Distance Measure Research Articles

Association between visual impairment and recurrent hospitalizations in older US adults.

Visual impairment (VI) is common in older adults and is associated with adverse health outcomes. However, the association between objectively assessed VI and recurrent hospitalization remains unclear. To investigate the association of different domains of visual function with recurrent hospitalization in older adults in the United States. We used data from Round 11 of the National Health and Aging Trends Study (NHATS), a nationally representative survey of Medicare beneficiaries, which included objective measures of distance and near visual acuity and contrast sensitivity. Using multivariable logistic regression models, we analyzed the association between VI (distance and near acuity <20/40, contrast sensitivity <1 SD below the sample mean) and prior year hospitalization and estimated marginal predicted probabilities of any (≥1) and recurrent (>1) hospitalization. Models were adjusted for demographic factors and comorbid medical conditions and accounted for NHATS complex survey design. The sample included 2960 respondents aged 71 and older (median age 81 years; 45% male, 82% non-Hispanic White). The predicted probability of hospitalization for those with any type of VI was 19.2% (15.9-22.6) versus 16.7% (14.9-18.6) for those without VI. The predicted probability of recurrent hospitalization for those with any type of VI was 7.2% (4.8-9.7) versus 4.1% (3.1-5.2) for those without VI. Near VI was significantly associated with recurrent hospitalization (OR = 2.04 [1.6, 3.61], p = 0.02), independent of other visual function measures, while other types of VI were not. Near VI is significantly associated with recurrent hospitalization in older US adults. Future studies should determine whether improving near vision affects the likelihood of recurrent hospitalization.

Improvement on Calibration Weightings in Stratified Random Sampling

Calibration weightings is the process of formulating calibration constraints using a given distance measure to obtain expression of the calibration weights. One of the major limitations of the simple calibration technique by Deville and Sarndal (1992); is that the calibration weights obtained by this process may be negative and or extremely large. To overcome this challenge, this study develops a new framework for obtaining optimum calibration weightings using inverse exponentiation. A new calibration regression estimator of population mean is proposed in stratified random sampling. Properties of the new estimator are derived and its efficacy established through empirical comparisons with existing estimators. Results of analysis showed that the new estimator obtained by the new calibration weightings is more precise and highly efficient than calibration estimators obtained by the simple calibration technique by Deville and Sarndal (1992), under the same optimum conditions. International Journal of Statistical Sciences, Vol. 24(2), November, 2024, pp 125-136

Probabilistic Seismic Hazard Assessment for the North China Plain Earthquake Belt: Sensitivity of Seismic Source Models and Ground Motion Prediction Equations

AbstractIn this study, a multi-source data fusion method was proposed for the development of a Hybrid seismic hazard model (HSHM) in China by using publicly available data of the 5th Seismic Ground Motion Parameter Zoning Map (NSGM) and historical seismic catalogues and integrating with modern ground motion prediction equations (GMPEs). This model incorporates the characteristics of smoothed seismicity and areal sources for regional seismic hazard assessment. The probabilistic seismic hazard for the North China Plain earthquake belt was investigated through sensitivity analysis related to the seismicity model and GMPEs. The analysis results indicate that the Hybrid model can produce a consistent result with the NSGM model in many cases. However, the NSGM model tends to overestimate hazard values in locations where no major events have occurred and underestimate hazard values in locations where major events have occurred. The Hybrid model can mitigate the degree of such biases. Compared to the modern GMPEs, the GMPE with epicentral distance measures significantly underestimate the seismic hazard under near-field and large-magnitude scenarios. In addition, a comparison of the uniform hazard spectra (UHS) obtained by the models, with China’s design spectrum, shows that the current design spectrum is more conservative than the calculated UHS.

Distance-based Similarity Measures of Hypersoft Sets under Uncertain Environment and Application in Customer Support Systems

Intuitionistic fuzzy hypersoft sets (IFHSS) represent a novel conceptual framework poised to overcome the limitations associated with intuitionistic fuzzy soft sets (IFSS) concerning the representation of multi-argument domains for parameter approximation. This model offers enhanced flexibility and reliability by facilitating the categorization of parameters into pertinent parametric valued sets. This study investigates the application of the IFHSS theory in enhancing similarity measurement within ChatBot systems. Through experimentation and analysis, the research demonstrates the efficacy of IFHSS-based approaches in handling uncertainties inherent in natural language interactions. We introduce distance measures (DM) along with their corresponding similarity measures (SM). These SMs tailored for IFHSS play a significant role in assessing similarity and facilitating the comparison of various factors. This article aims to develop six SMs based on their DMs and their axiomatic properties, theorems, and illustrative examples. Furthermore, we employ these measures to address real-world problems, particularly in the domain of computer sciences. By leveraging various technical factors, our analysis aids in pinpointing the best ChatBot for the satisfaction of customers. The methodologies proposed in this study hold promise for future case studies involving complex features and multiple decision-makers. Moreover, the suggested approach can be seamlessly integrated with existing structures.

