Symmetric LINEX loss twin support vector machine for robust classification and its fast iterative algorithm

Twin support vector machine (TSVM) is a practical machine learning algorithm, whereas traditional TSVM can be limited for data with outliers or noises. To address this problem, we propose a novel TSVM with the symmetric LINEX loss function (SLTSVM) for robust classification. There are several advantages of our method: (1) The performance of the proposed SLTSVM for data with outliers or noise can be improved by using the symmetric LINEX loss function. (2) The introduction of regularization term can effectively improve the generalization ability of our model. (3) An efficient iterative algorithm is developed to solve the optimization problems of our SLTSVM. (4) The convergence and time complexity of the iterative algorithm are analyzed in detail. Furthermore, our model does not involve loss function parameter, which makes our method more competitive. Experimental results on synthetic, benchmark and image datasets with label noises and feature noises demonstrate that our proposed method slightly outperforms other state-of-the-art methods on most datasets.

Robust transformed l1 metric for fluorescence molecular tomography

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l₂-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed.

METHODS

In this study, we propose a novel robust transformed l₁ (TL1) metric that interpolates l₀ and l₁ norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the l_p-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly.

RESULTS

Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery.

CONCLUSIONS

The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.

Fast iterative reconstruction for photoacoustic tomography using learned physical model: Theoretical validation

Iterative reconstruction has demonstrated superior performance in medical imaging under compressed, sparse, and limited-view sensing scenarios. However, iterative reconstruction algorithms are slow to converge and rely heavily on hand-crafted parameters to achieve good performance. Many iterations are usually required to reconstruct a high-quality image, which is computationally expensive due to repeated evaluations of the physical model. While learned iterative reconstruction approaches such as model-based learning (MBLr) can reduce the number of iterations through convolutional neural networks, it still requires repeated evaluations of the physical models at each iteration. Therefore, the goal of this study is to develop a Fast Iterative Reconstruction (FIRe) algorithm that incorporates a learned physical model into the learned iterative reconstruction scheme to further reduce the reconstruction time while maintaining robust reconstruction performance. We also propose an efficient training scheme for FIRe, which releases the enormous memory footprint required by learned iterative reconstruction methods through the concept of recursive training. The results of our proposed method demonstrate comparable reconstruction performance to learned iterative reconstruction methods with a 9x reduction in computation time and a 620x reduction in computation time compared to variational reconstruction.

An iterative reconstruction algorithm without system matrix for EPR imaging

Electron paramagnetic resonance (EPR) imaging is an advanced oxygen imaging modality for oxygen-image guided radiation. The iterative reconstruction algorithm is the research hot-point in image reconstruction for EPR imaging (EPRI) for this type of algorithm may incorporate image-prior information to construct advanced optimization model to achieve accurate reconstruction from sparse-view projections and/or noisy projections. However, the system matrix in the iterative algorithm needs complicated calculation and needs huge memory-space if it is stored in memory. In this work, we propose an iterative reconstruction algorithm without system matrix for EPRI to simplify the whole iterative reconstruction process. The function of the system matrix is to calculate the projections, whereas the function of the transpose of the system matrix is to perform backprojection. The existing projection and backprojection methods are all based on the configuration that the imaged-object remains stationary and the scanning device rotates. Here, we implement the projection and backprojection operations by fixing the scanning device and rotating the object. Thus, the core algorithm is only the commonly-used image-rotation algorithm, while the calculation and store of the system matrix are avoided. Based on the idea of image rotation, we design a specific iterative reconstruction algorithm for EPRI, total variation constrained data divergence minimization (TVcDM) algorithm without system matrix, and named it as image-rotation based TVcDM (R-TVcDM). Through a series of comparisons with the original TVcDM via real projection data, we find that the proposed algorithm may achieve similar reconstruction accuracy with the original one. But it avoids the complicated calculation and store of the system matrix. The insights gained in this work may be also applied to other imaging modalities, for example computed tomography and positron emission tomography.

