Kernel-based Framework Research Articles

A fast and adaptive detection framework for genome-wide chromatin loop mapping from Hi-C data.

Chromatin loop identification plays an important role in molecular biology and 3D genomics research, as it constitutes a fundamental process in transcription and gene regulation. Such precise chromatin structures can be identified across genome-wide interaction matrices via Hi-C data analysis, which is essential for unraveling the intricacies of transcriptional regulation. Given the increasing number of genome-wide contact maps, derived from both in situ Hi-C and single-cell Hi-C experiments, there is a pressing need for efficient and resilient algorithms capable of processing data from diverse experiments rapidly and adaptively. Here, we propose YOLOOP, a novel detection-based framework that is different from the conventional paradigm. YOLOOP stands out for its speed, surpassing the performance of previous state-of-the-art (SOTA) chromatin loop detection methods. It achieves a 30-fold acceleration compared with classification-based methods, up to 20-fold acceleration compared with the SOTA kernel-based framework, and a fivefold acceleration compared with statistical algorithms. Furthermore, the proposed framework is capable of generalizing across various cell types, multiresolution Hi-C maps, and diverse experimental protocols. Compared with the existing paradigms, YOLOOP shows up to a 10% increase in recall and a 15% increase in F1-score, particularly noteworthy in the GM12878 cell line. YOLOOP also offers fast adaptability with straightforward fine-tuning, making it readily applicable to extremely sparse single-cell Hi-C contact maps. It maintains its exceptional speed, completing genome-wide detection at a 10 kb resolution for a single-cell contact map within 1 min and for a 900-cell-superimposed contact map within 3 min, enabling fast analysis of large-scale single-cell data.

Kernel-based framework for improved prediction of discharge coefficient in vertically supported cylindrical weirs

ABSTRACT The present study represents the first use of kernel-based models to predict discharge coefficient (Cd) for two distinct types of cylindrical weirs, featuring vertical support and a 30-degree upstream ramp. For this purpose, kernel-based methods, including support vector machine, Gaussian process regression (GPR), Kernel extreme learning machine, and Kernel ridge regression, were used, as they offer notable advantages compared to other machine learning models, such as flexibility in handling various data patterns, robustness against overfitting, and effectiveness in high-dimensional data scenarios. The results indicated that the GPR model, with statistical metrics of R = 0.967, Nash–Sutcliffe efficiency (NSE) = 0.935, and root-mean-square error (RMSE) = 0.027, demonstrates superior accuracy in modeling the overall dataset collected from two distinct types of weirs. Through a conducted sensitivity analysis, it was identified that the upstream Froude number is pivotal in accurately predicting the Cd of a cylindrical weir. The modeling conducted for two distinct weir types revealed that a cylindrical weir with vertical support exhibits enhanced predictive capabilities (R = 0.997, NSE = 0.994, and RMSE = 0.007) for Cd. The findings indicate that the introduction of the upstream ramp alters hydraulic conditions, resulting in reduced modeling accuracy (R = 0.760, NSE = 0.529, and RMSE = 0.060).

Combining multiple biomarkers linearly to minimize the Euclidean distance of the closest point on the receiver operating characteristic surface to the perfection corner in trichotomous settings.

The performance of individual biomarkers in discriminating between two groups, typically the healthy and the diseased, may be limited. Thus, there is interest in developing statistical methodologies for biomarker combinations with the aim of improving upon the individual discriminatory performance. There is extensive literature referring to biomarker combinations under the two-class setting. However, the corresponding literature under a three-class setting is limited. In our study, we provide parametric and nonparametric methods that allow investigators to optimally combine biomarkers that seek to discriminate between three classes by minimizing the Euclidean distance from the receiver operating characteristic surface to the perfection corner. Using this Euclidean distance as the objective function allows for estimation of the optimal combination coefficients along with the optimal cutoff values for the combined score. An advantage of the proposed methods is that they can accommodate biomarker data from all three groups simultaneously, as opposed to a pairwise analysis such as the one implied by the three-class Youden index. We illustrate that the derived true classification rates exhibit narrower confidence intervals than those derived from the Youden-based approach under a parametric, flexible parametric, and nonparametric kernel-based framework. We evaluate our approaches through extensive simulations and apply them to real data sets that refer to liver cancer patients.