A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making

Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) and similarity (BP-similarity) until now. In this work, we propose a novel framework for the belief and plausibility of intuitionistic fuzzy sets (BP-IFSs) and their BP-distance and BP-similarity measures. We modified steps 4 and 5 of the classical TOPSIS method, utilizing both distance and similarity measures to rank the alternatives that satisfy all necessary axioms of distance and similarity. We present numerical examples involving pattern recognition, linguistic variables, and clustering to illustrate the efficiency of these measures, and we develop belief and plausibility TOPSIS (BP-TOPSIS) using the proposed criteria and apply it to complex multicriteria decision-making (MCDM) challenges. The results demonstrate the practicality and effectiveness of our approach.

Unsupervised machine learning in financial anomaly detection: clustering algorithms vs. dedicated methods

The article presents the application of selected clustering algorithms for detecting anomalies in financial data compared to several dedicated algorithms for this problem. To apply clustering algorithms for anomaly detection, the Determine Abnormal Clusters Algorithm (DACA) was developed and implemented. This parameterized script (DACA) allows clusters containing anomalies to be automatically detected on the basis of defined distance measures. This kind of operation allows clustering algorithms to be quickly and efficiently adapted to anomaly detection. The prepared test environment has allowed for the comparison of selected clustering algorithms. K-Means, Hierarchical Cluster Analysis, K-Medoids, and anomaly detection: Stochastic Outlier Selection, Isolation Forest, Elliptic Envelope. The research has been carried out on real financial data, in particular on the income declared in the asset declarations of the targeted professional group. The experience of financial experts has been used to assess anomalies. Furthermore, the results have been evaluated according to a number of popular classification and clustering measures. The highest result for the investigated financial problem was provided by the K-Medoids algorithm in combination with the DACA script. It is worthwhile to conduct future research on the introduced solutions as an ensemble method.

Empirical Likelihood Ratio Based K-Nearest Neighbours Regression

Regression models play a pivotal role in real-life applications by enabling the analysis and prediction of continuous outcomes. Among these, the k-Nearest Neighbours (KNN) model stands out as a significant advancement in machine learning. KNN's ability to make predictions based on the proximity of data points has found wide-ranging applications in various fields. However, the traditional KNN regression model has its limitations, including sensitivity to noise and an uneven distribution of neighbours. In response, this paper introduces a novel approach: an empirical likelihood ratio (ELR) based regression algorithm. The ELR technique offers distinct advantages over distance-based nearest neighbour computations, particularly in handling skewed data distributions and minimizing the impact of outliers. The proposed ELRbased KNN regression model is rigorously assessed through both simulation studies and real-life scenarios. The results explicitly demonstrate the enhanced performance of the ELR-based approach over the conventional KNN model. This research contributes to a deeper understanding of regression techniques and underscores the practical significance of leveraging empirical likelihood ratios in refining predictive models for real-world applications.. KEYWORDS :Regression model, k-Nearest neighbours, Empirical likelihood ratio, Distance measures, Data distributions.

The distance and entropy measures-based intuitionistic fuzzy C-means and similarity matrix clustering algorithms and their applications

Determining the similarity between datasets by distance/similarity measures is important in most clustering algorithms. Therefore, this paper characterizes two clustering algorithms with improved distance measures. In the similarity matrix clustering algorithm, the mixed correlation coefficient and two probability parameters are suggested into the weighted probabilistic Euclidean distance (WPED) measure, which expresses the randomness and fuzziness of intuitionistic fuzzy sets. Second, based on the characteristics of dynamic time warping (DTW), a DTW-based probabilistic Euclidean distance (PED-DTW) method is introduced. The attribute ordering rule is developed with the help of entropy, which is beneficial for PED-DTW in achieving optimal path matching. Furthermore, a DTW-based intuitionistic fuzzy C-means algorithm is constructed. Finally, we performed experiments using car datasets and 7 UCI datasets. Compared with the existing method, the similarity matrix clustering algorithm is feasible. The DTW-based intuitionistic fuzzy C-means algorithms is compared with six clustering methods on four performance metrics, and the performance of our algorithm is analyzed. Our algorithm performs well on four performance metrics. Experimental results indicate that the clustering algorithms proposed in this paper are practical and outperform their existing counterparts. Also, the proposed algorithm gives good results in image segmentation.

