• Title/Summary/Keyword: Least Squares Minimization

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Object Tracking Based on Exactly Reweighted Online Total-Error-Rate Minimization (정확히 재가중되는 온라인 전체 에러율 최소화 기반의 객체 추적)

  • JANG, Se-In;PARK, Choong-Shik
    • Journal of Intelligence and Information Systems
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    • v.25 no.4
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    • pp.53-65
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    • 2019
  • Object tracking is one of important steps to achieve video-based surveillance systems. Object tracking is considered as an essential task similar to object detection and recognition. In order to perform object tracking, various machine learning methods (e.g., least-squares, perceptron and support vector machine) can be applied for different designs of tracking systems. In general, generative methods (e.g., principal component analysis) were utilized due to its simplicity and effectiveness. However, the generative methods were only focused on modeling the target object. Due to this limitation, discriminative methods (e.g., binary classification) were adopted to distinguish the target object and the background. Among the machine learning methods for binary classification, total error rate minimization can be used as one of successful machine learning methods for binary classification. The total error rate minimization can achieve a global minimum due to a quadratic approximation to a step function while other methods (e.g., support vector machine) seek local minima using nonlinear functions (e.g., hinge loss function). Due to this quadratic approximation, the total error rate minimization could obtain appropriate properties in solving optimization problems for binary classification. However, this total error rate minimization was based on a batch mode setting. The batch mode setting can be limited to several applications under offline learning. Due to limited computing resources, offline learning could not handle large scale data sets. Compared to offline learning, online learning can update its solution without storing all training samples in learning process. Due to increment of large scale data sets, online learning becomes one of essential properties for various applications. Since object tracking needs to handle data samples in real time, online learning based total error rate minimization methods are necessary to efficiently address object tracking problems. Due to the need of the online learning, an online learning based total error rate minimization method was developed. However, an approximately reweighted technique was developed. Although the approximation technique is utilized, this online version of the total error rate minimization could achieve good performances in biometric applications. However, this method is assumed that the total error rate minimization can be asymptotically achieved when only the number of training samples is infinite. Although there is the assumption to achieve the total error rate minimization, the approximation issue can continuously accumulate learning errors according to increment of training samples. Due to this reason, the approximated online learning solution can then lead a wrong solution. The wrong solution can make significant errors when it is applied to surveillance systems. In this paper, we propose an exactly reweighted technique to recursively update the solution of the total error rate minimization in online learning manner. Compared to the approximately reweighted online total error rate minimization, an exactly reweighted online total error rate minimization is achieved. The proposed exact online learning method based on the total error rate minimization is then applied to object tracking problems. In our object tracking system, particle filtering is adopted. In particle filtering, our observation model is consisted of both generative and discriminative methods to leverage the advantages between generative and discriminative properties. In our experiments, our proposed object tracking system achieves promising performances on 8 public video sequences over competing object tracking systems. The paired t-test is also reported to evaluate its quality of the results. Our proposed online learning method can be extended under the deep learning architecture which can cover the shallow and deep networks. Moreover, online learning methods, that need the exact reweighting process, can use our proposed reweighting technique. In addition to object tracking, the proposed online learning method can be easily applied to object detection and recognition. Therefore, our proposed methods can contribute to online learning community and object tracking, detection and recognition communities.

Multiobjective Space Search Optimization and Information Granulation in the Design of Fuzzy Radial Basis Function Neural Networks

  • Huang, Wei;Oh, Sung-Kwun;Zhang, Honghao
    • Journal of Electrical Engineering and Technology
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    • v.7 no.4
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    • pp.636-645
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    • 2012
  • This study introduces an information granular-based fuzzy radial basis function neural networks (FRBFNN) based on multiobjective optimization and weighted least square (WLS). An improved multiobjective space search algorithm (IMSSA) is proposed to optimize the FRBFNN. In the design of FRBFNN, the premise part of the rules is constructed with the aid of Fuzzy C-Means (FCM) clustering while the consequent part of the fuzzy rules is developed by using four types of polynomials, namely constant, linear, quadratic, and modified quadratic. Information granulation realized with C-Means clustering helps determine the initial values of the apex parameters of the membership function of the fuzzy neural network. To enhance the flexibility of neural network, we use the WLS learning to estimate the coefficients of the polynomials. In comparison with ordinary least square commonly used in the design of fuzzy radial basis function neural networks, WLS could come with a different type of the local model in each rule when dealing with the FRBFNN. Since the performance of the FRBFNN model is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials present in the consequent parts of the rules, we carry out both structural as well as parametric optimization of the network. The proposed IMSSA that aims at the simultaneous minimization of complexity and the maximization of accuracy is exploited here to optimize the parameters of the model. Experimental results illustrate that the proposed neural network leads to better performance in comparison with some existing neurofuzzy models encountered in the literature.