Kernel methods are competitive for operator learning

We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Networks (DeepONet) [46] and Fourier Neural Operator (FNO) [45]. We consider the setting where the input/output spaces of target operator G†:U→V are reproducing kernel Hilbert spaces (RKHS), the data comes in the form of partial observations ϕ(ui),φ(vi) of input/output functions vi=G†(ui) (i=1,…,N), and the measurement operators ϕ:U→Rn and φ:V→Rm are linear. Writing ψ:Rn→U and χ:Rm→V for the optimal recovery maps associated with ϕ and φ, we approximate G† with G¯=χ∘f¯∘ϕ where f¯ is an optimal recovery approximation of f†:=φ∘G†∘ψ:Rn→Rm. We show that, even when using vanilla kernels (e.g., linear or Matérn), our approach is competitive in terms of cost-accuracy trade-off and either matches or beats the performance of NN methods on a majority of benchmarks. Additionally, our framework offers several advantages inherited from kernel methods: simplicity, interpretability, convergence guarantees, a priori error estimates, and Bayesian uncertainty quantification. As such, it can serve as a natural benchmark for operator learning.

Gradient COBRA: A kernel-based consensual aggregation for regression

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators r1, ..., rM using a weighted average where the weights are defined based on predicted features given by all the basic estimators and some kernel function. This work extends the context of Biau et al. (2016) to a more general kernel-based framework. We show that this more general configuration also inherits the consistency of the basic consistent estimators, and the same convergence rate as in the classical method is achieved. Moreover, an optimization method based on gradient descent algorithm is proposed to efficiently and rapidly estimate the key parameter of the strategy. Various of numerical experiments carried out on several simulated and real datasets are also provided to illustrate the efficiency and accuracy of the method with the introduction of gradient descent algorithm and smoother kernel functions respectively. Moreover, a domain adaptation-like property of the method is also illustrated on a physics data provided by Commissariat à l'Énergie Atomique (CEA).

Kernel-Based Models for System Analysis

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input-output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input-output requirements of system analysis and physical modeling.

Machine learning-based RC beam-column model parameter estimation and uncertainty quantification for seismic fragility assessment

The simplicity and computational efficiency of lumped plasticity beam-column element models have been widely utilized for nonlinear response estimation of reinforced concrete (RC) frame elements under seismic shaking. At present, a prevalent approach for estimating modeling parameters includes linear regression-based semi-empirical equations developed after calibration of experimental column test results with varying design details. Since the choice of modeling parameters affects the prediction of complex seismic behavior, an underlying assumption of static linear relationships may not be valid. Furthermore, experimental column test data is limited and typically sourced from multiple independent studies, reflecting significant heterogeneity prevailing in column properties. Consequently, the homoskedastic assumption of the prediction uncertainty in linear regression is questionable. This study addresses the above drawbacks through a Gaussian process regression (GPR) approach that is capable of analyzing nonlinear patterns in data sets, despite small sample sizes. The kernel-based framework of GPR also efficiently estimates the pointwise prediction uncertainty as opposed to the homoskedastic assumption of linear regression. Using a case study example of an archetypical reinforced concrete moment resisting frame building, the prediction uncertainty is propagated in the collapse fragility framework. Results reveal that overall fragility uncertainty can substantially change through the consideration of pointwise prediction uncertainty and better fitting models.

On a linear fused Gromov-Wasserstein distance for graph structured data

We present a framework for embedding graph structured data into a vector space, taking into account node features and structures of graphs into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named LinearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it takes into account node features and structures of graphs for measuring the dissimilarity between graphs in a kernel-based framework, 2) it is more efficient for computing a kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein [1], making it possible to deal with large-scale data sets. Our theoretical analysis and experimental results demonstrate that our proposed distance leads to an increase in performance compared to the existing state-of-the-art graph distances when evaluated on graph classification and clustering tasks.

