Euclidean Distance Function Research Articles

Semi-supervised orthogonal discriminant analysis with relative distance : integration with a MOO approach

In discriminant analysis, trace ratio is an important criterion for minimizing the between-class similarity and maximizing the within-class similarity, simultaneously. In brief, we address the trace ratio problem associated with many semi-supervised discriminant analysis algorithms as they use the normal Euclidean distances between training data samples. Based on this problem, we propose a new semi-supervised orthogonal discriminant analysis technique with relative distance constraints called SSODARD. Different from the existing semi-supervised dimensionality reduction algorithms, our algorithm is more consistent in propagating the label information from the labeled data to the unlabeled data because of the use of relative distance function instead of normal Euclidean distance function. For finding this appropriate relative distance function, we use pairwise constraints generated from labeled data and satisfy them using Bregman projection. Since the projection is not orthogonal, we require an appropriate subset of constraints. In order to select such a subset of constraints, we further develop a framework called MO-SSODARD, which uses evolutionary algorithm while optimizing various validity indices simultaneously. The experimental results on various datasets show that our proposed approaches are superior than the state-of-the-art discriminant algorithms with respect to various validity indices.

Texture Spectrum Coupled with Entropy and Homogeneity Image Features for Myocardium Muscle Characterization

Background:People in middle/later age often suffer from heart muscle damage due to coronary artery disease associated to myocardial infarction. In young people, the genetic forms of cardiomyopathies (heart muscle disease) are the utmost protuberant cause of myocardial disease.Objective:Accurate early detected information regarding the myocardial tissue structure is a key answer for tracking the progress of several myocardial diseases. associations while known disease-lncRNA associations are required only.Method:The present work proposes a new method for myocardium muscle texture classification based on entropy, homogeneity and on the texture unit-based texture spectrum approaches. Entropy and homogeneity are generated in moving windows of size 3x3 and 5x5 to enhance the texture features and to create the premise of differentiation of the myocardium structures. The texture is then statistically analyzed using the texture spectrum approach. Texture classification is achieved based on a fuzzy c–means descriptive classifier. The proposed method has been tested on a dataset of 80 echocardiographic ultrasound images in both short-axis and long-axis in apical two chamber view representations, for normal and infarct pathologies.Results:The noise sensitivity of the fuzzy c–means classifier was overcome by using the image features. The results established that the entropy-based features provided superior clustering results compared to homogeneity.Conclusion:Entropy image feature has a lower spread of the data in the clusters of healthy subjects and myocardial infarction. Also, the Euclidean distance function between the cluster centroids has higher values for both LAX and SAX views for entropy images.</P>

A framework for semi-supervised metric transfer learning on manifolds

A common assumption of statistical learning theory is that the training and testing data are drawn from the same distribution. However, in many real-world applications, this assumption does not hold true. Hence, a realistic strategy, Cross Domain Adaptation (DA) or Transfer Learning (TA), can be used to employ previously labelled source domain data to boost the task in the new target domain. Previously, Cross Domain Adaptation methods have been focused on re-weighting the instances or aligning the cross-domain distributions. However, these methods have two significant challenges: (1) There is no proper consideration of the unlabelled data of target task as in the real-world, an abundant amount of unlabelled data is available, (2) The use of normal Euclidean distance function fails to capture the appropriate similarity or dissimilarity between samples. To deal with this issue, we have proposed a Semi-Supervised Metric Transfer Learning framework called SSMT that reduces the distribution between domains both statistically and geometrically by learning the instance weights, while a regularized distance metric is learned to minimize the within-class co-variance and maximize the between-class co-variance simultaneously for the target domain. Compared with the previous works where Mahalanobis distance metric and instance weights are learned by using the labelled data or in a pipelined framework that leads to a decrease in the performance, our proposed SSMT attempts to learn a regularized distance metric and instance weights by considering unlabelled data in a parallel framework. Experimental evaluation on three cross-domain visual data sets, e.g., PIE Face, Handwriting Digit Recognition on MNIST–USPS and Object Recognition, demonstrates the effectiveness of our designed approach on facilitating the unlabelled target task learning, compared to current state-of-the-art domain adaptation approaches.