Estimation of Remaining Useful Life (RUL) for Pneumatic Actuator without apriori RUL History: A Hybrid Prognostic Approach

Predicting the Remaining Useful Life (RUL) of an industrial pneumatic actuator is crucial for enhancing maintenance strategies, reducing downtime and optimizing resource allocation. However, estimation becomes challenging when no historical RUL data is available for modeling. In this paper, a novel hybrid prognostic approach that combines Dynamic Time Warping (DTW), Exponential Degradation Model (EDM) and Random Forest Regressor (RFR) is proposed to estimate the RUL of pneumatic actuators under the absence of apriori RUL history. The DTW technique is employed to identify the onset of potential degradation. By aligning the healthy and faulty data, DTW provides a robust measure of distance and time at the point of deviation as the threshold value. Subsequently, the EDM is introduced to capture the degradation pattern in the actuator behavior. The EDM accounts for the relationship between threshold value, operating conditions, degradation rate and exponential coefficients through curve fitting methods. To further enhance prediction accuracy, RFR is employed to predict the RUL based on input features of aligned data from DTW and the derived degradation rates from EDM. In the simulation studies, the proposed methodology is applied to a synthetic dataset and benchmark DAMADICS dataset of the industrial pneumatic actuator in sugar processing unit to estimate RUL. The estimated RUL for each health indicator is quantified and the severity of each fault is discussed. The proposed method is implemented on a real time laboratory setup. The results are also validated on the benchmark NASA turbo-engine dataset by comparing the actual and estimated RULs, achieving 82.5% range-based accuracy.

Ensemble responses of auditory midbrain neurons in the cat to speech stimuli at different signal-to-noise ratios

Originally reserved for those who are profoundly deaf, cochlear implantation is now common for people with partial hearing loss, particularly when combined with a hearing aid. This combined intervention enhances speech comprehension and sound quality when compared to electrical stimulation alone, particularly in noisy environments, but the physiological basis for the benefits is not well understood. Our long-term aim is to elucidate the underlying physiological mechanisms of this improvement, and as a first step in this process, we have investigated in normal hearing cats, the degree to which the patterns of neural activity evoked in the inferior colliculus (IC) by speech sounds in various levels of noise allows discrimination between those sounds. Neuronal responses were recorded simultaneously from 32 sites across the tonotopic axis of the IC in anaesthetised normal hearing cats (n=7). Speech sounds were presented at 20, 40 and 60dB SPL in quiet and with increasing levels of additive noise (signal-to-noise ratios (SNRs) –20, –15, –10, –5, 0, +5, +10, +15, +20dB). Neural discrimination was assessed using a Euclidean measure of distance between neural responses, resulting in a function reflecting speech sound differentiation across various SNRs. Responses of IC neurons reliably encoded the speech stimuli when presented in quiet, with optimal performance when an analysis bin-width of 5-10ms was used. Discrimination thresholds did not depend on stimulus level and were best for shorter analysis binwidths. This study sheds light on how the auditory midbrain represents speech sounds and provides baseline data with which responses to electro-acoustic speech sounds in partially deafened animals can be compared.

Machine learning materials properties with accurate predictions, uncertainty estimates, domain guidance, and persistent online accessibility

Abstract One compelling vision of the future of materials discovery and design involves the use of machine learning (ML) models to predict materials properties and then rapidly find materials tailored for specific applications. However, realizing this vision requires both providing detailed uncertainty quantification (model prediction errors and domain of applicability) and making models readily usable. At present, it is common practice in the community to assess ML model performance only in terms of prediction accuracy (e.g. mean absolute error), while neglecting detailed uncertainty quantification and robust model accessibility and usability. Here, we demonstrate a practical method for realizing both uncertainty and accessibility features with a large set of models. We develop random forest ML models for 33 materials properties spanning an array of data sources (computational and experimental) and property types (electrical, mechanical, thermodynamic, etc). All models have calibrated ensemble error bars to quantify prediction uncertainty and domain of applicability guidance enabled by kernel-density-estimate-based feature distance measures. All data and models are publicly hosted on the Garden-AI infrastructure, which provides an easy-to-use, persistent interface for model dissemination that permits models to be invoked with only a few lines of Python code. We demonstrate the power of this approach by using our models to conduct a fully ML-based materials discovery exercise to search for new stable, highly active perovskite oxide catalyst materials.

