Euclidean Distance Function Research Articles

Effect of the distance functions on the distance-based instance selection for the feed-forward neural network

The distance-based instance selection algorithm for the feed-forward neural network is a numerosity reduction technique. It selects only the instances at the decision boundary between consecutive classes of data to lessen the number of instances in the original training set using the Euclidean distance function. This paper studies improvement of the reduction performance and the classification performance of the nine distance functions in the distance-based instance selection algorithm. The evaluation was conducted on the real-world data sets from the UCI machine learning repository and ELENA project. The data reduction performance results confirmed that the Chebyshev, Cosine, and Minkowski distance functions are recommended for the integer data type. The Minkowski distance function is recommended for the categorical data type. The Jaccard distance function is recommended for the real data type. The selection of the initial distance function based on the data type can make the distance-based instance selection algorithm produce the best classification performance.

Marginal and average weight-enabled data aggregation mechanism for the resource-constrained networks

In Wireless Sensor Networks (WSNs), data redundancy is a challenging issue that not only introduces network congestion but also consumes a considerable amount of sensor node resources. Data redundancy occurs due to the spatial and temporal correlation among the data gathered by the neighboring nodes. Data aggregation is a prominent technique that performs in-network filtering of the redundant data and accelerates the knowledge extraction by eliminating the correlated data. However, most of the data aggregation techniques have lower accuracy as they do not cater for erroneous data from faulty nodes and pose an open research challenge. To address this challenge, we have proposed a novel, lightweight, and energy-efficient function-based data aggregation approach for a cluster-based hierarchical WSN. Our proposed approach works at two levels, i.e., at the node level and at the cluster head level. At the node level, the data aggregation is performed using Exponential Moving Average (EMA) and a threshold-based mechanism is adopted to detect any outliers for improving the accuracy of aggregated data. At the cluster head level, we have employed a modified version of Euclidean distance function to provide highly-refined aggregated data to the base station. Our experimental results show that our approach reduces the communication cost, transmission cost, energy consumption at the nodes and cluster heads, and delivers highly-refined and fused data to the base station.

Lightweight boundary refinement module based on point supervision for semantic segmentation

An effective semantic segmentation approach should contain fine object boundaries and continuous regions. However, recent mask-based segmentation cannot extract boundary features well on the coarse prediction, which causes obvious problems of blurry edges. Although several segmentation methods embed boundary detection branch to calculate contours directly, this type of architecture will lead to the increased computational complexity and miss the edge detailed information such as inter-class distinction. In order to obtain fine boundaries, we present a lightweight boundary refinement module with point supervision named BRPS to improve the boundary quality for the segmentation result generated by various existing segmentation models. Firstly, a direction field is learned to complete the initial feature rectification, which is defined as pointing away from the nearest object boundary to each pixel, where the weighted Euclidean and Cosine distance function is used as the loss between predicted boundary pixels and Ground-truth labels. Then, point-based supervised learning is performed at uncertain and certain locations including random distribution and key feature points based on a new point convolutional operation to output final crisp object boundaries. Finally, we verify that our BRPS module can effectively reduce the prediction errors for segmentation results generated from various state-of-the-art models such as DeepLabv3 and HRNet on the Pascal VOC2012, NYUD v2 datasets, Cityscapes and BDD100K datasets.

Phylogenetics of Indo-European Language Families via an Algebro-Geometric Analysis of Their Syntactic Structures

Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The two main sources of syntactic data are the SSWL database and Longobardi’s recent data of syntactic parameters. We compute phylogenetic invariants and estimates of the Euclidean distance functions for two sets of Germanic languages, a set of Romance languages, a set of Slavic languages and a set of early Indo-European languages, and we compare the results with what is known through historical linguistics.