Ultimate: Unearthing Latent Time Profiled Temporal Associations

Discovery of temporal association patterns, temporal association rules from temporal databases is extensively studied by academic research community and applied in various industrial applications. Temporal association pattern discovery is extended to similarity based temporal association pattern discovery from time-stamped transaction datasets by researchers Yoo and Sashi Sekhar. They introduced methods for pruning through distance bounds, and have also introduced SEQUENTIAL and SPAMINE algorithms for pattern mining that are based on snapshot data scan and lattice data scan strategies respectively. Our previous research introduced algorithms G-SPAMINE, MASTER, Z-SPAMINE for time profiled association pattern discovery. These algorithms applied distance measures SRIHASS, ASTRA, and KRISHNA SUDARSANA for similarity computations. SEQUENTIAL, SPAMINE, G-SPAMINE, MASTER, Z-SPAMINE approaches are all based on snapshot and lattice database scan strategies and prunes temporal itemsets by making use of lower bound, upper bound support time sequences and upper-lower distance bound, lower bound distance values. The major limitation of all these algorithms is their inevitability to eliminate dataset scanning process for knowing true supports of itemsets and essential need to have dataset available in memory. To eliminate the requirement of retaining dataset in main memory, algorithms VRKSHA and GANDIVA are two pioneering research contributions that introduced tree structure for time profiled temporal association mining. VRKSHA is based on snapshot tree scan technique while GANDIVA is a lattice tree scan based approach. VRKSHA and GANDIVA both apply Euclidean distance function, but they do not estimate support and distance bounds. This research introduces the pioneering work ULTIMATE that uses a novel tree structure. The tree is generated using similarity measure ASTRA. ULTIMATE uses support bound and distance bound computations for pruning temporal patterns. Experiment results showed that ULTIMATE outperforms SEQUENTIAL, SPAMINE, G-SPAMINE, MASTER, VRKSHA, GANDIVA algorithms.

Krishna Sudarsana—A Z-Space Interest Measure for Mining Similarity Profiled Temporal Association Patterns

Similarity profiled association mining from time stamped transaction databases is an important topic of research relatively less addressed in the field of temporal data mining. Mining temporal patterns from these time series databases requires choosing and applying similarity measure for similarity computations and subsequently pruning temporal patterns. This research proposes a novel z-space based interest measure named as Krishna Sudarsana for time-stamped transaction databases by extending interest measure Srihass proposed in previous research. Krishna Sudarsana is designed by using the product based fuzzy Gaussian membership function and performs similarity computations in z-space to determine the similarity degree between any two temporal patterns. The interest measure is designed by considering z-values between z = 0 and z = 3.09. Applying the Krishna Sudarsana requires moving the threshold value given by user to a different transformation space (z-space) which is a defined as a function of standard deviation. In addition to proposing interest measure, new expressions for standard deviation and equivalent z-space threshold are derived for similarity computations. For experimental evaluation, we considered Naive, Sequential and Spamine algorithms that applies Euclidean distance function and compared performance of these three approaches to Z-Spamine algorithm that uses Krishna Sudarsana by choosing various test cases. Experiment results proved the performance of the proposed approach is better to Sequential approach that uses snapshot database scan strategy and Spamine approach that uses lattice based database scan strategy.

