Non-negativity Constraints Research Articles

Analyzing the Influence of Telematics-Based Pricing Strategies on Traditional Rating Factors in Auto Insurance Rate Regulation

This study examines how telematics variables such as annual percentage driven, total miles driven, and driving patterns influence the distributional behaviour of conventional rating factors when incorporated into predictive models for capturing auto insurance risk in rate regulation. To effectively manage the complexity inherent in telematics data, we advocate for the adoption of non-negative sparse principal component analysis (NSPCA) as a structured approach for data dimensionality reduction. By emphasizing sparsity and non-negativity constraints, NSPCA enhances the interpretability and predictive power of models concerning both loss severity and claim counts. This methodological innovation aims to advance statistical analyses within insurance pricing frameworks, ensuring the robustness of predictive models and providing insights crucial for rate regulation strategies specific to the auto insurance sector. Results show that, to enhance auto insurance risk pricing models, it is essential to address data dimension reduction challenges when integrating telematics data variables. Our findings underscore that integrating telematics variables into predictive models maintains the integrity of risk relativity estimates associated with traditional policy variables.

Non-negative least-squares variance and covariance component estimation using the positive-valued function for errors-in-variables models

Abstract Although (co)variance component estimation has been widely applied in the errors-in-variables (EIV) model, the occurrence of negative variance components is still a major issue in the estimated variance components. This problem may be due to the following unfavorable factors: 1) unreasonable selection of initial variance values; 2) low redundancy in the EIV functional model; 3) improper design in the EIV stochastic model, and 4) other data quality problems. Many attempts have been made to prevent the appearance of negative variance components. In this contribution, a novel and efficient non-negative least-squares variance component estimation using the PVF (PVF-NLS-VCE) is introduced, which can simultaneously estimate the unknown (co)variance components in the EIV stochastic model and the parameters in the EIV functional model. Its principle is to implicitly impose a non-negative constraint by replacing the variance component with the positive-valued function (PVF) whose range is the set of positive real numbers. Two numerical examples using real and simulated data are presented. The numerical results of linear regression are identical to those obtained based on least-squares variance component estimation (LS-VCE) with positive initial values of variance components. The numerical results of two-dimensional affine transformation are shown to prevent negative variance components and precede those obtained by LS-VCE with a negative initial value of variance component. Both numerical examples verify the effectiveness of the PVF-NLS-VCE method whether the initial values of variance components are positive or negative. The proposed PVF-NLS-VCE is a simple, convenient and flexible method to achieve the non-negative estimates of variance components, which can reduce sensitivity to initial value selection and automatically guarantee a non-negative definite covariance matrix.

PARAFAC under non-negativity constraint is adapted to recover the underlying Beer-Lambert law of the excitation-emission fluorescence matrix measurements acquired from analyte-triggered semiconductor QDs photoluminescence modulation. When and why?

BackgroundAnalyte-triggered semiconductor quantum dots (QDs) modulation in the presence of non-consistently responsive fluorescent species represents a challenging analytical issue in concrete multi-way data handling. QDs with heterogeneous sizes and/or uneven distribution of functional moieties on their surfaces exhibit significant fluctuations in the fluorescent response components, known as chemical rank, across different excitation/emission modes. This phenomenon may lead to a substantial deviation from the proportionality prescribed by Beer-Lambert law. Nonetheless, even in the presence of such deviation, a multi-way model may be successfully selected after determining a proper chemical rank in a QDs system. ResultsWe show that in a valid PARAllel FACtor (PARAFAC) model under properly determined chemical rank, meaningfully resolved pure spectral profiles can be reached for each fluorescent responsive constituent in the original excitation-emission fluorescence matrix (EEFM) measurements. This was thoroughly illustrated by applying PARAFAC trilinear decomposition of a three-way data array of two distinct datasets acquired from semiconductor QDs sensing systems with low-rank trilinear assumption. The first dataset, presented here for the first time, comprises EEFM measurements of the ligand-driven quenching of thiomalic acid (TMA)-capped AgInS2 (AIS) QDs by vomitoxin. The second dataset, employed for illustrative purposes, comprises EEFM measurements of the quenching, via cation bridging, of glutathione (GSH)-capped CdTe QDs by Pb(II). The results of this study enabled the determination of vomitoxin at a ppb level in real samples of fish feeds, showcasing the efficacy of the PARAFAC model in resolving spectral signatures (loadings) and pure concentration profiles (scores). SignificancePARAFAC under a properly examined chemical rank can be easily adapted for retrieval the underlying Beer-Lambert law of the original EEFM measurements with a low-rank trilinear structure through the chemically meaningful information either when (i) no deviation of Beer-Lambert law was observed as deeply discussed in connection with the dataset acquired from vomitoxin-driven molecular sensing through TMA-capped AIS QDs, or when (ii) substantial deviations of the Beer-Lambert law are evident, as discussed in connection with the dataset collected from sensing ionic species through Pb(II) bridging of GSH-capped CdTe QDs.

Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability

We show that feasibility of the $t^\text{th}$ level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class $\mathcal{L}_t$ of graphs such that graphs $G$ and $H$ are not distinguished by the $t^\text{th}$ level of the Lasserre hierarchy if and only if they admit the same number of homomorphisms from any graph in $\mathcal{L}_t$. By analysing the treewidth of graphs in $\mathcal{L}_t$, we prove that the $3t^\text{th}$ level of Sherali--Adams linear programming hierarchy is as strong as the $t^\text{th}$ level of Lasserre. Moreover, we show that this is best possible in the sense that $3t$ cannot be lowered to $3t-1$ for any $t$. The same result holds for the Lasserre hierarchy with non-negativity constraints, which we similarly characterise in terms of homomorphism indistinguishability over a family $\mathcal{L}_t^+$ of graphs. Additionally, we give characterisations of level-$t$ Lasserre with non-negativity constraints in terms of logical equivalence and via a graph colouring algorithm akin to the Weisfeiler--Leman algorithm. This provides a polynomial time algorithm for determining if two given graphs are distinguished by the $t^\text{th}$ level of the Lasserre hierarchy with non-negativity constraints.

Optimal fare and headway for a demand adaptive paired-line hybrid transit system in a rectangular area with elastic demand

Demand adaptive paired-line hybrid transit systems that integrate fixed- and flex-route transit have emerged in the last decade and attracted increasing attention because of their potential to improve accessibility for passengers. To facilitate the operation of such a hybrid transit system, this study develops a model to determine the optimal fare and headways associated with fixed- and flex-route transit along a rectangular corridor. Compared with existing literature, the novelty of this study lies in designing the fare structure while simultaneously considering demand elasticity and passenger behaviour. A continuous approximation modelling approach is employed to derive the agency’s and travellers’ cost components. Using these, a nonlinear programming optimisation model is formulated to minimise the total user cost subject to the agency’s nonnegative revenue constraints and passengers’ route choice behaviour, which is characterised as a path-size logit model. Numerical experiments are performed using a stylised network to examine the properties of the model, in which the solution is obtained by combining a brute force method that enumerates headway and fare combinations and an iterative method that determines equilibrated passenger choices. The results show that as potential demand density increases, fare and headway fluctuate and drop, while the percentage of passengers choosing to ride on flex-route transit increases. In addition, there may be an optimal maximum offset distance, which is defined as the width of the corridor to be covered by the transit system, when the potential demand density is low, leading to minimum user cost and maximum travel demand within the service area.

Improved modulus-based matrix splitting iteration methods for a class of horizontal implicit complementarity problems

Recently, the modulus-based matrix splitting (MMS) iteration method has been successfully extended to solve the horizontal implicit complementarity problem (HICP). However, due to the existence of two system matrices and one nonlinear term, in addition to an equivalent fixed-point equation of the HICP, a system of linear equations has to be solved at each iteration to satisfy both the nonnegative constraint and the orthogonal constraint. This costs very expensive. In this paper, by introducing an additional judgement criterion after obtaining the approximate solution, a class of improved MMS (IMMS) iteration methods are proposed. By suitably choosing the judgement criterion, the IMMS iteration methods do not need to solve such system of linear equations at each iteration and thus greatly improves the computing efficiency. Convergence conditions of the IMMS iteration methods are studied when the system matrices are positive definite matrices and H+-matrices, respectively. Finally, two numerical examples are presented to show the effectiveness of the proposed IMMS iteration methods and their advantages over the existing MMS iteration methods when solving the HICP.

