Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009622
Ming Li, Wei Yi, L. Kong
This paper focuses on addressing the data fusion problems in asynchronous sensor networks using distribute particle filter (DPF). Generally, the type of the local information communicated between sensors and the time synchronization of the local information are two major issues for DPF algorithms, which have significant influence on fusion accuracy and communication requirements. To address these issues, in this paper, a likelihood-based asynchronous batch estimation (ABE) scheme is developed, wherein local likelihood function is regarded as the local information to ensure a high fusion accuracy, and the asynchronous likelihood functions of the multiple sensors during a predefined update period are fused to jointly estimate the target states. Then, to implement this framework distributively using particle filter, a likelihood-based ABE DPF (LB-ABE-DPF) algorithm is proposed. In addition, to achieve low communication requirements, the likelihood function is parametrically represented by polynomial approximation and least square (LS) approximation strategies. Numerical results show the efficiency of the proposed algorithm.
{"title":"A likelihood-based distributed particle filter for asynchronous sensor networks","authors":"Ming Li, Wei Yi, L. Kong","doi":"10.23919/ICIF.2017.8009622","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009622","url":null,"abstract":"This paper focuses on addressing the data fusion problems in asynchronous sensor networks using distribute particle filter (DPF). Generally, the type of the local information communicated between sensors and the time synchronization of the local information are two major issues for DPF algorithms, which have significant influence on fusion accuracy and communication requirements. To address these issues, in this paper, a likelihood-based asynchronous batch estimation (ABE) scheme is developed, wherein local likelihood function is regarded as the local information to ensure a high fusion accuracy, and the asynchronous likelihood functions of the multiple sensors during a predefined update period are fused to jointly estimate the target states. Then, to implement this framework distributively using particle filter, a likelihood-based ABE DPF (LB-ABE-DPF) algorithm is proposed. In addition, to achieve low communication requirements, the likelihood function is parametrically represented by polynomial approximation and least square (LS) approximation strategies. Numerical results show the efficiency of the proposed algorithm.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129024763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009682
Henri Nurminen, R. Piché, S. Godsill
We propose a deterministic recursive algorithm for approximate Bayesian filtering. The proposed filter uses a function referred to as the approximate Gaussian flow transformation that transforms a Gaussian prior random variable into an approximate posterior random variable. Given a Gaussian filter prediction distribution, the succeeding filter prediction is approximated as Gaussian by applying sigma point moment-matching to the composition of the Gaussian flow transformation and the state transition function. This requires linearising the measurement model at each sigma point, solving the linearised models analytically, and introducing the measurement information gradually to improve the linearisation points progressively. Computer simulations show that the proposed method can provide higher accuracy and better posterior covariance matrix approximation than some state-of-the art computationally light approximative filters when the measurement model function is nonlinear but differentiable and the noises are additive and Gaussian. We also present a highly nonlinear scenario where the proposed filter occasionally diverges. In the accuracy-computational complexity axis the proposed algorithm is between Kalman filter extensions and Monte Carlo methods.
{"title":"Gaussian flow sigma point filter for nonlinear Gaussian state-space models","authors":"Henri Nurminen, R. Piché, S. Godsill","doi":"10.23919/ICIF.2017.8009682","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009682","url":null,"abstract":"We propose a deterministic recursive algorithm for approximate Bayesian filtering. The proposed filter uses a function referred to as the approximate Gaussian flow transformation that transforms a Gaussian prior random variable into an approximate posterior random variable. Given a Gaussian filter prediction distribution, the succeeding filter prediction is approximated as Gaussian by applying sigma point moment-matching to the composition of the Gaussian flow transformation and the state transition function. This requires linearising the measurement model at each sigma point, solving the linearised models analytically, and introducing the measurement information gradually to improve the linearisation points progressively. Computer simulations show that the proposed method can provide higher accuracy and better posterior covariance matrix approximation than some state-of-the art computationally light approximative filters when the measurement model function is nonlinear but differentiable and the noises are additive and Gaussian. We also present a highly nonlinear scenario where the proposed filter occasionally diverges. In the accuracy-computational complexity axis the proposed algorithm is between Kalman filter extensions and Monte Carlo methods.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128572538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009758
Salma Ben Dhaou, Kuang Zhou, M. Kharoune, Arnaud Martin, B. B. Yaghlane
Currently, there are many approaches designed for the task of detecting communities in social networks. Among them, some methods only consider the topological graph structure, while others can take use of both the graph structure and the node attributes. In real-world networks, there are many uncertain and noisy attributes in the graph. In this paper, we will present how we can detect communities for graphs with uncertain attributes in the first step. The numerical, probabilistic as well as evidential attributes are generated according to the graph structure. In the second step, some noise will be added to the attributes. We perform experiments on graphs with different types of attributes and compare the detection results in terms of the Normalized Mutual Information (NMI) values. The experimental results show that the clustering with evidential attributes give better results comparing to those with probabilistic and numerical attributes. This illustrates the advantages of evidential attributes.
