Cancer therapy prognosis using quantitative ultrasound spectroscopy and a kernel-based metric

Tensor dimensionality reduction (TDR) is a hot research topic in machine learning, which learns data representations by preserving the original data structure while avoiding convert samples into vectors and solving the problem of the curse of dimensionality of tensor data. In the work, a novel TDR approach based on mode product and Hilbert–Schmidt Independence criterion (HSIC) is proposed. The contributions of authors' work is described as following: (1) HSIC measures the statistical correlation of two random variables. However, instead of measuring the statistical correlation of two random variables directly, HSIC first transforms the two random variables into two reproducing kernel Hilbert spaces (RKHSs), and then measures the statistical correlation of transformed random variables by using Hilbert–Schmidt operators between the two RKHSs. The exploitation of RKHS increases the flexibility and applicability of HSIC. Although HSIC is widely used in machine learning, the authors have not seen its application to dimensionality reduction (DR)(except for authors' previous work). (2) A novel HSIC‐based TDR approach is proposed, which first applies HSIC to capture statistical information of tensor data set for DR. The authors give the mathematical derivation of HSIC for tensor data and establish a framework of TDR based on HSIC, named HSIC‐TDR for short, which aims to improve the DR results of tensor by exploring and preserving the statistical information of original data set. (3) Furthermore, to solve the out‐of‐sample problem, the authors learn an explicit expression between the dimensionality‐reduced tensors and the higher‐dimensional tensors by introducing mode product to HSIC‐TDR. The experimental results between the proposed method and other state‐of‐the‐art algorithm on various datasets demonstrate the well performance of the proposed method.

Multivariate tests of independence based on a new class of measures of independence in Reproducing Kernel Hilbert Space

We introduce a general nonparametric independence test between right-censored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the Hilbert–Schmidt Independence Criterion (HSIC) test-statistic. We study the asymptotic properties of the test, finding sufficient conditions to ensure our test correctly rejects the null hypothesis under any alternative. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild Bootstrap procedure. Extensive investigations on both simulated and real data suggest that our testing procedure generally performs better than competing approaches in detecting complex nonlinear dependence.

Purpose:Clarity Autoscan ultrasound monitoring system allows acquisition of raw radiofrequency (RF) ultrasound data prior and during radiotherapy. This enables the computation of 3D Quantitative Ultrasound (QUS) tissue parametric maps from. We aim to evaluate whether QUS parameters undergo changes with radiotherapy and thus potentially be used as early predictors and/or markers of treatment response in prostate cancer patients.Methods:In‐vivo evaluation was performed under IRB protocol to allow data collection in prostate patients treated with VMAT whereby prostate was imaged through the acoustic window of the perineum. QUS spectroscopy analysis was carried out by computing a tissue power spectrum normalized to the power spectrum obtained from a quartz to remove system transfer function effects. A ROI was selected within the 3D image volume of the prostate. Because longitudinal registration was optimal, the same features could be used to select ROIs at roughly the same location in images acquired on different days. Parametric maps were generated within the rectangular ROIs with window sizes that were approximately 8 times the wavelength of the ultrasound. The mid‐band fit (MBF), spectral slope (SS) and spectral intercept (SI) QUS parameters were computed for each window within the ROI and displayed as parametric maps. Quantitative parameters were obtained by averaging each of the spectral parameters over the whole ROI.Results:Data was acquired for over 21 treatment fractions. Preliminary results show changes in the parametric maps. MBF values decreased from −33.9 dB to −38.7 dB from pre‐treatment to the last day of treatment. The spectral slope increased from −1.1 a.u. to −0.5 a.u., and spectral intercept decreased from −28.2 dB to −36.3 dB over the 21 treatment regimen.Conclusion:QUS parametric maps change over the course of treatment which warrants further investigation in their potential use for treatment planning and predicting treatment outcomes.Research was supported by Elekta.