Wormhole Restrictions from Quantum Energy Inequalities

Wormhole solutions, bridges that connect different parts of spacetime, were proposed early in the history of General Relativity. Soon after, it was shown that all wormholes violate classical energy conditions, which are non-negativity constraints on contractions of the stress–energy tensor. Since these conditions are violated by quantum fields, it was believed that wormholes can be constructed in the context of semiclassical gravity. But negative energies in quantum field theory are not without restriction: quantum energy inequalities (QEIs) control renormalized negative energies averaged over a geodesic. Thus, QEIs provide restrictions on the construction of wormholes. This work is a review of the relevant literature, thus focusing on results where QEIs restrict traversable wormholes. Both ‘short’ and ‘long’ (without causality violations) wormhole solutions in the context of semiclassical gravity are examined. A new result is presented on constraints on the Maldacena, Milekhin, and Popov ‘long’ wormhole from the recently derived doubled smeared null energy condition.

A feature selection method for overlapping peaks in vibrational spectroscopy using nonnegatively constrained classical least squares

Chemometric models for multicomponent mixture analysis are reliant upon representative and accurate training data. However, the required amount of training data can increase exponentially with the number of constituents. Shifting spectral baselines and changing process objectives may necessitate recurring calibration data collection. Furthermore, all possible constituents may not be known prior to analysis. Here, we introduce a preprocessing procedure that reduces the burden of collecting extensive calibration datasets by filtering out non-target species (species that are not part of the calibration data) in real-time. The method, nonnegatively constrained classical least squares (NCCLS), utilizes a spectral nonnegativity constraint on non-target species to remove them from mixture spectra. The preprocessing method is physically motivated, does not rely on time-series data, and can operate in real-time. NCCLS is compared to established methods using in silico data and an experimental dataset comprised of Raman spectra and attenuated total reflectance - Fourier transform infrared spectra.

Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations

This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the preservation of non-negativity and mass constraints for the density, and gradient-robustness. The later property dramatically enhances the accuracy in well-balanced situations, such as the hydrostatic balance where the pressure gradient balances the gravity force. One of the studied schemes employs an H(div)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H(\ extrm{div})$$\\end{document}-conforming velocity ansatz space which ensures all mentioned properties, while a fully discontinuous method is shown to satisfy all properties but the gradient-robustness. Also higher-order schemes for both variants are presented and compared in three numerical benchmark problems. The final example shows the importance also for non-hydrostatic well-balanced states for the compressible Navier–Stokes equations.

Solving constrained consumption–investment problems by decomposition algorithms

Consumption–investment problems with maximizing utility agents are usually considered from a theoretical viewpoint, aiming at closed-form solutions for the optimal policy. However, such an approach requires that the model be relatively simple: even the inclusion of nonnegativity constraints can prevent the derivation of explicit solutions. In such cases, it is necessary to solve the problem numerically, but standard dynamic programming algorithms can only solve small problems due to the curse of dimensionality. In this paper, we adapt the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve dynamic constrained consumption–investment problems with stochastic labor income numerically. Unlike classical dynamic programming approaches, SDDP allows us to analyze problems with multiple assets, and an internal sampling procedure allows the problems to have a very large, or even infinite, number of scenarios. We start with a simpler problem for which a closed-form solution is known and compare it to the optimal policy obtained by SDDP. We then illustrate the flexibility of our approach by solving a defined contribution pension fund problem with multiple assets, for which no closed-form solution is available.

