Kernel Rank Research Articles

A spectral approach for the dynamic Bradley–Terry model

SummaryThe dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time‐dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time‐dependent modelling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley–Terry model, utilising a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations and allows for real‐time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared with the gold standard in sports, the Arpad Elo rating system.

Optimizing echo state networks for continuous gesture recognition in mobile devices: A comparative study

Continuous gesture recognition can be used to enhance human-computer interaction. This can be accomplished by capturing human movement with the use of the Inertial Measurement Units in smartphones and using machine learning algorithms to predict the intended gestures. Echo State Networks (ESNs) consist of a fixed internal reservoir that is able to generate rich and diverse nonlinear dynamics in response to input signals that capture temporal dependencies within the signal. This makes ESNs well-suited for time series prediction tasks, such as continuous gesture recognition. However, their application has not been rigorously explored, with regard to gesture recognition. In this study, we sought to enhance the efficacy of ESN models in continuous gesture recognition by exploring diverse model structures, fine-tuning hyperparameters, and experimenting with various training approaches. We used three different training schemes that used the Leave-one-out Cross-validation (LOOCV) protocol to investigate the performance in real-world scenarios with different levels of data availability: Leaving out data from one user to use for testing (F1-score: 0.89), leaving out a fraction of data from all users to use in testing (F1-score: 0.96), and training and testing using LOOCV on a single user (F1-score: 0.99). The obtained results outperformed the Long Short-Term Memory (LSTM) performance from past research (F1-score: 0.87) while maintaining a low training time of approximately 13 seconds compared to 63 seconds for the LSTM model. Additionally, we further explored the performance of the ESN models through behaviour space analysis using memory capacity, Kernel Rank, and Generalization Rank. Our results demonstrate that ESNs can be optimized to achieve high performance on gesture recognition in mobile devices on multiple levels of data availability. These findings highlight the practical ability of ESNs to enhance human-computer interaction.

Noisy quantum kernel machines

In the noisy intermediate-scale quantum era, an important goal is the conception of implementable algorithms that exploit the rich dynamics of quantum systems and the high dimensionality of the underlying Hilbert spaces to perform tasks while prescinding from noise-proof physical systems. An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. Here, we study how dissipation and decoherence affect their performance. We address this issue by investigating the expressivity and the generalization capacity of these models within the framework of kernel theory. We introduce and study the effective kernel rank, a figure of merit that quantifies the number of independent features a noisy quantum kernel is able to extract from input data. Moreover, we derive an upper bound on the generalization error of the model that involves the average purity of the encoded states. Thereby we show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines. As an illustrative example, we report exact finite-size simulations of machines based on chains of driven-dissipative quantum spins to perform a classification task, where the input data are encoded into the driving fields and the quantum physical system is fixed. We determine how the performance of noisy kernel machines scales with the number of nodes (chain sites) as a function of decoherence and examine the effect of imperfect measurements.

EFFECT OF SEED MULTIPLICATION PROGRAM ON IMPROVING SEED PRODUCTION, QUALITY AND ITS IMPLICATIONS FOR THE REALITY OF AGRICULTURAL SECTOR (A PROGRAM OF MULTIPLICATION OF SEEDS OF THE HIGHER RANKS OF THE WHEAT CROP IN IRAQ AS A CASE STUDY)

The government sector contributes to providing the basic development requirements of the agricultural sector. A number of national programs have been established to improve and multiply the seeds of strategic grain crops. The most important of which is the program to multiply the seeds of the higher ranks of the wheat crop, as it represents the basic food of the people, on which the political, economic and social stability of the country depends. Providing improved, high-yielding seeds is a key element in achieving food security. The results of the implementation of the program showed an increase in the quantities produced from the seeds of the higher ranks, as the quantity of seeds of the kernel rank increased from about 3.63 tons in the first season to reach about 18.45 tons in the sixth season, while the quantities of seeds of the rank increased from 20.12 tons In the first season, it reached about 183.36 tons in the sixth season, and the amount of base seeds produced from the activities of the program increased from 91.04 tons in the first season to reach 1325.8 tons in the last season. The results of the economic evaluation showed that the use of the program's improved seeds led to an increase in farmers' returns from 299,000 dinars/ ton to 459,000 dinars / ton. The (EIA) analysis showed that the program has a positive economic impact on the national economy through the expected returns to be obtained from the production of improved seeds. Through these results, many conclusions can be reached, perhaps the most important of which is that the program has achieved a positive development in the seed production sector and in achieving profits for seed producers. The study recommended the need to continue the work of the program as it contributes to increasing production and achieving food security in Iraq.