Joint Data-Driven Estimation of Origin–Destination Demand and Travel Latency Functions in Multiclass Transportation Networks

The traffic assignment problem is a widely used formulation for designing, analyzing, and evaluating transportation networks. The inputs to this model, besides the network topology, are the origin–destination (OD) demand matrix and travel latency cost functions. It has been observed that small perturbations to these inputs have a large impact on the solution. However, most efforts on estimating these using data do so separately and are typically based on parametric models or surveys. In this article, we present a kernel-based framework that jointly estimates the OD demand matrix and the travel latency function in single- and multiclass vehicle networks. To that end, we formulate a bilevel optimization problem, and then, we transform it to a quadratically constrained quadratic program (QCQP). To solve this QCQP, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trust-region feasible direction</i> algorithm that sequentially solves a quadratic program. In addition, we also provide an alternating optimization method. Our results show that the QCQP method achieves better estimates when compared with disjoint and sequential methods. We show the applicability of the method by performing case studies using data for the transportation networks of Eastern Massachusetts Area and New York City.

Fault diagnosis method of bearing utilizing GLCM and MBASA-based KELM

In this study, fault diagnosis method of bearing utilizing gray level co-occurrence matrix (GLCM) and multi-beetles antennae search algorithm (MBASA)-based kernel extreme learning machine (KELM) is presented. In the proposed method, feature extraction of time–frequency image based on GLCM is proposed to extract the features of the bearing vibration signal, and multi-beetles antennae search algorithm-based KELM (MBASA-KELM) is presented to recognize the states of bearing. KELM employs the kernel-based framework, which has better generalization than traditional extreme learning machine, and it is necessary to look for an excellent optimization algorithm to select appropriate regularization parameter and kernel parameter of the KELM model because these parameters of the KELM model can affect its performance. As traditional beetle antennae search algorithm only employs one beetle, which is difficult to find the optimal parameters when the ranges of the parameters to be optimized are wide, multi-beetles antennae search algorithm (MBASA) employing multi-beetles is presented to select the regularization parameter and kernel parameter of KELM. The experimental results demonstrate that MBASA-KELM has stronger fault diagnosis ability for bearing than LSSVM, and KNN.

Kernel-based learning of birth process from evolving spatiotemporal RFS data stream in SMC[sbnd]CPHD filter for multi-target tracking

This paper presents a kernel-based framework to estimate the birth process in the sequential Monte Carlo cardinalized probability hypothesis density (SMCCPHD) filter from the evolving spatiotemporal birth random finite set data stream that can enhance the performance of the SMCCPHD based trackers when tracking targets with no a priori information on where and when targets can appear. The time-varying spatial distribution of birth events is modelled as a map with adaptive grid points and their corresponding density values. While the spatial distribution of birth density is estimated from the elements of the birth random finite sets (RFSs), the time-varying birth cardinality distribution is estimated from the cardinality of the birth RFSs. The corresponding estimations are eventually used by a SMCCPHD based tracker to adjust its filtering strength spatially and temporally for target tracking. Experimental results on both the synthetic and real video surveillance datasets show that the proposed algorithm can improve the tracking accuracy by more precisely eliminating clutters and more effectively capturing newborn targets.

Virtual Conjugate Coil for Improving KerNL Reconstruction.

Ker NL is a general kernel-based framework for auto calibrated reconstruction method, which does not need any explicit formulas of the kernel function for characterizing nonlinear relationships between acquired and unacquired k-space data. It is non-iterative without requiring a large amount of computational costs. Since the limited autocalibration signals (ACS) are acquired to perform KerNL calibration and the calibration suffers from the overfitting problem, more training data can improve the kernel model accuracy. In this work, virtual conjugate coil data are incorporated into the KerNL calibration and estimation process for enhancing reconstruction performance. Experimental results show that the proposed method can further suppress noise and aliasing artifacts with fewer ACS data and higher acceleration factors. Computation efficiency is still retained to keep fast reconstruction with the random projection.