{"title":"The advantage of evidential attributes in social networks","authors":"Salma Ben Dhaou, Kuang Zhou, M. Kharoune, Arnaud Martin, B. B. Yaghlane","doi":"10.23919/ICIF.2017.8009758","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009758","url":null,"abstract":"Currently, there are many approaches designed for the task of detecting communities in social networks. Among them, some methods only consider the topological graph structure, while others can take use of both the graph structure and the node attributes. In real-world networks, there are many uncertain and noisy attributes in the graph. In this paper, we will present how we can detect communities for graphs with uncertain attributes in the first step. The numerical, probabilistic as well as evidential attributes are generated according to the graph structure. In the second step, some noise will be added to the attributes. We perform experiments on graphs with different types of attributes and compare the detection results in terms of the Normalized Mutual Information (NMI) values. The experimental results show that the clustering with evidential attributes give better results comparing to those with probabilistic and numerical attributes. This illustrates the advantages of evidential attributes.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116202983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009710
Yuxuan Xia, Karl Granström, L. Svensson, Á. F. García-Fernández
In this paper, we evaluate the performance of labelled and unlabelled multi-Bernoulli conjugate priors for multi-target filtering. Filters are compared in two different scenarios with performance assessed using the generalised optimal sub-pattern assignment (GOSPA) metric. The first scenario under consideration is tracking of well-spaced targets. The second scenario is more challenging and considers targets in close proximity, for which filters may suffer from coalescence. We analyse various aspects of the filters in these two scenarios. Though all filters have pros and cons, the Poisson multi-Bernoulli filters arguably provide the best overall performance concerning GOSPA and computational time.
{"title":"Performance evaluation of multi-bernoulli conjugate priors for multi-target filtering","authors":"Yuxuan Xia, Karl Granström, L. Svensson, Á. F. García-Fernández","doi":"10.23919/ICIF.2017.8009710","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009710","url":null,"abstract":"In this paper, we evaluate the performance of labelled and unlabelled multi-Bernoulli conjugate priors for multi-target filtering. Filters are compared in two different scenarios with performance assessed using the generalised optimal sub-pattern assignment (GOSPA) metric. The first scenario under consideration is tracking of well-spaced targets. The second scenario is more challenging and considers targets in close proximity, for which filters may suffer from coalescence. We analyse various aspects of the filters in these two scenarios. Though all filters have pros and cons, the Poisson multi-Bernoulli filters arguably provide the best overall performance concerning GOSPA and computational time.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131420051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009824
Huilong Zhang, F. Dufour, Jonatha Anselmi, D. Laneuville, A. Negre
We investigate the problem of determining the trajectory that an observer should follow to be able to accurately track a target in a bearings-only measurements context. We assume that the target's motion is uniform and that the measurements are corrupted by an additive Gaussian white noise. Though, in theory, this process is observable if the observer maneuvers with turns or accelerations, the quality of the resulting estimation strongly depends on the trajectory chosen by the observer. In this paper, we present a numerical method to compute a trajectory of a maneuvering observer with the objective of maximizing the cumulative sum of bearing rates between the target and observer. Our approach is based on the piecewise stochastic control of a finite-horizon Markov process. A quantization method is applied to transform the problem into a discrete domain. We show that this transformation allows for a numerically tractable solution able to accurately track the target in a number of practical scenarios.