Hyperspectral Image Classification Using Similarity Measurements-Based Deep Recurrent Neural Networks

Classification is a common objective when analyzing hyperspectral images, where each pixel is assigned to a predefined label. Deep learning-based algorithms have been introduced in the remote-sensing community successfully in the past decade and have achieved significant performance improvements compared with conventional models. However, research on the extraction of sequential features utilizing a single image, instead of multi-temporal images still needs to be further investigated. In this paper, a novel strategy for constructing sequential features from a single image in long short-term memory (LSTM) is proposed. Two pixel-wise-based similarity measurements, including pixel-matching (PM) and block-matching (BM), are employed for the selection of sequence candidates from the whole image. Then, the sequential structure of a given pixel can be constructed as the input of LSTM by utilizing the first several matching pixels with high similarities. The resulting PM-based LSTM and BM-based LSTM are appealing, as all pixels in the whole image are taken into consideration when calculating the similarity. In addition, BM-based LSTM also utilizes local spectral-spatial information that has already shown its effectiveness in hyperspectral image classification. Two common distance measures, Euclidean distance and spectral angle mapping, are also investigated in this paper. Experiments with two benchmark hyperspectral images demonstrate that the proposed methods achieve marked improvements in classification performance relative to the other state-of-the-art methods considered. For instance, the highest overall accuracy achieved on the Pavia University image is 96.20% (using both BM-based LSTM and spectral angle mapping), which is an improvement compared with 84.45% overall accuracy generated by 1D convolutional neural networks.

A kernel semi-supervised distance metric learning with relative distance: Integration with a MOO approach

Metric learning, which aims to determine an appropriate distance function to measure the similarity and dissimilarity between data points accurately, is one of the most popular methods to enhance the performance of many machine learning methods such as K-means clustering and K nearest neighbor classifier algorithms. These algorithms may not perform well because of the use of normal Euclidean distance function that ignores any statistical regularities that might be estimated from a large training set of labeled examples. In many real-world applications, the Euclidean distance may not be fit to capture the intrinsic similarity and dissimilarity between the data points. Compared to existing metric learning algorithms, which use large amount of labeled data in the form of must-link (ML) and cannot-link constraints as side information where the granularity of true clustering is unknown, our proposed approach uses few labeled data in the form of relative-distance constraints such as equality constraints, Ceq, and inequality constraints, Cneq. For satisfying such constraints, we need to project the initial Euclidean distance matrix by using Bregman projection on the convex subset of constraints in such a way that all the constraints are satisfied. Since Bregman projection is not orthogonal, means while satisfying the current constraint previously satisfied constraints may get unsatisfied, we need to select a proper subset of constraints for learning better distance function. The multi-objective framework is utilized for selecting a good subset of constraints which can help in getting the proper labeling of the data set. The selected subset of constraints is used for adjusting the initial kernel-matrix. K-means clustering technique is applied to the adjusted kernel matrix to label the data set. In order to evaluate the quality of obtained labeling, different external and internal cluster validity indices are deployed. The values of these indices are simultaneously optimized using the search capability of MOO with the aim of selecting the appropriate subset of constraints. The proposed approach is evaluated on UCI Human Activity Recognition using Smartphone Dataset v1.0 along with nine other popular data sets. Results show that our approach outperforms the state of the art semi-supervised metric learning algorithms with respect to different internal and external cluster validity indices.

An improved <i>k</i>NN text classification method

This paper proposes an improved kNN text classification method. The kNN algorithm in vector space models (VSM) has several limitations, such as occupying excessive storage space and all dimensions in the kNN algorithm share the same weight, making classification inaccurate. To solve these problems, this paper proposes a SOM neural network with principal component weighting. In this model, the principal component analysis process is embedded into the SOM neural network. Specifically, principal component analysis is used to extract the main feature components of the assessed target. Then, it is inputted into the network for computation. Meanwhile, variance contribution rates of principal components are introduced into the Euclidean distance function in the forms of weights. Using the principal component weighting SOM algorithm to compute the weights of VSM dimensions together with the kNN algorithm could effectively reduce dimensions of a vector space, and increase the precision and speed of the kkNN text classification method.