Application of HRGS for forensic characterization of uranium oxides, pure uranium metals and uranium alloys

A nondestructive iterative method for uranium-bearing material characterization with HRGS developed earlier in Burdeinyi et al. (2020) is applied to determine matrix densities, uranium mass fraction and uranium isotope masses of uranium ore, UO₂ and U₃O₈ powders, fuel elements in the form of UO₂ microspheres, uranium metal and uranium alloys. It is shown that U₃O₈ powders with uranium mass fraction of about 84% can be distinguished from the powders of UO₂ with uranium mass fraction of about 87%; uranium products in the form of liquid or loose powder with matrix density of 0.5-2.0g/cm³ can be distinguished from uranium products in the form of compacted fuel elements with matrix density of 6.0-10.0g/cm³ and from pure metal uranium and uranium alloys with matrix density of 14.0-19.0g/cm³. In fuel microspheres based on UO₂ the uranium mass fraction 88.02% measured by HRGS is consistent, within the measurement uncertainties, with the results of isotope dilution mass spectrometry 87.76±0.64% and also is confirmed by X-ray diffraction technique. The uranium mass fraction of the uranium ore estimated as 0.08% by HRGS is consistent, within the measurement uncertainties, with the value 0.09±0.01% determined with WDXRF. Densities of two different uranium metal samples, estimated as 18.42g/cm³ and 19.33g/cm³ by HRGS are consistent with values 18.24±0.55g/cm³ and 18.86±0.59g/cm³, respectively, obtained by the gas pycnometry technique.

Capped L2,p-norm metric based robust least squares twin support vector machine for pattern classification

Least squares twin support vector machine (LSTSVM) is an effective and efficient learning algorithm for pattern classification. However, the distance in LSTSVM is measured by squared L₂-norm metric that may magnify the influence of outliers. In this paper, a novel robust least squares twin support vector machine framework is proposed for binary classification, termed as CL_2,p-LSTSVM, which utilizes capped L_2,p-norm distance metric to reduce the influence of noise and outliers. The goal of CL_2,p-LSTSVM is to minimize the capped L_2,p-norm intra-class distance dispersion, and eliminate the influence of outliers during training process, where the value of the metric is controlled by the capped parameter, which can ensure better robustness. The proposed metric includes and extends the traditional metrics by setting appropriate values of p and capped parameter. This strategy not only retains the advantages of LSTSVM, but also improves the robustness in solving a binary classification problem with outliers. However, the nonconvexity of metric makes it difficult to optimize. We design an effective iterative algorithm to solve the CL_2,p-LSTSVM. In each iteration, two systems of linear equations are solved. Simultaneously, we present some insightful analyses on the computational complexity and convergence of algorithm. Moreover, we extend the CL_2,p-LSTSVM to nonlinear classifier and semi-supervised classification. Experiments are conducted on artificial datasets, UCI benchmark datasets, and image datasets to evaluate our method. Under different noise settings and different evaluation criteria, the experiment results show that the CL_2,p-LSTSVM has better robustness than state-of-the-art approaches in most cases, which demonstrates the feasibility and effectiveness of the proposed method.

Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

The study of efficient iterative algorithms for addressing nonlinear least-squares (NLS) problems is of great importance. The NLS problems, which belong to a special class of unconstrained optimization problems, are of particular interest because of the special structure of their gradients and Hessians. In this paper, based on the spectral parameters of Barzillai and Borwein (1998), we propose three structured spectral gradient algorithms for solving NLS problems. Each spectral parameter in the respective algorithms incorporates the structured gradient and the information gained from the structured Hessian approximation. Moreover, we develop a safeguarding technique for the first two structured spectral parameters to avoid negative curvature directions. Moreso, using a nonmonotone line-search strategy, we show that the proposed algorithms are globally convergent under some standard conditions. The comparative computational results on some standard test problems show that the proposed algorithms are efficient.

Reducing metal artifacts by restricting negative pixels

When the object contains metals, its x-ray computed tomography (CT) images are normally affected by streaking artifacts. These artifacts are mainly caused by the x-ray beam hardening effects, which deviate the measurements from their true values. One interesting observation of the metal artifacts is that certain regions of the metal artifacts often appear as negative pixel values. Our novel idea in this paper is to set up an objective function that restricts the negative pixel values in the image. We must point out that the naïve idea of setting the negative pixel values in the reconstructed image to zero does not give the same result. This paper proposes an iterative algorithm to optimize this objective function, and the unknowns are the metal affected projections. Once the metal affected projections are estimated, the filtered backprojection algorithm is used to reconstruct the final image. This paper applies the proposed algorithm to some airport bag CT scans. The bags all contain unknown metallic objects. The metal artifacts are effectively reduced by the proposed algorithm.