Dual space-based fuzzy graphs and orthogonal basis clustering for unsupervised feature selection

Unsupervised feature selection (UFS) takes an important position because gaining the class labels is laborious or even impossible. In the domain of UFS, clustering is a major means to exploit label information. The existing methods either could not model a clear clustering structure or could not utilize the local structure of data. Consequently, a new clustering method in combination with graph learning is proposed in this work. Specifically, for clustering, orthogonal basis clustering is introduced, where orthogonal constraints are imposed on the cluster center matrix and the clustering matrix. The clustering indicator matrix is also imposed by a non-negative constraint. A clearer clustering structure and more independent clustering centers are obtained through these constraints. For local preservation, given that traditional graphs for keeping the local manifold are faced with the problem of imbalanced neighbors, the fuzzy graph is introduced to acquire a robust structure, which is applied to both data space and feature space. The topological structure in these spaces can be well maintained. For the choice of salient features, ℓ2,0-norm regularization is imposed on the projection matrix. The object function is solved alternately. Then, a feature selection algorithm is designed. Experiments are designed and performed on nine real-world data sets. The results attest to the effectiveness of the proposed algorithm compared with other relevant algorithms.

Non-negative consistency affinity graph learning for unsupervised feature selection and clustering

Feature selection plays a crucial role in data mining and pattern recognition tasks. This paper proposes an efficient method for robust unsupervised feature selection, called joint local preserving and low-rank representation with nonnegative and symmetric constraint (JLPLRNS). This approach utilizes an indicator matrix instead of the row sparsity of the projection matrix to directly select some significant features from the original data and adaptively preserves the local geometric structure of original data into the low-dimensional embedded feature subspace via learned indicator matrix. By simultaneously imposing nonnegative symmetric and low-rank constraints on the representation coefficient matrix, it cannot only make this matrix discriminative, sparse and weight consistency for each pair of data, but also uncover the global structure of original data. These effectively will improve clustering performance. An algorithm based on the augmented Lagrange multiplier method with an alternating direction strategy is designed to resolve this model. Experimental results on various real datasets show that the proposed method can effectively identify some important features in data and outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering performance.

Sparse multi-view image clustering with complete similarity information

Multi-view image clustering aims to efficiently divide the collection of images by studying the characteristics of different views. Many studies performed Laplacian dimensionality reduction on the original image to avoid noise interference in constructing the similarity matrix. However, they ignored the problem that local similarity information and isolated image information are lost due to dimensionality reduction. These problems will result in the similarity matrix being insufficient to accurately describe the similarity between images, which in turn affects the clustering accuracy. Therefore, we propose a sparse multi-view spectral clustering model with complete similarity information between images (SMSC-CSI). The model combines the original image space and the low-dimensional spectral embedding space based on the adaptive neighbors method to learn the initial similarity matrices of each view jointly. On the one hand, the original space can retain all the similarity information between images so that the initial similarity matrix can accurately describe the similarity between images, which is conducive to accurate clustering. On the other hand, the low-dimensional space can avoid noise interference and retain the main structure of high-dimensional data, improving the robustness of the initial similarity matrix. Meanwhile, to ensure consistency among the views, the model minimizes the difference between the initial similarity matrix and the central fusion matrix by alternately updating to obtain the optimal weights and central fusion matrix for each view. Finally, we can obtain ideal clustering results directly with low model complexity and without post-processing steps such as K-means by adding non-negative Laplace rank constraints and ℓ0-norm constraints to the model objective function. Experimental results on different real image datasets show that SMSC-CSI can outperform some traditional clustering models and recent models on multi-view image clustering.

A new method to quantify the source contribution of mixed biodegraded oil based on pareto-optimized nonnegative matrix factorization and chord diagram visualization