Optimal echo state network parameters based on behavioural spaces

The quantitative analysis of neural networks is a critical issue to improve performance. In this work, we extend the ideas of this adaptation method to the more commonly used behavioural spaces. The aim is to construct an echo state network (ESN) behavioural space through the generalization rank, kernel rank, and memory capacity. After deriving behavioural spaces, we investigate the influencing factors and methods of reducing the search complexity of behavioural spaces. This investigation reveals that the rule converges to the expected space distributions, even in a random ESN. We propose an optimization algorithm that adopts the novel search genetic algorithm (NSGA), which combines the novelty and quality of individuals. In the novel search process, because the time needed to construct the behaviour space is much lower than the network training time, the network optimization efficiency is greatly improved. According to the characteristics of the behaviour space distribution, we propose a method to shrink the search space to solve the problem of a large search space. This method overcomes the difficulties in traditional ESN parameter selection and the long optimization time of a genetic algorithm and provides behavioural space theory to clarify the influence of reservoir performance on tasks.

Optimality of regularized least squares ranking with imperfect kernels

Ranking is one of the central machine learning tasks arising from supervised learning and has many important applications in information retrieval. Many ranking approaches have been designed and extensively studied. In this paper we study two kernel ranking algorithms, the regularized least square ranking and its bias corrected version, which learn scoring functions from reproducing kernel Hilbert spaces (RKHSs). We say a kernel is perfect for ranking if an optimal scoring function lies in the associated RKHS. It is imperfect if an optimal scoring function can be approximated by the RKHS. The two regularized kernel ranking algorithms have been shown theoretically justified and empirically effective when the kernel is perfectly chosen. In practice, however, kernels are usually selected via cross validation process. It is more common than not that the kernel is imperfectly chosen. We develop a novel leave-two-out analysis technique to evaluate the generalization performance of the two regularized ranking algorithms in this situation. We show that they are still effective and can achieve the capacity independent optimal convergence rates.

Characterization of nonlinear spin-wave interference by reservoir-computing metrics

We study the computational potential of a spin-wave (SW) substrate by applying two metrics known from reservoir computing. At low intensities, SW scatterers can perform linear operations, while at higher intensities, nonlinear phenomena dominate, possibly enabling high-function, general-purpose computing. The transition between the linear and nonlinear regimes can be quantified by the intensity-dependent kernel rank (KR) and generalization rank (GR). The KR and GR metrics prove that the SW substrate displays the nonlinearities required for computing and give recipes for device designs that utilize nonlinearity.

Online social image ranking in diversified preferences

Due to the prevalence of social media service, effective and efficient online image retrieval is in urgent need to satisfy diversified requirements of Web users. Previous studies are mainly focusing on bridging the semantic gap by well-established content modeling with semantic information and social tagging information, but they are not flexible in aggregating the diversified expectations of the online users. In this paper, we present OSIR, a solution framework to facilitate the diversified preference styles in online social media image searching by textual query inputs. First, we propose an efficient Online Multiple Kernel Ranking (OMKR) model which is constructed on multiple query dimensions and complimentary feature channels, and trained by minimizing the triplet loss on hard negative samples. By optimizing the ranking performance with multi-dimensional queries, the semantic consistency between the image ranking and textual query input is directly maximized without relying on the intermediate semantic annotation procedure. Second, we construct random walk-based preference modeling by domain-specific similarity calculation on heterogeneous social attributes. By re-ranking the rank output of OMKR based on each preference ranking model, we obtain a set of ranking lists encoding different potential aspects of user preference. Last, we propose an effective and efficient position-sensitive rank aggregation approach to aggregate multiple ranking results based on the user preference specification. Extensive experiment on two social media datasets demonstrates the advantages of our approach in both retrieval performance and user experience.