Triplet Loss with Channel Attention for Person Re-identification

The triplet loss function has seen extensive use within person re-identification. Most works focus on either improving the mining algorithm or adding new terms to the loss function itself. Our work instead concentrates on two other core components of the triplet loss that have been under-researched. First, we improve the standard Euclidean distance with dynamic weights, which are selected based on the standard deviation of features across the batch. Second, we exploit channel attention via a squeeze and excitation unit in the backbone model to emphasise important features throughout all layers of the model. This ensures that the output feature vector is a better representation of the image, and is also more suitable to use within our dynamically weighted Euclidean distance function. We demonstrate that our alterations provide significant performance improvement across popular reidentification data sets, including almost 10% mAP improvement on the CUHK03 data set. The proposed model attains results competitive with many state-of-the-art person re-identification models.

An Adaptive Density Peaks Clustering Method With Fisher Linear Discriminant

Clustering is one of the most important topics in data mining and machine learning. The density peaks clustering (DPC) algorithm is a well-known density-based clustering method that can efficiently and effectively deal with non-spherical clusters. However, the computational methods of the local density and the distance measure are simple and easily ignore the correlation and the similarity between samples, and the manual setting of parameters has a great influence on the clustering results; therefore, the clustering performance of DPC is poor on the high-dimensional datasets. To address these issues, this paper presents an adaptive DPC algorithm with Fisher linear discriminant for the clustering of complex datasets, called ADPC-FLD. First, the kernel density estimation function is introduced to calculate the local density of the sample points. Pearson correlation coefficient between samples as weight is employed to construct a weighted Euclidean distance function to measure the distance between samples. This considers both the spatial structure and the correlation of the samples. Then, a novel density estimation entropy is proposed, and based on the minimization of density estimation entropy, the density estimation parameters are adaptively selected according to the distribution characteristics of the data, which can efficiently eliminate the influence of manual setting. Third, an adaptive strategy of cluster center selection is designed to avoid the error caused by the noise data as the cluster centers and the uncertainty of manually selecting the cluster centers. Finally, Fisher linear discriminant algorithm is used to eliminate the irrelevant information and reduce the dimensionality of high-dimensional data, following on which an adaptive DPC method is implemented on six synthetic datasets, thirteen UCI datasets and seven gene expression datasets for comparing with other related algorithms. The experimental results on 26 datasets show that the proposed algorithm significantly outperforms several outstanding clustering approaches in terms of clustering accuracy and efficiency.

Non-smooth Non-convex Bregman Minimization: Unification and New Algorithms

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, Gradient Descent, Forward-Backward Splitting, ProxDescent, without the common requirement of a Lipschitz continuous gradient. In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions), replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and non-linear inverse problems in signal/image processing and machine learning.

A Study of the Normalization Functions on a Distance-Based Instance Selection: A Data Reduction Technique

Minimum-margin nearest neighbor instance selection is one of the data reduction techniques for the feed-forward neural network that can improve the scalability and make incremental learning computationally feasible. The technique utilizes the Euclidean distance function to produce a reduced training set that can conserve the distribution model of the original training set and yield a comparable level of the classification accuracy of the neural network as the original training set. Nevertheless, the technique does not consider the range of the attributes, causing some attributes to dominate the other attributes on the Euclidean distance calculation. This paper studies an integration of six normalization techniques; Min-Max, Z-score, Mean MAD, Median MAD, Hyperbolic Tangent Estimator, and Modified Hyperbolic Tangent, with the minimum-margin nearest neighbor instance selection algorithms to improve the data reduction performance, the execution time reduction performance of the data reduction techniques, and the classification performance of the feedforward neural network. The experimental results on the real-world datasets from the UCI database and ELENA project confirmed that the Min-Max, Z-score, Mean MAD, and Median MAD normalization techniques could improve the data reduction performance more efficient than the Modified Hyperbolic Tangent and Hyperbolic Tangent Estimator normalization techniques. The Median MAD normalization could improve the execution time reduction performance of the data reduction techniques most efficiently. Besides, most normalization techniques could improve the accuracy, error rate, precision, recall, and F1-score of the feed-forward neural network when the final training set included both the normalized original training sets and the reduced normalized training sets.