Missing data imputation for transfer passenger flow identified from in-station WiFi systems

This paper presents a new perspective for in-station transfer flow estimation, utilising data collected by WiFi sensor system, which is critical for path choice modelling and pedestrian management. The full in-station transfer flow can be estimated by scaling up a ‘seed matrix’, which is constructed based on the identification of inter-platform transfer activities. Due to sensor failures, the main problem comes from handling the missing elements in the constructed ‘seed matrix’. We address this problem with a novel kernel-based framework, named self-measuring multi-task Gaussian process (SM-MTGP). The heterogeneous correlations in temporal features are captured by the designed task-based and input-based kernels separately. Moreover, a self-measuring kernel is designed for learning the correlations carried by the observations. The performance of the proposed method is validated with data from a busy railway station. The results show that the proposed algorithm achieves the best imputation accuracy in both accuracy and robustness, especially at high missing rates.

Kernel-based framework to estimate deformations of pneumothorax lung using relative position of anatomical landmarks

In video-assisted thoracoscopic surgeries, successful procedures of nodule resection are highly dependent on the precise estimation of lung deformation between the inflated lung in the computed tomography (CT) images during preoperative planning and the deflated lung in the treatment views during surgery. Lungs in the pneumothorax state during surgery have a large volume change from normal lungs, making it difficult to build a mechanical model.The purpose of this study is to develop a deformation estimation method of 3D surface of a deflated lung from a few partial observations. To estimate deformations for a largely deformed lung, a kernel regression-based solution was introduced. The proposed method used a few landmarks to capture the partial deformation between the 3D surface mesh obtained from preoperative CT and the intraoperative anatomical positions. The deformation for each vertex of the entire mesh model was estimated per-vertex as a relative position from the landmarks. The landmarks were placed in the anatomical position of the lung’s outer contour. The method was applied on nine datasets of the left lungs of live beagle dogs. Contrast-enhanced CT images of the lungs were acquired.The proposed method achieved a local positional error of vertices of 2.74 mm, Hausdorff distance of 6.11 mm, and Dice similarity coefficient of 0.94. Moreover, the proposed method achieved the estimation lung deformations from a small number of training cases and a small observation area.This study contributes to data-driven modeling of pneumothorax deformation of the lung.

Kernel-based framework to estimate deformations of pneumothorax lung using anatomical landmarks

Kernel-based framework to estimate deformations of pneumothorax lung using anatomical landmarks

Drill-Core Hyperspectral and Geochemical Data Integration in a Superpixel-Based Machine Learning Framework

The analysis of drill-core samples is one of the most important steps in the mining industry for the exploration and discovery of mineral resources. Geochemical assays are a common approach to represent the abundance of different chemical elements and aid at quantifying the concentrations of the important ore accumulations. However, their acquisition is time-consuming and usually averages of long core portions. Hyperspectral data are increasingly being used in the mining industry to complement the analysis of drill-cores due to their efficiency and fast turn-around time. Moreover, hyperspectral imaging is a technique able to provide data with high spatial resolution. In this article, we propose to integrate the complementary information derived from hyperspectral and geochemical data via a superpixel-based machine learning framework. This framework considers the difference in spatial resolution through segmentation. We extract labels from the geochemical assays and select, from the hyperspectral data, representative samples for each measurement. A supervised machine learning classification (composite kernel support vector machine) is then used to extrapolate the elements relative abundance to the entire core length. We propose an innovative integration of hyperspectral data covering different regions of the electromagnetic spectrum in a kernel-based framework to facilitate the identification of a larger amount of elements. A qualitative and quantitative evaluation of the results demonstrates the capabilities of the proposed method, which provides approximately 20% more accurate results than the pixel-based approach. Results also imply that the method could be beneficial for the reduction of geochemical assays needed for the detailed analysis of the cores.

