of each factor input in the seven provinces was zero. An increase in citrus yield per hectare was recorded, in which the highest was in Guangdong. In each province, high emissions of total nitrogen and phosphorus generally caused the decrease in citrus production efficiency.

Research on the Evaluation of the Effectiveness of Industry-Teaching Integration Construction of Higher Vocational Excellence Courses--Based on Network DEA Model Analysis

Abstract The integration of industry and education is an important model for building high-level higher vocational colleges and universities, and it is also a necessary way to promote the modernization and development of higher vocational education. Based on Hall’s three-dimensional structural model, this paper explores the specific process of the construction of industry-teaching integration of high-level, high-quality courses and evaluates the effectiveness of the construction of industry-teaching integration of high-level, high-quality courses using the network SBM-DEA model. The evaluation index system was first constructed according to the questionnaire survey method, Delphi method, and hierarchical analysis method, and then the indexes were screened and applied to the empirical analysis of the effectiveness of the construction of industry-teaching fusion of higher vocational boutique courses. The average overall operational efficiency of the industry-teaching fusion of boutique courses at 45 higher vocational colleges and universities is 0.547, which is the average level. However, the efficiency of the two phases still has some differences between the average efficiency value of the resource construction phase and the outcome output phase. The correlation coefficient between the efficiency of the outcome output stage and the overall operational efficiency is 0.885, which is highly correlated. Most institutions pay more attention to the operation of the outcome output stage. The R² of the fit between pure technical efficiency and comprehensive efficiency is 0.731, and the R² of the fit between scale efficiency and comprehensive efficiency is 0.264, indicating that pure technical efficiency is the dominant factor affecting the comprehensive efficiency of institutions. In the two stages of resource construction and output of results, the output side shows insufficient output, while the input side shows input redundancy, indicating that the input resources are not effectively utilized. This paper provides a direction of action to strengthen the deep integration of industry and education in higher vocational boutique courses and to promote complementary resources and a benign interaction between schools and enterprises.

Energy efficiency assessment of wastewater treatment plants in China based on multiregional input–output analysis and data envelopment analysis

Wastewater treatment plants (WWTPs) play a pivotal role in natural water recycling and safeguarding the water security of approximately 42% of the world's population, yet they confront challenges posed by escalating energy consumption and regional energy constraints. In this study, we developed an evaluation framework that integrated regional energy scarcity with the operation conditions of WWTPs to quantify their energy efficiencies by applying multiregional input–output (MRIO) analysis and data envelopment analysis (DEA). A case study using this framework was conducted on 3776 WWTPs in 30 provinces in China. The results showed that the average scarcity-based energy efficiency level of WWTPs in China was low, of which those in northern provinces were higher compared to southeastern provinces. Furthermore, only 24 WWTPs in China attained the highest efficiency levels, while the rest had different degrees of input redundancy, indicating an energy-saving potential of 9.05 × 109 kWh. This paper enables the development of optimal efficiency strategies for WWTPs in different provinces considering the potential energy scarcity risks caused by trading activities.

Sustainability in the evaluation of urban rail transit considering both firms and passengers perspectives: A dynamic network data envelopment analysis approach

This paper divides the operation of urban rail transit into sustainable production stage and sustainable consumption stage from the perspective of firms and passengers, and includes service input, service output, service consumption in a unified model. A dynamic network epsilon based measure model is proposed to measure the production efficiency, service effectiveness and operational effectiveness of urban rail transit respectively, which is used to evaluate the operational sustainability of urban rail transit. Taking 23 urban rail transit systems in China from 2015 to 2021 as an example, the research results show that urban rail transit production efficiency is superior to service effectiveness, but most urban rail transit operational effectiveness is not high, and a large amount of input redundancy in the current urban rail transit sustainable consumption stage comes from vehicle speed. At the same time, the perennial shortage of passengers and passenger miles is the main reason leading to the low service effectiveness. In addition, there is heterogeneity in urban rail transit service effectiveness among different city sizes, and there is a significant positive correlation between operational effectiveness and service effectiveness. Therefore, improving service effectiveness is the key to ensure sustainable urban rail transit operation.

Input redundancy under input and state constraints

For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily applies to any input-to-output mapping. As an illustration of this potentiality, this paper tackles the case where input and state constraints are imposed on the system. This context is indeed of foremost importance since input redundancy has been historically regarded as a way to deal with input saturations. An example illustrating how constraints can challenge redundancy is offered right at the outset. A more complex phenomenology is highlighted. This motivates the enrichment of the existing framework on redundancy. Then, a sufficient condition for redundancy to be preserved when imposing constraints is offered in the most general context of arbitrary constraints. It is shown that redundancy can be destroyed only when input and state trajectories lie on the border of the set of constraints almost all the time. Finally, those results are specialized and expanded under the assumption that input and state constraints are linear.

What causes green efficiency losses in Chinese agriculture? A perspective based on input redundancy

Incompatibility between agricultural production inputs and the resource environment leads to efficiency losses and has an impeding effect on sustainable agricultural development. However, efficiency loss in agriculture is a blind spot in current research. To explore the green development performance and efficiency losses in China's agricultural modernization process, this paper measures the green efficiency of China's agriculture from static and dynamic perspectives. An in-depth analysis of efficiency losses in the efficiency measurement process was conducted. It was found that the overall agricultural green efficiency (AGE) of China showed a continuous upward trend from 2006 to 2019 and the average growth rate is 4.1 %. The utilization efficiency of agricultural inputs in China increased significantly, but the regional variations in the redundancy of agricultural inputs widened. Both agricultural modernization and environmental regulations are associated negatively with labor redundancy, and environmental regulations are associated negatively with fertilizer and machinery redundancy. The effective substitution of labor production factors by agricultural modernization can reduce labor redundancy and release a large amount of rural labor engaged in primary agricultural production, and environmental regulations effectively inhibit the waste of fertilizer, labor, and machinery inputs.

Carbon Emission Efficiency and Reduction Potential Based on Three-Stage Slacks-Based Measure with Data Envelopment Analysis and Malmquist at the City Scale in Fujian Province, China

Increased carbon emissions led to extreme weather, global warming, and other environmental problems. In order to control energy input and reduce carbon emissions, this study first combines a three-stage Slacks-Based Measure with Data Envelopment Analysis (SBM-DEA) and uses the Malmquist index to quantify energy consumption at the city scale and the related carbon emission efficiency in Fujian Province for the period 2015–2020. Second, we explore the carbon reduction potential on the city scale from the perspective of improving carbon emission efficiency. Our results demonstrate that (i) the carbon emission efficiency of the nine cities increases overall in the first stage, when technical efficiency approaches the efficiency frontier state and efficiency shortage is mainly caused by the lack of pure technical efficiency. (ii) Regression by stochastic frontier analysis in the second stage reveals that the secondary industry correlates positively at 1% significance with fossil energy consumption and power consumption, indicating that the carbon emission efficiency decreases as the secondary industry increases. (iii) Putian and Xiamen reduced their carbon emission efficiency in the third stage due to (a) the input redundancy of fossil energy and social power consumption and (b) excessive undesirable output carbon emissions. (iv) There were improvements in carbon emission efficiency peaks in 2015, with Longyan, Ningde, and Sanming improving by about 50%. This improvement then decreased up to the year 2020, when the improvement in the carbon emission efficiency of Ningde and Zhangzhou was 6.02% and 9.50%, respectively, and that of all other cities was less than 1%. Therefore, we suggest that carbon emission reduction in the future can be further improved by improving technology, optimizing industrial structure, and various other ways to further improve carbon emission efficiency.