A chord error conforming tool path B-spline fitting method for NC machining based on energy minimization and LSPIA

  • He, Shanshan;Ou, Daojiang;Yan, Changya;Lee, Chen-Han
    • Journal of Computational Design and Engineering
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    • v.2 no.4
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    • pp.218-232
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    • 2015
  • Piecewise linear (G01-based) tool paths generated by CAM systems lack $G_1$ and $G_2$ continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA) is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA) to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1) an improved technique for initial control point determination over Dominant Point Method, (2) an algorithm that updates foot point parameters as needed, (3) analysis of the degrees of freedom of control points to insert new control points only when needed, (4) chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution.

Determination of Multisine Coefficients for Power Amplifier Testing

  • Park, Youngcheol;Yoon, Hoijin
    • Journal of electromagnetic engineering and science
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    • v.12 no.4
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    • pp.290-292
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    • 2012
  • This paper proposes a setup for a best multisine design method that uses a time-domain optimization. The method is based on minimization of the time-domain error, so its resulting multisine has a very accurate ACLR estimation. This is because its probability distribution and sample-to-sample correlation are close to those of the original signal, which are crucial for the testing of nonlinear power amplifiers. In addition, a hyperbolic-tangent function is introduced to control the ripple of tone magnitudes within signal bandwidth. For the verification, multisines were generated and compared for many aspects such as normalized error, in-band ripple, and ACLR estimation. Test results with different numbers of tones provide supporting evidence that the suggested multisine design has better ripple suppression, by up to 7 dB, and better accuracy, by up to 0.2 dB, when compared to the conventional method. The accuracy of the ACLR was improved by about 5 dB when the number of tones was 4. The suggested method improves the ACLR estimation performance of multisine testing due to its closer resemblance to the target modulation signal.

Analysis of axisymmetric extrusion through curved dies by using the method of weighted residuals (가중잔류항법을 이용한 곡면금형의 축대칭 전방압출해석)

  • 조종래;양동열
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.3
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    • pp.509-518
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    • 1987
  • The paper is concerned with the analysis of axisymmetric forward extrusion by using the method of weighted residuals. In the method of weighted residuals, the flow function and the stress functions are assumed so as to cover the global control volume. The derived stress and strain components are used to formulate a constitutive equation in the error form, so that the error is minimized to determine the stress and strain components. The method of least squares is then chosen for the minimization of errors. The distribution of stresses and strains and the forming load are determined for the workhardening material considering the frictional effect at the die surface. The computed results are very similar to those obtained by the finite element method. The method is simpler in application and requires less computational time than the finite element method. Experiments are carried out for aluminum and steel specimens using curved dies. It is found that the experimental observation is mostly in agreement with the computed results by the method of weighted residuals.

Large-scaled truss topology optimization with filter and iterative parameter control algorithm of Tikhonov regularization

  • Nguyen, Vi T.;Lee, Dongkyu
    • Steel and Composite Structures
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    • v.39 no.5
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    • pp.511-528
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    • 2021
  • There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

Application of 3D magnetotelluric investigation for geothermal exploration - Examples in Japan and Korea

  • Uchida Toshihiro;Song Yoonho;Mitsuhata Yuji;Lee Seong Kon
    • 한국지구물리탐사학회:학술대회논문집
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    • 2003.11a
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    • pp.390-397
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    • 2003
  • A three-dimensional (3D) inversion technique has been developed for interpretation of magnetotelluric (MT) data. The inversion method is based on the linearized least-squares (Gauss-Newton) method with smoothness regularization. In addition to the underground 3D resistivity distribution, static shifts are also treated as unknown parameters in the inversion. The forward modeling is by the staggered-grid finite difference method. A Bayesian criterion ABle is applied to search the optimum trade-off among the minimization of the data misfit, model roughness and static shifts. The method has been applied to several MT datasets obtained at geothermal fields in Japan and other Asian countries. In this paper, two examples will be discussed: one is the data at the Ogiri geothermal area, southwestern Japan, and the other is at the Pohang low-enthalpy geothermal field, southeastern Korea. The inversion of the Ogiri data has been performed stably, resulting in a good fitting between the observed and computed apparent resistivities and phases. The recovered 3D resistivity structure is generally similar to the two-dimensional (2D) inversion models, although the deeper portion of the 3D model seems to be more realistic than that of the 2D model. The 3D model is also in a good agreement with the geological model of the geothermal reservoirs. 3D interpretation of the Pohang MT data is still preliminary. Although the fitting to the observed data is very good, the preliminary 3D model is not reliable enough because the station coverage is not sufficient for a 3D inversion.