{"title":"Piecewise optimal trajectories of observer for bearings-only tracking by quantization","authors":"Huilong Zhang, F. Dufour, Jonatha Anselmi, D. Laneuville, A. Negre","doi":"10.23919/ICIF.2017.8009824","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009824","url":null,"abstract":"We investigate the problem of determining the trajectory that an observer should follow to be able to accurately track a target in a bearings-only measurements context. We assume that the target's motion is uniform and that the measurements are corrupted by an additive Gaussian white noise. Though, in theory, this process is observable if the observer maneuvers with turns or accelerations, the quality of the resulting estimation strongly depends on the trajectory chosen by the observer. In this paper, we present a numerical method to compute a trajectory of a maneuvering observer with the objective of maximizing the cumulative sum of bearing rates between the target and observer. Our approach is based on the piecewise stochastic control of a finite-horizon Markov process. A quantization method is applied to transform the problem into a discrete domain. We show that this transformation allows for a numerically tractable solution able to accurately track the target in a number of practical scenarios.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"2 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133481811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009762
Simen Hexeberg, A. Flåten, Bjørn-Olav H. Eriksen, E. Brekke
In order for autonomous surface vessels (ASVs) to avoid collisions at sea it is necessary to predict the future trajectories of surrounding vessels. This paper investigate the use of historical automatic identification system (AIS) data to predict such trajectories. The availability of AIS data have steadily increased in the last years as a result of more regulations, together with wider coverage through AIS integration on satellites and more land based receivers. Several AIS-based methods for predicting vessel trajectories already exist. However, these prediction techniques tend to focus on time horizons in the level of hours. The prediction time of our interest typically ranges from a few minutes up to about 15 minutes, depending on the maneuverability of the ASV. This paper presents a novel datadriven approach which recursively use historical AIS data in the neighborhood of a predicted position to predict next position and time. Three course and speed prediction methods are compared for one time step predictions. Lastly, the algorithm is briefly tested for multiple time steps in curved environments and shows good potential.
{"title":"AIS-based vessel trajectory prediction","authors":"Simen Hexeberg, A. Flåten, Bjørn-Olav H. Eriksen, E. Brekke","doi":"10.23919/ICIF.2017.8009762","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009762","url":null,"abstract":"In order for autonomous surface vessels (ASVs) to avoid collisions at sea it is necessary to predict the future trajectories of surrounding vessels. This paper investigate the use of historical automatic identification system (AIS) data to predict such trajectories. The availability of AIS data have steadily increased in the last years as a result of more regulations, together with wider coverage through AIS integration on satellites and more land based receivers. Several AIS-based methods for predicting vessel trajectories already exist. However, these prediction techniques tend to focus on time horizons in the level of hours. The prediction time of our interest typically ranges from a few minutes up to about 15 minutes, depending on the maneuverability of the ASV. This paper presents a novel datadriven approach which recursively use historical AIS data in the neighborhood of a predicted position to predict next position and time. Three course and speed prediction methods are compared for one time step predictions. Lastly, the algorithm is briefly tested for multiple time steps in curved environments and shows good potential.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131028366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009672
Jonatan Olofsson, Clas Veiback, Gustaf Hendeby
In polar region operations, drift ice positioning and tracking is useful for both scientific and safety reasons. At its core is a Multi-Target Tracking (MTT) problem in which currents and winds make motion modeling difficult. One recent algorithm in the MTT field, employed in this paper, is the Labeled Multi-Bernoulli (LMB) filter. In particular, a proposed reformulation of the LMB equations exposes a structure which is exploited to propose a compact algorithm for the generation of the filter's posterior distribution. Further, spatial indexing is applied to the clustering process of the filter, allowing efficient separation of the filter into smaller, independent parts with lesser total complexity than that of an unclustered filter. Many types of sensors can be employed to generate detections of sea ice, and in this paper a recorded dataset from a Terrestrial Radar Interferometer (TRI) is used to demonstrate the application of the Spatially Indexed Labeled Multi-Bernoulli filter to estimate the currents of an observed area in Kongsfjorden, Svalbard.