Cross-sectional photoacoustic tomography image reconstruction with a multi-curve integration model

BACKGROUND AND OBJECTIVE

In acoustic inversion of photoacoustic tomography (PAT), an imaging model that precisely describes both the ultrasonic wave propagation and the detector properties is of crucial importance. Inspired by the multi-stripe integration model in clinical X-ray computed tomography systems, in this work, we introduce the Multi-Curve-Integration-based acoustic inversion for cross-sectional Photoacoustic Tomography (MCI-PAT).

METHODS

We assumed that in cross-sectional PAT system, the three-dimensional (3-D) wave propagation problem could be reduced to a two-dimensional (2-D) problem in a limited, yet sufficient field of view. Under such condition, the MCI-PAT imaging model is generated by integrating several circular acoustic curves, the centers of which are points evenly distributed on the finite-size ultrasonic transducer surface. In this way, the spatial detector response is taken into account, while its computational burden does not largely increase because the integration process is performed only on a 2-D plane.

RESULTS

As proven by simulation, phantom and in vivo small animal experiments, the MCI-PAT method leads to promising improvement in PAT image quality. Comparing to traditional imaging models that considered only a single acoustic curve, our proposed method successfully improved the visibility of small structures and achieved evident enhancement on signal-to-noise ratio.

CONCLUSIONS

The performance of the MCI-PAT method demonstrates that for cross-sectional PAT, a 2-D simplification of the propagation of multiple photoacoustic waves is feasible. Due to its simplicity, our method can be used as an add-on to current system models considering only a single acoustic curve.

Finding the peak of dynamic oxygen uptake during fatiguing exercise in fish

As fish approach fatigue at high water velocities in a critical swimming speed (U _crit) test, their swimming mode and oxygen cascade typically move to an unsteady state because they adopt an unsteady, burst-and-glide swimming mode despite a constant, imposed workload. However, conventional rate of oxygen uptake (Ṁ _O2 ) sampling intervals (5-20 min) tend to smooth any dynamic fluctuations in active Ṁ _O2  (Ṁ _O2active) and thus likely underestimate the peak Ṁ _O2active Here, we used rainbow trout (Oncorhynchus mykiss) to explore the dynamic nature of Ṁ _O2active near U _crit using various sampling windows and an iterative algorithm. Compared with a conventional interval regression analysis of Ṁ _O2active over a 10-min period, our new analytical approach generated a 23% higher peak Ṁ _O2active Therefore, we suggest that accounting for such dynamics in Ṁ _O2active with this new analytical approach may lead to more accurate estimates of maximum Ṁ _O2  in fishes.

Boundary crash data assignment in zonal safety analysis: An iterative approach based on data augmentation and Bayesian spatial model

Boundary effect refers to the issue of ambiguous allocation of crashes occurred on or near the boundaries of neighboring zones in zonal safety analysis. It results in bias estimates for associate measure between crash occurrence and possible zonal factors. It is a fundamental problem to compensate for the boundary effect and enhance the model predictive performance. Compared to conventional approaches, it might be more reasonable to assign the boundary crashes according to the crash predisposing agents, since the crash occurrence is generally correlated to multiple sources of risk factors. In this study, we proposed a novel iterative aggregation approach to assign the boundary crashes, according to the ratio of model-based expected crash number in adjacent zones. To verify the proposed method, a case study using a dataset of 738 Traffic Analysis Zones (TAZs) from the county of Hillsborough in Florida was conducted. Using Bayesian spatial models (BSMs), the proposed approach demonstrated the capability in reasonably compensating for the boundary effect with better model estimation and predictive performance, as compared to three conventional approaches (i.e., half and half ratio method, one to one ratio method, and exposure ratio method). Results revealed that several factors including the number of intersections, road segment length with 35 mph speed limit, road segment length with 65 mph speed limit and median household income, were sensitive to the boundary effect.