Lie group convolution neural networks with scale-rotation equivariance

The weight-sharing mechanism of convolutional kernels ensures the translation equivariance of convolutional neural networks (CNNs) but not scale and rotation equivariance. This study proposes a SIM(2) Lie group-CNN, which can simultaneously keep scale, rotation, and translation equivariance for image classification tasks. The SIM(2) Lie group-CNN includes a lifting module, a series of group convolution modules, a global pooling layer, and a classification layer. The lifting module transfers the input image from Euclidean space to Lie group space, and the group convolution is parameterized through a fully connected network using the Lie Algebra coefficients of Lie group elements as inputs to achieve scale and rotation equivariance. It is worth noting that the mapping relationship between SIM(2) and its Lie Algebra and the distance measure of SIM(2) are defined explicitly in this paper, thus solving the problem of the metric of features on the space of SIM(2) Lie group, which contrasts with other Lie groups characterized by a single element, such as SO(2). The scale-rotation equivariance of Lie group-CNN is verified, and the best recognition accuracy is achieved on three categories of image datasets. Consequently, the SIM(2) Lie group-CNN can successfully extract geometric features and perform equivariant recognition on images with rotation and scale transformations.

Integrated MADM approach based on extended MABAC method with Aczel–Alsina generalized weighted Bonferroni mean operator

Currently, q-rung orthopair (q-ROF) set theory is one of the most effective set theories in dealing uncertainty associated with imprecise information. In complex decision-making problems, input variables can be described by q-ROF numbers to cope ambiguity. While, generalized weighted Bonferroni mean (GWBM) operator can reflect correlation among input arguments. Aczel–Alsina operations underline fair and accurate evaluation of decision-makers. Harnessing these benefits, a pioneering extension of the GWBM operator based on Aczel–Alsina operations is introduced. Simultaneously, a novel generalized distance measure is crafted, drawing inspiration from Dice and Jaccard similarities. Beside these, using stepwise weight assessment ratio analysis (SWARA) and multi-attribute border approximation area comparison (MABAC) methods, this study pioneers an integrated method, q-ROF-SWARA-MABAC for assessing and prioritizing factors and alternatives on q-ROF environment. Later, with the suggested model, a case study on high-speed rail corridor (HSRC) for India is solved, revealing Varanasi-Howrah HSRC as the most preferable choice.. Moving forward, detailed sensitive analysis of suggested model is performed to explore the pertinence and supremacy. Eventually, the outcomes manifest that novel framework is flexible, reliable, accurate and could be viable option to consider for future use.

Fuzzy clustering of mixed data with spatial regularization

A fuzzy clustering model for data with mixed features and spatial constraints is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute employing a weighting scheme, to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. A spatial term is taken into account, considering a wide definition of contiguity, either physical contiguity or the adjacency matrix in a network. Simulation studies and two empirical applications, including both physical and abstract definitions of contiguity are presented that show the effectiveness of the proposed clustering model.

Realizability of free spaces of curves

The free space diagram is a popular tool to compute the well-known Fréchet distance. As the Fréchet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often the question arises whether a certain pattern in the free space diagram is “realizable”, i.e., whether there exists a pair of polygonal chains whose free space diagram corresponds to it. The answer to this question may help in deciding the computational complexity of these distance measures, as well as allowing to design more efficient algorithms for restricted input classes that avoid certain free space patterns. Therefore we study the inverse problem: Given a potential free space diagram, do there exist curves that generate this diagram?Our problem of interest is closely tied to the classic Distance Geometry problem. We settle the complexity of Distance Geometry in R>2, showing ∃R-hardness. We use this to show that for curves in R≥2 the realizability problem is ∃R-complete, both for continuous and discrete Fréchet distances. We prove that the continuous case in R1 is only weakly NP-hard, and we provide a pseudo-polynomial time algorithm and show that it is fixed-parameter tractable. Interestingly, for the discrete case in R1 we show that the problem becomes solvable in polynomial time.