{"title":"Sea ice tracking with a Spatially Indexed Labeled Multi-Bernoulli filter","authors":"Jonatan Olofsson, Clas Veiback, Gustaf Hendeby","doi":"10.23919/ICIF.2017.8009672","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009672","url":null,"abstract":"In polar region operations, drift ice positioning and tracking is useful for both scientific and safety reasons. At its core is a Multi-Target Tracking (MTT) problem in which currents and winds make motion modeling difficult. One recent algorithm in the MTT field, employed in this paper, is the Labeled Multi-Bernoulli (LMB) filter. In particular, a proposed reformulation of the LMB equations exposes a structure which is exploited to propose a compact algorithm for the generation of the filter's posterior distribution. Further, spatial indexing is applied to the clustering process of the filter, allowing efficient separation of the filter into smaller, independent parts with lesser total complexity than that of an unclustered filter. Many types of sensors can be employed to generate detections of sea ice, and in this paper a recorded dataset from a Terrestrial Radar Interferometer (TRI) is used to demonstrate the application of the Spatially Indexed Labeled Multi-Bernoulli filter to estimate the currents of an observed area in Kongsfjorden, Svalbard.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123590872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009720
Ruilong Chen, M. Hawes, Olga Isupova, L. Mihaylova, Hao Zhu
Vehicle logo recognition is an important part of vehicle identification in intelligent transportation systems. State-of-the-art vehicle logo recognition approaches typically consider training models on large datasets. However, there might only be a small training dataset to start with and more images can be obtained during the real-time applications. This paper proposes an online image recognition framework which provides solutions for both small and large datasets. Using this recognition framework, models are built efficiently using a weight updating scheme. Another novelty of this work is that the Cauchy prior logistic regression with conjugate gradient descent is proposed to deal with the multinomial classification tasks. The Cauchy prior results in a quicker convergence speed for the weight updating process which could decrease the computational cost for both online and offline methods. By testing with a publicly available dataset, the Cauchy prior logistic regression deceases the classification time by 59%. An accuracy of up to 98.80% is achieved when the proposed framework is applied.
{"title":"Online vehicle logo recognition using Cauchy prior logistic regression","authors":"Ruilong Chen, M. Hawes, Olga Isupova, L. Mihaylova, Hao Zhu","doi":"10.23919/ICIF.2017.8009720","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009720","url":null,"abstract":"Vehicle logo recognition is an important part of vehicle identification in intelligent transportation systems. State-of-the-art vehicle logo recognition approaches typically consider training models on large datasets. However, there might only be a small training dataset to start with and more images can be obtained during the real-time applications. This paper proposes an online image recognition framework which provides solutions for both small and large datasets. Using this recognition framework, models are built efficiently using a weight updating scheme. Another novelty of this work is that the Cauchy prior logistic regression with conjugate gradient descent is proposed to deal with the multinomial classification tasks. The Cauchy prior results in a quicker convergence speed for the weight updating process which could decrease the computational cost for both online and offline methods. By testing with a publicly available dataset, the Cauchy prior logistic regression deceases the classification time by 59%. An accuracy of up to 98.80% is achieved when the proposed framework is applied.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124602894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009640
Yuxin Zhao, C. Fritsche, F. Gunnarsson
Assessing the fundamental performance limitations in Bayesian filtering can be carried out using the parametric Cramér-Rao bound (CRB). The parametric CRB puts a lower bound on mean square error (MSE) matrix conditioned on a specific state trajectory realization. In this work, we derive the parametric CRB for state-space models, where the measurement equation is modeled by a Gaussian process regression. These models appear, for instance in proximity report-based positioning, where proximity reports are obtained by hard thresholding of received signal strength (RSS) measurements, that are modeled through Gaussian process regression. The proposed parametric CRB is evaluated on selected state trajectories and further compared with the positioning performance obtained by the particle filter. The results corroborate that the positioning accuracy achieved in this framework is close to the parametric CRB.
{"title":"Parametric lower bound for nonlinear filtering based on Gaussian process regression model","authors":"Yuxin Zhao, C. Fritsche, F. Gunnarsson","doi":"10.23919/ICIF.2017.8009640","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009640","url":null,"abstract":"Assessing the fundamental performance limitations in Bayesian filtering can be carried out using the parametric Cramér-Rao bound (CRB). The parametric CRB puts a lower bound on mean square error (MSE) matrix conditioned on a specific state trajectory realization. In this work, we derive the parametric CRB for state-space models, where the measurement equation is modeled by a Gaussian process regression. These models appear, for instance in proximity report-based positioning, where proximity reports are obtained by hard thresholding of received signal strength (RSS) measurements, that are modeled through Gaussian process regression. The proposed parametric CRB is evaluated on selected state trajectories and further compared with the positioning performance obtained by the particle filter. The results corroborate that the positioning accuracy achieved in this framework is close to the parametric CRB.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127498604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-10DOI: 10.23919/ICIF.2017.8009753
Jianbo Li, Jie Zhou, Bin Zhang, X. Li
This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.
{"title":"Estimation of high dimensional covariance matrices by shrinkage algorithms","authors":"Jianbo Li, Jie Zhou, Bin Zhang, X. Li","doi":"10.23919/ICIF.2017.8009753","DOIUrl":"https://doi.org/10.23919/ICIF.2017.8009753","url":null,"abstract":"This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.","PeriodicalId":148407,"journal":{"name":"2017 20th International Conference on Information Fusion (Fusion)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134348267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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