Bias corrected regularization kernel method in ranking

We propose a bias corrected regularization kernel ranking (BCRKR) method and characterize the asymptotic bias and variance of the estimated ranking score function. The results show that BCRKR has smaller asymptotic bias than the traditional regularization kernel ranking (RKR) method. The variance of BCRKR has the same order of decay as that of RKR when the sample size goes to infinity. Therefore, BCRKR is expected to be as effective as RKR and its smaller bias favors its use in block wise data analysis such as distributed learning for big data. The proofs make use of a concentration inequality of integral operator U-statistic.

An efficient numerical method for a mathematical model of a transport of coagulating particles

A new computational algorithm based on a fast way of computing integral operators describing the coagulation process is proposed for a mathematical model of coagulating particles. Using this algorithm, the computational complexity of each timestep of an explicit difference scheme can be substantially reduced. For each step, the complexity of execution is reduced from O(NM2) arithmetic operations to O(NMRlnM), where N is the number of mesh points along the physical coordinates of particles, M is the number of mesh points in a grid corresponding to sizes of coagulating particles, and R is the rank of a matrix corresponding to the values of the function of a coagulation kernel at mesh points. Using this approach, computations can be greatly accelerated, provided that kernel rank R is small.

Bounding the difference between RankRC and RankSVM and application to multi-level rare class kernel ranking

Rapid explosion in data accumulation has yielded large scale data mining problems, many of which have intrinsically unbalanced or rare class distributions. Standard classification algorithms, which focus on overall classification accuracy, often perform poorly in these cases. Recently, Tayal et al. (IEEE Trans Knowl Data Eng 27(12):3347---3359, 2015) proposed a kernel method called RankRC for large-scale unbalanced learning. RankRC uses a ranking loss to overcome biases inherent in standard classification based loss functions, while achieving computational efficiency by enforcing a rare class hypothesis representation. In this paper we establish a theoretical bound for RankRC by establishing equivalence between instantiating a hypothesis using a subset of training points and instantiating a hypothesis using the full training set but with the feature mapping equal to the orthogonal projection of the original mapping. This bound suggests that it is optimal to select points from the rare class first when choosing the subset of data points for a hypothesis representation. In addition, we show that for an arbitrary loss function, the Nystrom kernel matrix approximation is equivalent to instantiating a hypothesis using a subset of data points. Consequently, a theoretical bound for the Nystrom kernel SVM can be established based on the perturbation analysis of the orthogonal projection in the feature mapping. This generally leads to a tighter bound in comparison to perturbation analysis based on kernel matrix approximation. To further illustrate computational effectiveness of RankRC, we apply a multi-level rare class kernel ranking method to the Heritage Health Provider Network's health prize competition problem and compare the performance of RankRC to other existing methods.

Personalised face neutralisation based on subspace bilinear regression

Expression face neutralisation helps to improve the performance of expressive face recognition with one single neutral sample in gallery per subject. For learning‐based expression neutralisation, the virtual neutral face totally relies on training samples, which removes person‐specific characters from the neutralised face. Bilinear kernel rank reduced regression (BKRRR) algorithm is designed in a virtual subspace to simultaneously and efficiently generate both virtual expressive and neutral images from training samples. An expression mask is then established using grey and gradient differences of the two images. The test expression image is transformed to neutral template by piece‐wise affine warp (PAW). Using the virtual BKRRR neutral image as source, the PAW image as destination and the area covered by expression mask as clone area, an image fusion strategy based on Poisson equation is then designed, which achieves virtual neutralised face image with person‐specific characters preserved. From experiments on the CMU Multi‐PIE databases, it could be observed that the neutral faces synthesised by the proposed method could effectively approximate the real ground truth expressive faces, and greatly improve the performance of classic face recognition algorithms on expression variant problems.