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

Distance and similarity measures have recently been investigated in-depth within the context of hesitant fuzzy sets. By analyzing the existing studies concerning distance measures for hesitant fuzzy sets, we find that they have some limitations. To address the flaws, this study develops some novel distance measures for hesitant fuzzy sets, including the normalized Euclidean distance measure, the Hausdorff metric distance measure, the normalized generalized distance measure, and their corresponding weighted distance measures. The proposals of this study not only hold many ideal characteristics but also do not consider the lengths of hesitant fuzzy elements as well as the arrangement of their possible values. To deal with the situations where both of the universe of discourse and the weight of element are continuous, some continuous hesitant fuzzy distance measures are also investigated. Based on the relationship between distance measure and similarity measure, some novel similarity measures for hesitant fuzzy sets can be further deduced from the proposed distance measures. Finally, two numerical examples are given to demonstrate the applicability and validity of the proposed hesitant fuzzy distance measures.

Breast cancer remains the most commonly diagnosed malignancy and a leading cause of cancer-related mortality among women worldwide. Neoadjuvant chemotherapy (NAC) is increasingly used, particularly in aggressive subtypes such as HER2-positive and triple-negative breast cancer, where achieving a pathological complete response (pCR) is strongly associated with improved outcomes. Early and accurate assessment of therapeutic response is therefore essential to enable timely treatment adaptation. Conventional imaging methods-including magnetic resonance imaging (MRI), computed tomography (CT), mammography, and B-mode ultrasound-mainly detect macroscopic tumor shrinkage and often lagging behind biological alterations, as they rely primarily on size-based assessment. Quantitative ultrasound (QUS) is an emerging, non-invasive technique that analyzes raw radiofrequency (RF) ultrasound data to extract spectral, scattering, and attenuation parameters, allowing detailed characterization of tumor microstructure. When combined with parametric mapping, texture analysis, and advanced radiomic or deep learning approaches, QUS can capture subtle tissue alterations at an early stage of therapy and help predict pathological response before conventional imaging detects morphologic change. Integration with molecular and clinical data further enhances predictive performance, enabling adaptive and personalized treatment strategies. This narrative review summarizes current evidence on the clinical utility of QUS in monitoring NAC response in breast cancer, outlines the methodological foundations of this technology, and discusses key challenges to its broader implementation-particularly the need for standardized acquisition and processing protocols, robust interpretive algorithms and large, prospective, multicenter validations to confirm its impact on clinical decision-making and patient outcomes, and to accelerate its translation into precision oncology practice.

The dynamic time warping (DTW) is state-of-the-art distance measure widely used in sequential pattern matching and it outperforms Euclidean distance in most cases because its matching is elastic and robust. It is tempting to substitute DTW distance for Euclidean distance in the Gaussian RBF kernel and plug it into the state-of-the art classifier support vector machines (SVMs) for sequence classification. However, it is not straightforward that DTW also outperforms Euclidean distance in kernel machines. While counter-examples can be found to numerically prove that DTW is not positive definite symmetric (PDS)acceptable by SVM, little is known why it can not be PDS theoretically. We analyze the DTW kernel and complete a theoretical proof via the connection between PDS kernel and reproducing kernel Hilbert space (RKHS). Our analysis leads to a better understanding that all Hilbertian metrics can be be converted to a PDS kernel in the Gaussian form, while the reverse is not true. The proof can be extended to conclude that elastic matching distance is not eligible to construct PDS kernels (e.g., Edit distance). Experiments were conducted to compare the RBF-kernel and DTW kernel in SVM classifications and the results show that simple Euclidean distance outperforms DTW in kernel machines.