The biogenic information of different components in crude oils with varying degrees of biodegradation is partially obscured, making traditional molecular indicators ineffective in determining the contributions of mixed sources. Previous studies have mainly focused on calculating mixed source proportion for normal oils, with few investigations involving biodegraded mixed oils. Developing a quantitative method for the mixed source contribution of biodegraded oils using machine learning (ML) algorithms is a significant attempt both to the exploration practice and theoretical progress. Taking the biomarker parameters resistant to biodegradation of 150 oil samples as input datasets, a new method called Pareto-Optimized NMF (PONMF) was proposed in this study, which combines multi-objective optimization (Pareto optimization) with non-negative matrix factorization (NMF) to analyze the relationship between biodegraded oils in the absence of source rock samples or original end-member (EM) oils while satisfying non-negativity constraints and additional constraint conditions. This method decomposes the matrix of crude oil samples into multiple end-members, each representing a possible input from a hydrocarbon source rock. Analysis of the end-member characteristics facilitates the deduction of potential hydrocarbon source layers and the traits of their depositional environments. This examination is supported by data derived from 15 prospective hydrocarbon source rock samples, which were employed to ascertain the actual geological significance of the end-members. The chord diagram depicts the visualization results of the overall relative contribution of source rock end members to crude oil in each area after the PONMF calculation results. The relative contribution of source rocks in different areas to the investigated crude oil samples is proportionate, and the arc length can reflect the contribution of the three sets of source rocks to a certain area. The findings indicate that the oils extracted from the stratified reservoirs in Eastern Chepaizi are primarily derived from the Permian source strata within the Shawan Depression, with a significant contribution ranging from 30% to 90% (EM2), and a lesser extent from the Carboniferous sources, contributing between 5% and 30% (EM1). Conversely, the provenance of oil in Western Chepaizi is overwhelmingly attributed to the Jurassic source interval located in the Sikeshu Depression, where EM3 accounts for over 85% of the source. Meanwhile, the oils in the Central Zone exhibit a composite origin, intermingling contributions from both EM1 and EM3. The advantage of this method is that it does not require direct access to hydrocarbon source rock samples or end-member oils but infers potential hydrocarbon source layers through the existing mixed-source oil samples. The PONMF method provides an effective tool for identifying the sources of biodegraded oils and can be used to study potential hydrocarbon source rock analysis for oils that have undergone biodegradation after hydrocarbon accumulation.

Synchronous deautoconvolution algorithm for discrete-time positive signals via [formula omitted]-divergence approximation

We pose the problem of the optimal approximation of a given nonnegative signal yt with the scalar autoconvolution (x∗x)t of a nonnegative signal xt, where xt and yt are signals of equal length. The I-divergence has been adopted as optimality criterion, being well suited to incorporate nonnegativity constraints. To find a minimizer we derive an iterative descent algorithm of the alternating minimization type. The algorithm is based on the lifting of the original problem to a larger space, a relaxation technique developed by Csiszár and Tusnády in [Statistics & Decisions (S1) (1984), 205–237] which, in the present context, requires the solution of a hard partial minimization problem. We study the asymptotic behavior of the algorithm exploiting the optimality properties of the partial minimization problems and prove, among other results, that its limit points are Kuhn–Tucker points of the original minimization problem. Numerical experiments illustrate the results.

Positive Competitive Networks for Sparse Reconstruction.

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with nonnegativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including, for example, neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence depends only on a property of the dictionary and is linear-exponential in the sense that initially, the convergence rate is at worst linear and then, after a transient, becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without nonnegativity constraints. Finally, we validate the effectiveness of our approach using a numerical example.

Crop water requirement and irrigation scheduling under climate change scenario, and optimal cropland allocation in lower kulfo catchment