Pose robust face recognition based on kernel regression in Bayesian framework

To reduce the effect brought by variation of pose, a face recognition system is proposed, in which the correlation between two faces by probabilistic models is computed and the gallery is extended with profile faces generated by a regression-based method. Each face is divided into 3 × 3 regions, and by measuring the distance between the two corresponding regions the distributions of similarities are learned and Bayesian models are formed for each region. These probabilistic models are used to determine whether two faces belong to the same subject. Besides, the gallery is expanded with profile facial images. With this approach, the landmarks on non-frontal faces can be estimated from their frontal landmarks by the mappings learned offline via kernel rank reduced regression (KRRR). Then the profile images are achieved by piecewise affine warping from the corresponding frontal face. Experiments indicate the proposed method performed well, especially when the head rotation angle is large.

Improving Semantic Concept Detection Through Optimizing Ranking Function

In this paper, a kernel-based learning algorithm, kernel rank, is presented for improving the performance of semantic concept detection. By designing a classifier optimizing the receiver operating characteristic (ROC) curve using kernel rank, we provide a generic framework to optimize any differentiable ranking function using effective smoothing functions. kernel rank directly maximizes a 1-D quality measure of ROC, i.e., AUC (area under the ROC). It exploits the kernel density estimation to model the ranking score distributions and approximate the correct ranking count. The ranking metric is then derived and the learnable parameters are naturally embedded. To address the issues of computation and memory in learning, an efficient implementation is developed based on the gradient descent algorithm. We apply kernel rank with two types of kernel density functions to train the linear discriminant function and the Gaussian mixture model classifiers. From our experiments carried out on the development set for TREC Video Retrieval 2005, we conclude that (1) kernel rank is capable of training any differentiable classifier with various kernels; and (2) the learned ranking function performs better than traditional maximization likelihood or classification error minimization based algorithms in terms of AUC and average precision (AP).

Punctual Hilbert schemes and resolutions of multiple point singularities

If f : X" ~ YP is a morphism of smooth complex analytic varieties with n < p, then the multiple points of order k of f i n the target are those y E YP with k preimages, each preimage counted with proper multiplicity. It is clear that to understand the geometry o f f it is necessary to understand these multiple point sets and their closures. Much work has also been done recently to calculate characteristic class formulas for these sets and their relatives in the source off(cf . [1, 10, 17]). One approach to the problem of calculating the characteristic class formula of a singularity involves finding resolutions of the singularities [4, 15, 18]. Traditionally in singularities of maps, one uses multi-jet bundles to study and control multiple point singularities. Jet bundles often enter also in the constructions made to resolve singularities. Unfortunately, as will be discussed in detail later, multi-jet bundles are difficult to work with if not useless when the problem involves the closure of the set of multiple points. In this paper we give a new construction, using punctual Hilbert schemes, which we offer as an alternative to multi-jets in the study of multiple point singularities. As an illustration of its usefulness, we use it to find a resolution of the closure of the triple point set of any "good" map f (Theorem 2.3), and of the multiple point set of a " g o o d " f o f any order, provided the m a p f has kernel rank at most 2 (Theorem 1.6). (Recall that the kernel rank of f a t x is the dimension of the kernel of Df(x).) This construction also provides a useful starting point for finding resolutions of multiple point sets for general f, by reducing the problem of resolving the singularity of f t o the problem of resolving the singularities of the corresponding Hilbert schemes. In a later paper we will show how a modification of our construction allows one to resolve triple points in the source as well.

Parametrization of a Singular Lagrangian Variety

We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol’d and Givental’. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thom and Mather) of kernel rank one.

Parametrization of a singular Lagrangian variety

We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol’d and Givental’. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thom and Mather) of kernel rank one.