QuestionsWhich clustering algorithms are most effective according to different cluster validity evaluators? Which distance or dissimilarity measure is most suitable for clustering algorithms?LocationHyrcanian forest, Iran (Asia), Virginia region forest, United States (North America), beech forests, Ukraine (Europe).MethodsWe tested 25 clustering algorithms with nine vegetation data sets comprised of three real data sets and six simulated data sets exhibiting different cluster separation values. The clustering algorithms included both hierarchical and non‐hierarchical partitioning. Five evaluators were employed on each cluster solution to evaluate different clustering algorithms. Algorithms were ranked from best to worst on each clustering evaluator for each data set.ResultsThe comparison revealed that the OPTSIL initiated from a Flexible‐β (−0.25) solution achieved particularly good performance. We also found that Ward's method and Flexible‐β (−0.1) implementations were accurate. K‐means with Hellinger distance was superior to Partitioning Around Medoids (PAM) algorithms. Accordance between distance measures and clustering algorithms was also observed. Bray–Curtis dissimilarity combined with a range of clustering algorithms was successful in most cases. Bray–Curtis dissimilarity proved superior to other distance measures for heterogeneous data sets.ConclusionsAll in all, the results demonstrate that choosing the most suitable method before clustering is critical for achieving maximally interpretable clusters. The complexity of vegetation data sets makes this issue even more important. The choice of distance measure had more effect than the choice of clustering method on the quality of results. Our results illustrate that OPTSIL Flexible‐β (−0.1) and OPTPART could prove superior to alternative conventional clustering algorithms when internal evaluation criteria are used to optimize clustering.

Multiple color representation and fusion for diabetes mellitus diagnosis based on back tongue images

Effect of feature-type in selecting distance measure for an artificial immune system as a pattern recognizer

Nine oat cultivars and experimental lines from four diverse germ plasm sources were crossed in a diallel mating design, without reciprocals. Heterosis for grain yield was evaluated in two experiments and 48 F2-derived lines from each of the 36 matings were evaluated for bundle weight, grain yield, straw yield, harvest index, and heading date in two experiments. The number of transgressive segregates per trait and generalized genetic variances were calculated for each mating. Euclidean distance between parents was calculated by using the first five principal components of the parental correlation matrix. The distance measures of W. D. Hanson and E. Casas (1968. Biometrics, 24: 867–880) and T. S. Cervantes, M. M. Goodman, E. Casas, and J. O. Rawlings (1978. Genetics, 90: 339–348) were calculated for each of two experiments. The relationships between the three distance measures and the three types of breeding behavior were examined via correlation and regression. Euclidean distance was negatively correlated with transgressive segregation and generalized genetic variances. Hanson and Casas' distance measure was positively correlated with transgressive segregation and generalized genetic variances. The distance measure of Cervantes et al. was negatively correlated with heterosis in one experiment. Regressions on the three distances measures, when significant, were linear. The single exception was the regression of heterosis on Euclidean distance, which had significant linear and quadratic coefficients and high R2. No distance measure was closely associated with all three types of breeding behavior. Using information from more than one measure improved the R2 value for polynomial regressions. Key words: oats, genetic distance, heterosis, generalized variances.

BackgroundGene expression divergence is a phenotypic trait reflecting evolution of gene regulation and characterizing dissimilarity between species and between cells and tissues within the same species. Several distance measures, such as Euclidean and correlation-based distances have been proposed for measuring expression divergence.ResultsWe show that different distance measures identify different trends in gene expression patterns. When comparing orthologous genes in eight rat and human tissues, the Euclidean distance identified genes uniformly expressed in all tissues near the expression background as genes with the most conserved expression pattern. In contrast, correlation-based distance and generalized-average distance identified genes with concerted changes among homologous tissues as those most conserved. On the other hand, correlation-based distance, Euclidean distance and generalized-average distance highlight quite well the relatively high similarity of gene expression patterns in homologous tissues between species, compared to non-homologous tissues within species.ConclusionsDifferent trends exist in the high-dimensional numeric data, and to highlight a particular trend an appropriate distance measure needs to be chosen. The choice of the distance measure for measuring expression divergence can be dictated by the expression patterns that are of interest in a particular study.ReviewersThis article was reviewed by Mikhail Gelfand, Eugene Koonin and Subhajyoti De (nominated by Sarah Teichmann).

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig’s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig’s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig’s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable tool for decision-makers in real-life situations. It enables the evaluation of alternatives by considering interactions between criteria, providing a more comprehensive perspective for decision-making.

Optimized distance metrics for differential evolution based nearest prototype classifier