Crop water requirement and irrigation scheduling in Lower Kulfo Catchment of southern Ethiopia have not assessed under climate change scenarios, and the allocation of crop land also not optimal that signifcantly challenges to crop productivity.Therefore, this study was conducted to evaluate the effects of climate change on future crop water requirements, and irrigation scheduling, and to allocate cropland optimally. Bias of projected precipitation and temperature were corrected by utilizing Climate Model data with the hydrologic modeling tool (CMhyd). Alongside, crop water requirements and irrigation scheduling were assessed using Crop Water Assessment Tool. After estimating crop water requirement, crop land were allocated optimally using General Algebraic Modeling System programming with non-negativity constraints (scenario 1), and non-negativity constraints based on farmers adaptation (scenario 2). Average reference evapotranspiration from 2030 to 2050 and 2060 to 2080 was increased by 11.9 %, and 16.2 %, respectively compared with the reference period (2010–2022). The total seasonal crop water requirements were 4,529 mm, 4866.7 mm, and 5272.2 mm under 2010 to 2022, 2030 to 2050, and 2060 to 2080 climate change scenarios, respectively. The meean irrigation interval in 2010–2022, 2030 to 2050, and 2060 to 2080 climate change scenarios were 8 days, 7 days, and 5 days, respectively. This irrigation interval was decreased by 14 % (2030–2050), and 34 % (2060–2080) compared with the reference period. In 2030 to 2050 and 2026 to 2080 climate change scenarios, the required irrigation water at the inlet of main canal increased by 6.8 %, and 18 %, respectively. The optimal allocated area for tomato (60.4 %), maize (20.8 %), and watermelon (18.8 %) in scenario 1 with net benefit of 1.47*108 Ethiopian Birr. The allocated areas in scenario 2 were (48 %) for maize, (31.6 %) for tomato, and (20.4 %) for watermelon with 1.34*108 Ethiopian Birr net benefit it was reduced by 19.1 % compared with the net benefit in scenario 1. Fruit crops alone may not suffice for local food needs and to address this, small farmers should grow maize, tomato, and watermelon. This research aids policymakers in encouraging climate-resilient agriculture and improving small-scale farmers' awareness through conducting workshops and training.

Nonnegative iterative reweighted method for sparse linear complementarity problem

Solution of sparse linear complementarity problem (LCP) has been widely discussed in many applications. In this paper, we consider the ℓp regularization problem with nonnegative constraint for sparse LCP, and propose algorithms based on the iterative reweighted method to approach a sparse solution of the LCP, and then show the convergence to the stationary point of ℓp regularization problem. Numerical results on simulated data exhibit an excellent performance of the proposed algorithms on approaching a sparse solution of the LCP. Finally, we apply this method to the frictional and frictionless contact problems. The numerical experiments demonstrate that the contact problems can be efficiently solved by the proposed algorithm.

Discriminative dictionary learning for nonnegative representation based classification

Representation based classification (RC) algorithms have been successfully applied to pattern classification. However, most existing RC algorithms are not robust to bad training samples, since they ignore learning more discriminative dictionary atoms and instead directly use training samples as dictionary atoms. In addition, in order to improve expression ability and recognition accuracy, RC algorithms often need to expand the number of dictionary atoms, resulting in a surge in storage and computing costs. To obtain a more discriminative and compact dictionary, this study proposes discriminative dictionary learning for nonnegative representation based classification (DDLNRC). Specifically, in the DDLNRC, this paper utilizes nonnegative constraint to obtain a nonnegative representation for each training sample on the dictionary. In the dictionary learning stage, for a training sample, the DDLNRC minimizes the intra-class reconstruction error of the training sample and simultaneously enlarges the distance between the training sample and the atom that has the most influence on inter-class reconstruction error. Experiments demonstrate the effectiveness of the DDLNRC. Combined with the deep neural network features, it also can achieve higher accuracy than using the Softmax.

Lp-norm relaxation approach for 3D measurement via instantaneous light field of ethylene premixed flames

Optical imaging technology based on flame spontaneous radiation is a promising tool for combustion diagnosis. However, the existing radiation thermometry technology faces the problems of low angular resolution and low efficiency in solving radiative transfer. Therefore, a novel optical imaging model is proposed, which combines light field imaging theory with equation-solving integral equation method based on radiation distribution factor to effectively decouple the radiative properties related to transfer process and the temperature-related source terms. Aiming at the problem that traditional method may cause over-smooth effect, Lp-norm regularization based on non-negative constraint is established. Results show that Lp-norm can improve reconstruction quality and robustness, but p value needs to be reasonably selected according to noise level and flame inhomogeneity. Experimental study of ethylene/air-premixed flames shows that the methodology can realize 3D measurement (900 ∼ 1550 K). Compared with laser absorption spectroscopy and thermocouple, error is better than 3 % at height above burner 15 mm.