Learning pairwise patterns in Community Question Answering

In recent years, forums offering community Question Answering (cQA) services gained popularity on the web, as they offer a new opportunity for users to search and share knowledge. In fact, forums allow users to freely ask questions and expect answers from the community. Although the idea of receivi ng a direct, targeted response from other users is very attractive, it is not rare to see long threads of comments, where only a small portion of them are actually valid answers. In many cases users start conversations, ask for other information, and discuss about things, which are not central to the original topic. Therefore, finding the desired information in a long list of answers might be very time-consuming. Designing automatic systems to select good answers is not an easy task. In many cases the question and the answer do not share a large textual content, and approaches based on measuring the question-answer similarity will often fail. A more intriguing and promising approach would be trying to define valid question-answer templates and use a system to understand whether any of these templates is satisfied for a given question-answer pair. Unfortunately, the manual definition of these templates is extremely complex and requires a domain-expert. In this paper, we propose a supervised kernel-based framework that automatically learns from training question-answer pairs the syntactic/semantic patterns useful to recognize good answers. We carry out a detailed experimental evaluation, where we demonstrate that the proposed framework achieves state-of-the-art results on the Qatar Living datasets released in three different editions of the Community Question Answering Challenge of SemEval.

A Kernel-Based Low-Rank (KLR) Model for Low-Dimensional Manifold Recovery in Highly Accelerated Dynamic MRI.

While many low rank and sparsity-based approaches have been developed for accelerated dynamic magnetic resonance imaging (dMRI), they all use low rankness or sparsity in input space, overlooking the intrinsic nonlinear correlation in most dMRI data. In this paper, we propose a kernel-based framework to allow nonlinear manifold models in reconstruction from sub-Nyquist data. Within this framework, many existing algorithms can be extended to kernel framework with nonlinear models. In particular, we have developed a novel algorithm with a kernel-based low-rank model generalizing the conventional low rank formulation. The algorithm consists of manifold learning using kernel, low rank enforcement in feature space, and preimaging with data consistency. Extensive simulation and experiment results show that the proposed method surpasses the conventional low-rank-modeled approaches for dMRI.

Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study

This work outlines a unified formulation to represent spectral approaches for both dimensionality reduction and clustering. Proposed formulation starts with a generic latent variable model in terms of the projected input data matrix.Particularly, such a projection maps data onto a unknown high-dimensional space. Regarding this model, a generalized optimization problem is stated using quadratic formulations and a least-squares support vector machine.The solution of the optimization is addressed through a primal-dual scheme.Once latent variables and parameters are determined, the resultant model outputs a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Particularly, proposedformulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.

Kernel Multivariate Spectral–Spatial Analysis of Hyperspectral Data

This paper contributes the concept of spectral-spatial kernel-based multivariate analysis (KMVSSA) based on the statistical principle of multivariate statistics. The essence of proposed framework is to expose the inherent structure and meaning revealed within spectral and spatial features through various statistical methods in hyperspectral remotely sensed data. This kernel-based framework is investigated to incorporate the spectral and spatial information simultaneously for dimension reduction and classification of hyperdimensional datasets. The method uses multivariate analysis to choose and apply a transform matrix that the transformed components are as orthogonal as possible. This nonlinear framework is derived by means of the theory of complete orthonormal systems. KMVSSA exhibits great flexibility by the combination of spectral and spatial features. We investigate the possibility of using KMVSSA for the classification of hyperspectral images and dimension reduction. The proposed framework is examined and compared in different merits with several hyperspectral images in different conditions (urban/agricultural area and size of the training set). Experimental results show that the proposed framework can meaningfully enhance the dimensionality reduction and also it greatly improves the overall as well as per class classification accuracies. We demonstrate a comprehensive comparison of some state of the art hyperspectral image classification methods.