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Image Denoising for Metal MRI Exploiting Sparsity and Low Rank Priors

  • Choi, Sangcheon;Park, Jun-Sik;Kim, Hahnsung;Park, Jaeseok
    • Investigative Magnetic Resonance Imaging
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    • v.20 no.4
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    • pp.215-223
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    • 2016
  • Purpose: The management of metal-induced field inhomogeneities is one of the major concerns of distortion-free magnetic resonance images near metallic implants. The recently proposed method called "Slice Encoding for Metal Artifact Correction (SEMAC)" is an effective spin echo pulse sequence of magnetic resonance imaging (MRI) near metallic implants. However, as SEMAC uses the noisy resolved data elements, SEMAC images can have a major problem for improving the signal-to-noise ratio (SNR) without compromising the correction of metal artifacts. To address that issue, this paper presents a novel reconstruction technique for providing an improvement of the SNR in SEMAC images without sacrificing the correction of metal artifacts. Materials and Methods: Low-rank approximation in each coil image is first performed to suppress the noise in the slice direction, because the signal is highly correlated between SEMAC-encoded slices. Secondly, SEMAC images are reconstructed by the best linear unbiased estimator (BLUE), also known as Gauss-Markov or weighted least squares. Noise levels and correlation in the receiver channels are considered for the sake of SNR optimization. To this end, since distorted excitation profiles are sparse, $l_1$ minimization performs well in recovering the sparse distorted excitation profiles and the sparse modeling of our approach offers excellent correction of metal-induced distortions. Results: Three images reconstructed using SEMAC, SEMAC with the conventional two-step noise reduction, and the proposed image denoising for metal MRI exploiting sparsity and low rank approximation algorithm were compared. The proposed algorithm outperformed two methods and produced 119% SNR better than SEMAC and 89% SNR better than SEMAC with the conventional two-step noise reduction. Conclusion: We successfully demonstrated that the proposed, novel algorithm for SEMAC, if compared with conventional de-noising methods, substantially improves SNR and reduces artifacts.

Study on Beamforming of Conformal Array Antenna Using Support Vector Regression (Support Vector Regression을 이용한 컨포멀 배열 안테나의 빔 형성 연구)

  • Lee, Kang-In;Jung, Sang-Hoon;Ryu, Hong-Kyun;Yoon, Young-Joong;Nam, Sang-Wook;Chung, Young-Seek
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.29 no.11
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    • pp.868-877
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    • 2018
  • In this paper, we propose a new beamforming algorithm for a conformal array antenna based on support vector regression(SVR). While the conventional least squares method(LSM) considers all sample errors, SVR considers errors beyond the given error bound to obtain the optimum weight vector, which has a sparse solution and the advantage of the minimization of the overfitting problem. To verify the performance of the proposed algorithm, we apply SVR to the experimentally measured active element patterns of the conformal array antenna and obtain the weights for beamforming. In addition, we compare the beamforming results of SVR and LSM.

Non-Fickian Diffusion of Organic Solvents in Fluoropolymeys (불소고분자내 유기용매의 비-픽 확산)

  • 이상화
    • Polymer(Korea)
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    • v.28 no.1
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    • pp.24-34
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    • 2004
  • Transient sorption experiments were conducted among several combinations of fluoropolymers and various organic solvents. Fully fluorinated polymer tended to exhibit ideal sorption behavior, while partially fluorinated polymers showed anomalous sorption behaviors with a drastic acceleration at the final stage of uptake. Minimization of least-squares of the measured and predicted fractional uptake, which indicated the increasing degree of deviation from Fickian diffusion, gave values of 3.0${\times}$10$\^$-4/, 1.75${\times}$10$\^$-3/, 8.68${\times}$10/sup-3/, 1.75${\times}$10$\^$-2/, respectively, for perfluoroalkoxy copolymer, poly(ethylene-co-tetrafluoroethylene), poly(vinylidene fluoride), poly(ethylene-co-chlorotrifluoroethylene). From stress-strain tests, it was confirmed that non-Fickian diffusion is closely related to the significant variation of mechanical properties (such as modulus and tensile strength) of swollen polymer. Anomalous sorption behavior stemmed from non-Fickian diffusion caused by nonlinear disruption of polar inter-segmental bonds due to solvent-induced plasticization. Thus, it is imperative to investigate the diffusion behavior of swelling solvents in partially fluorinated polymers, especially for the application to barrier materials or perm-selective membranes.