A data-driven metric learning-based scheme for unsupervised network anomaly detection

Most network anomaly detection systems (NADSs) rely on the distance between the connections’ feature vectors to identify attacks. Traditional distance metrics are inefficient for these systems as they deal with heterogeneous features of network connections. In this paper, we address a clustering-based NADS employing a data-driven distance metric. This metric is the outcome of a proposed metric learning method, which extracts its required side information from the training samples. The learned transformation matrix maps the connections’ features to a new feature space in which similar and dissimilar connections are more well-separated while the local neighborhood information of the connections’ features is preserved using the Laplacian Eigenmap technique. The proposed NADS is evaluated over the Kyoto 2006+ and NSL-KDD datasets. The experimental results show that it has superior performance in comparison with a recent SVM-clustering based NADS that employs the traditional Euclidean distance function.

A New Chaotic Starling Particle Swarm Optimization Algorithm for Clustering Problems

A new method using collective responses of starling birds is developed to enhance the global search performance of standard particle swarm optimization (PSO). The method is named chaotic starling particle swarm optimization (CSPSO). In CSPSO, the inertia weight is adjusted using a nonlinear decreasing approach and the acceleration coefficients are adjusted using a chaotic logistic mapping strategy to avoid prematurity of the search process. A dynamic disturbance term (DDT) is used in velocity updating to enhance convergence of the algorithm. A local search method inspired by the behavior of starling birds utilizing the information of the nearest neighbors is used to determine a new collective position and a new collective velocity for selected particles. Two particle selection methods, Euclidean distance and fitness function, are adopted to ensure the overall convergence of the search process. Experimental results on benchmark function optimization and classic clustering problems verified the effectiveness of this proposed CSPSO algorithm.

Individual Morphological Brain Network Construction Based on Multivariate Euclidean Distances Between Brain Regions.

Morphological brain network plays a key role in investigating abnormalities in neurological diseases such as mild cognitive impairment (MCI) and Alzheimer's disease (AD). However, most of the morphological brain network construction methods only considered a single morphological feature. Each type of morphological feature has specific neurological and genetic underpinnings. A combination of morphological features has been proven to have better diagnostic performance compared with a single feature, which suggests that an individual morphological brain network based on multiple morphological features would be beneficial in disease diagnosis. Here, we proposed a novel method to construct individual morphological brain networks for two datasets by calculating the exponential function of multivariate Euclidean distance as the evaluation of similarity between two regions. The first dataset included 24 healthy subjects who were scanned twice within a 3-month period. The topological properties of these brain networks were analyzed and compared with previous studies that used different methods and modalities. Small world property was observed in all of the subjects, and the high reproducibility indicated the robustness of our method. The second dataset included 170 patients with MCI (86 stable MCI and 84 progressive MCI cases) and 169 normal controls (NC). The edge features extracted from the individual morphological brain networks were used to distinguish MCI from NC and separate MCI subgroups (progressive vs. stable) through the support vector machine in order to validate our method. The results showed that our method achieved an accuracy of 79.65% (MCI vs. NC) and 70.59% (stable MCI vs. progressive MCI) in a one-dimension situation. In a multiple-dimension situation, our method improved the classification performance with an accuracy of 80.53% (MCI vs. NC) and 77.06% (stable MCI vs. progressive MCI) compared with the method using a single feature. The results indicated that our method could effectively construct an individual morphological brain network based on multiple morphological features and could accurately discriminate MCI from NC and stable MCI from progressive MCI, and may provide a valuable tool for the investigation of individual morphological brain networks.

An efficient approach for imputation and classification of medical data values using class-based clustering of medical records

Medical data is usually not free from missing values and this is also true when data is collected and sampled through various clinical trials. Existing Imputation techniques do not address the problem of high dimensionality and apply distance functions that also have the curse of high dimensionality. There is a need to turn up with innovative approaches and methods for accurate and efficient analysis of medical records. This research proposes an improved imputation approach called IM-CBC (Imputation based on class-based clustering) and a classifier termed as the Class-Based-Clustering Classifier(CBCC-IM). Experiments are performed on nine benchmark datasets and the recorded results using IM-CBC imputation approach are compared to ten imputation approaches using classifiers KNN, SVM and C4.5 and to the CBCC classifier using Euclidean distance and fuzzy gaussian similarity functions. Results obtained prove that the performance of classifiers is improved or atleast nearer to the existing approaches. CBCC-IM classifier records highest accuracy when compared to all other classifiers on benchmark datasets such as Cleveland, Ecoli, Iris, Pima, Wine and Wisconsin.