Sparse Tensor Decomposition for Haplotype Assembly of Diploids and Polyploids

BACKGROUND

Haplotype assembly is the task of reconstructing haplotypes of an individual from a mixture of sequenced chromosome fragments. Haplotype information enables studies of the effects of genetic variations on an organism's phenotype. Most of the mathematical formulations of haplotype assembly are known to be NP-hard and haplotype assembly becomes even more challenging as the sequencing technology advances and the length of the paired-end reads and inserts increases. Assembly of haplotypes polyploid organisms is considerably more difficult than in the case of diploids. Hence, scalable and accurate schemes with provable performance are desired for haplotype assembly of both diploid and polyploid organisms.

RESULTS

We propose a framework that formulates haplotype assembly from sequencing data as a sparse tensor decomposition. We cast the problem as that of decomposing a tensor having special structural constraints and missing a large fraction of its entries into a product of two factors, U and [Formula: see text]; tensor [Formula: see text] reveals haplotype information while U is a sparse matrix encoding the origin of erroneous sequencing reads. An algorithm, AltHap, which reconstructs haplotypes of either diploid or polyploid organisms by iteratively solving this decomposition problem is proposed. The performance and convergence properties of AltHap are theoretically analyzed and, in doing so, guarantees on the achievable minimum error correction scores and correct phasing rate are established. The developed framework is applicable to diploid, biallelic and polyallelic polyploid species. The code for AltHap is freely available from https://github.com/realabolfazl/AltHap .

CONCLUSION

AltHap was tested in a number of different scenarios and was shown to compare favorably to state-of-the-art methods in applications to haplotype assembly of diploids, and significantly outperforms existing techniques when applied to haplotype assembly of polyploids.

Fourier-Domain Analysis of the Iterative Landweber Algorithm

This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a two-dimensional (2D) tomography problem, which can be X-ray computed tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT). Two questions regarding to the linear iterative Landweber algorithm are considered. The first question is whether stopping early is equivalent to getting a minimum-norm solution. The second question is whether the low frequency components always converge first. Our answers to these two questions are No.

Resolution enhancement of electrical resistance tomography by iterative back projection method

Abstract

An iterative back projection method (i-BP) has been developed to improve the resolution of reconstructed images produced by electrical resistance tomography (ERT). This solution is based on an iterative calculation of the electrical fields and it is possible to reconstruct clearer images than those reconstructed by the conventional back projection method without divergence. However, it does take several minutes to finish the iteration process, and therefore this solution can be applied to flow fields that require high spatial resolution rather than short processing times, such as the accumulation of noble metals in glass melters. Numerical simulations and experiments using a simple model are performed in this study. The numerical simulations show that clear images are reconstructed both near the wall and at the center by i-BP. The conductivity correlation coefficient between the genuine distribution and the reconstructed image is improved from 0.4 to 0.9. The validity of the i-BP method is also confirmed by the experimental results. As a result, it is confirmed that ERT and i-BP are capable of reconstructing acceptable images and have potential for use in the visualization of the accumulation of noble metals in a glass melter.

Graphical Abstract

Modularity for Motor Control and Motor Learning

How the central nervous system (CNS) overcomes the complexity of multi-joint and multi-muscle control and how it acquires or adapts motor skills are fundamental and open questions in neuroscience. A modular architecture may simplify control by embedding features of both the dynamic behavior of the musculoskeletal system and of the task into a small number of modules and by directly mapping task goals into module combination parameters. Several studies of the electromyographic (EMG) activity recorded from many muscles during the performance of different tasks have shown that motor commands are generated by the combination of a small number of muscle synergies, coordinated recruitment of groups of muscles with specific amplitude balances or activation waveforms, thus supporting a modular organization of motor control. Modularity may also help understanding motor learning. In a modular architecture, acquisition of a new motor skill or adaptation of an existing skill after a perturbation may occur at the level of modules or at the level of module combinations. As learning or adapting an existing skill through recombination of modules is likely faster than learning or adapting a skill by acquiring new modules, compatibility with the modules predicts learning difficulty. A recent study in which human subjects used myoelectric control to move a mass in a virtual environment has tested this prediction. By altering the mapping between recorded muscle activity and simulated force applied on the mass, as in a complex surgical rearrangement of the tendons, it has been possible to show that it is easier to adapt to a perturbation that is compatible with the muscle synergies used to generate hand force than to a similar but incompatible perturbation. This result provides direct support for a modular organization of motor control and motor learning.