Novel distance measures on complex picture fuzzy environment: applications in pattern recognition, medical diagnosis and clustering

Novel distance measures on complex picture fuzzy environment: applications in pattern recognition, medical diagnosis and clustering

Enhancing decision-making with linear diophantine multi-fuzzy set: application of novel information measures in medical and engineering fields

This study offers a comprehensive analysis of novel information for linear diophantine multi-fuzzy sets and illustrates its applications in practical scenarios. We introduce innovative similarity metrics tailored for linear diophantine multi-fuzzy sets, including Cosine similarity, Jaccard similarity, and Exponential similarity. Additionally, we propose Entropy, Inclusion, and Distance measures, providing a robust theoretical foundation supported by developed theorems that explain the interactions between these metrics. The practical implications of these theoretical advancements are demonstrated through various case studies. Specifically, we apply the similarity measures to predict preeclampsia, a severe condition affecting pregnant women, showcasing their potential in medical diagnostics. The entropy measure is used to identify the optimal materials manufacturing method for medical surgical robots, underscoring its importance in ensuring patient safety and the effectiveness of medical procedures. Furthermore, the inclusion measure is employed in pattern recognition tasks, highlighting its utility in complex data analysis. The comparative and superiority analysis shows the effectiveness of our research. The novel aspect of this study is the implementation of information metrics for LDMFS. These efforts aim to enhance the impact and practical applicability of linear diophantine multi-fuzzy sets, fostering innovation and improving outcomes across multiple fields.

Depth gate tracking method based on historical sounding results in MBES

Gate tracking technology plays a crucial role in the autonomous detection of multi-beam echo sounding. The quality of the tracking algorithm directly impacts the quality of the estimate data. Here, we propose a new method for depth gate tracking in multi-beam echo sounding based on the assumption that historical sounding results are geometrically similar to the current ping results. Considering Hausdorff distance measures how far two subsets of a metric space are from each other. An evaluation method based on the concept of similarity distance that relies on the Modified Hausdorff distance is proposed here to measure the similarity between the detection results of different pings and determine the maximum number of historical pings that can be tracked. Then, this model is combined with the iterative closest point registration algorithm to align the bathymetric results of historical pings to the current ping, eliminating the need for prior registration. The registered data are used to initialize the particle distribution in the tracking particle filter and a distance-weighted importance function is established for each beam. Validation on measured data has shown that the proposed method is effective in tracking seabed topography and providing stable gate tracking results.

Fermatean fuzzy score function and distance measure based group decision making framework for household waste recycling plant location selection

The household waste (HW) disposal and recycling have become a significant challenge due to increasing quantities of generated household wastes and increased levels of urbanization. Selecting locations/sites for building new HW recycling plant comprises numerous sustainability dimensions, thus, this work aims to develop new decision-making model for evaluating and prioritizing the HW recycling plant locations. This paper is categorized into three phases. First, we propose new improved score function to compare the Fermatean fuzzy numbers. Moreover, an example is presented to validate the effectiveness of proposed score function over the extant ones. Second, we introduce new distance measure to estimate the discrimination degree between Fermatean fuzzy sets (FFSs) and further discuss its advantages over the prior developed Fermatean fuzzy distance measures. Third, we introduce an integrated methodology by combining the method with the removal effects of criteria (MEREC), the stepwise weight assessment ratio analysis (SWARA) and the measurement alternatives and the ranking according to compromise solution (MARCOS) approaches with Fermatean fuzzy (FF) information, and named as the “FF-MEREC-SWARA-MARCOS” framework. In this method, the FF-distance measure is used to find the weights of involved decision-making experts. Moreover, an integrated criteria weighting method is presented with the combination of MEREC and SWARA models under the context of FFSs, while the combined FF-MEREC-SWARA-MARCOS model is applied to evaluate and prioritize the locations for HW recycling plant development, which illustrates its feasibility of the developed framework. Comparative study and sensitivity assessment are conducted to validate the obtained outcomes. This work provides a hybrid decision analysis approach, which marks a significant impact to the HW recycling plant location selection process with uncertain information.

Selection of OAM signal constellations for atmospheric channels using optimal transport theory

We describe a method for determining optimal selections of orbital angular momentum (OAM) superpositions for OAM signal modulation in free-space optical communications using a measure of distance in the context of the Optimal Transport theory. Within the range of topological charges ℓ = −20 to ℓ = 20 we design OAM constellations using 16 to 128 symbols consisting of solos, duets, trios, and quartets of OAM modes. We propose a classification strategy requiring relatively low complexity to evaluate the performance of these constellations, achieving a classification error smaller than 1/1000 in weak to strong turbulence conditions for the 16-OAM constellation. We have found that the optimal set shows some dependence on the receiver’s architecture, so we offer results for optical detectors based on the conjugate projection, the mode sorter, and the Shack-Hartmann sensor.