Application of Euclidean distance mapping for assessment of basement membrane thickness distribution in asthma.

Abnormal thickening of the airway basement membrane is one of the hallmarks of airway remodeling in asthma. The present protocols for measuring the basement membrane involve the use of stained tissue sections and measurements of the basement membrane thickness at certain intervals, followed by the calculation of the geometric mean thickness for each airway. This report describes an automated, unbiased approach which uses color segmentation to identify structures of interest on stained sections and Euclidean distance mapping to measure the thickness distribution of airway structures. This method was applied to study the thickness distribution of the basement membrane and airway epithelium in lungs donated for research from seven nonasthmatic and eight asthmatic age- and sex-matched donors. A total of 60 airways were assessed. We report that the thickness and thickness distribution of the basement membrane and airway epithelium are increased in large and small airways of asthmatics compared with nonasthmatics. Using this method we were able to demonstrate the heterogeneity in the thickness of the basement membrane and airway epithelium within individual airways of asthmatic subjects. This new computational method enables comprehensive and objective quantification of airway structures, which can be used to quantify heterogeneity of airway remodeling in obstructive lung diseases such as asthma and chronic obstructive pulmonary disease.NEW & NOTEWORTHY The described application of Euclidean distance mapping provides an unbiased approach to study the extent and thickness distribution of changes in tissue structures. This approach will enable researchers to use computer-aided analysis of structural changes within lung tissue to understand the heterogeneity of airway remodeling in lung diseases.

A Vehicle Speed Estimation Algorithm Based on Dynamic Time Warping Approach

At present, the research of vehicle speed estimation algorithm based on wireless magnetic sensor networks has made great progress. The general idea of the existing algorithms is to calculate the similarity of two magnetic signatures by Euclidean distance or cross correlation function. However, these methods are not well suitable for the time distorted waveforms. This paper adopts the dynamic time warping (DTW) approach to measure the similarity, and then a speedup version of DTW is proposed. Experimental results are presented from a large number of vehicles to show that the proposed speedup DTW reduces the runtime and improves the accuracy of speed estimation.

Clustering Accuracies on Concepts of Mathematics

Fuzzy c-means algorithm (FCM) based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. Improved Normalized Mahalanobis Clustering Algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Mahalanobis Clustering Algorithm.

Automated Bone Segmentation and Surface Evaluation of a Small Animal Model of Post-Traumatic Osteoarthritis.

MicroCT imaging allows for noninvasive microstructural evaluation of mineralized bone tissue, and is essential in studies of small animal models of bone and joint diseases. Automatic segmentation and evaluation of articular surfaces is challenging. Here, we present a novel method to create knee joint surface models, for the evaluation of PTOA-related joint changes in the rat using an atlas-based diffeomorphic registration to automatically isolate bone from surrounding tissues. As validation, two independent raters manually segment datasets and the resulting segmentations were compared to our novel automatic segmentation process. Data were evaluated using label map volumes, overlap metrics, Euclidean distance mapping, and a time trial. Intraclass correlation coefficients were calculated to compare methods, and were greater than 0.90. Total overlap, union overlap, and mean overlap were calculated to compare the automatic and manual methods and ranged from 0.85 to 0.99. A Euclidean distance comparison was also performed and showed no measurable difference between manual and automatic segmentations. Furthermore, our new method was 18 times faster than manual segmentation. Overall, this study describes a reliable, accurate, and automatic segmentation method for mineralized knee structures from microCT images, and will allow for efficient assessment of bony changes in small animal models of PTOA.