Rockburst prediction for hard rock and deep-lying long tunnels based on the entropy weight ideal point method and geostress field inversion: a case study of the Sangzhuling Tunnel

To evaluate rockbursts in deep-lying long tunnels, a multiple factor analysis and predictions were conducted. It is necessary to establish whether the primary evaluation indexes cover the entire development–occurrence–evolution process for rockbursts and how best to determine the weights of the final selected indexes. We developed an evaluation model with attribute reduction and chose 5 out of 11 primary evaluation indexes to cover the typical characteristics of energy storage, rockburst proneness, and risk of failure. The weights of the primary evaluation indexes and the offset distance were then determined using the entropy weight ideal point method. Combining geostress field inversion and rock mechanic tests, the evaluation model was applied to the case of the Sangzhuling Tunnel along the Sichuan–Tibet railway. Rockburst prediction results achieved 41.2% and 94.1% accuracy when using the Manhattan and Euclidean distance functions, respectively. A more specific classification of the evaluation indexes may optimize the weight assignment and help obtain more accurate results. This paper provides a reliable method for rockburst predictions for hard rock and deep-lying long tunnels, which may have good prospects for engineering applications.

Selective Image Segmentation Models Using Three Distance Functions

Image segmentation can be defined as partitioning an image that contains multiple segments of meaningful parts for further processing. Global segmentation is concerned with segmenting the whole object of an observed image. Meanwhile, the selective segmentation model is concerned with segmenting a specific object required to be extracted. The Convex Distance Selective Segmentation (CDSS) model, which uses the Euclidean distance function as the fitting term, was proposed in 2015. However, the Euclidean distance function takes time to compute. This paper proposes the reformulation of the CDSS minimization problem by changing the fitting term with three popular distance functions, namely Chessboard, City Block, and Quasi-Euclidean. The proposed models are CDSSNEW1, CDSSNEW2, and CDSSNEW3, which apply the Chessboard, City Block, and Quasi-Euclidean distance functions respectively. In this study, the Euler-Lagrange (EL) equations of the proposed models were derived and solved using the Additive Operator Splitting method. Then, MATLAB coding was developed to implement the proposed models. The accuracy of the segmented image was evaluated using the Jaccard (JSC) and Dice Similarity Coefficients (DSC). The execution time was recorded to measure the efficiency of the models. Numerical results showed that the proposed CDSSNEW1 model based on the Chessboard distance function could segment the specific object successfully for all grayscale images with the fastest execution time compared to other models.

A new framework for contour tracing using Euclidean distance mapping

A new framework for contour tracing using Euclidean distance mapping

A new framework for contour tracing using Euclidean distance mapping

In this paper, a new fast, efficient and accurate contour extraction method, using eight sequential Euclidean distance map and connectivity criteria based on maximal disk, is proposed. The connecti...

Deep Semantic Cross Modal Hashing Based on Graph Similarity of Modal-Specific

With the advantages of low storage cost and fast query speed, cross modal hashing has attracted increasing attention recently. However, most existing cross-modal hashing methods adopt the same measurement metric when processing data of different modalities or cannot explore heterogeneous correlation between different modalities well, which will result in information loss and heterogeneous correlation cannot be solved. In this paper, we propose a Deep semantic Cross Modal Hashing based on Graph similarity of Modal-Specific (DCMHGMS) method, which not only considers the inter-modal similarity but also designs two graphs to characterize the intra-modal similarity of modal-specific models. First, we use a weighted measurement metric of Euclidean distance and cosine distance to measure the inter-modal similarity between image and text, which can solve the heterogeneous correlation problem. Next, for image graph, we build the intra-modal similarity with Euclidean distance function. Then, for text graph, we build the intra-modal similarity with cosine distance function. Paying attention to the specifics of each modality can improve the retrieval accuracy, thus solving the problem of information loss. Moreover, the semantic information embedding, quantization loss, and bit balanced constraint are considered in this model. Experimental results on two datasets show the effectiveness of our proposed DCMHGMS method.

An energy-efficient data aggregation approach for cluster-based wireless sensor networks

In wireless sensor networks (WSNs), data redundancy is a challenging issue that not only introduces network congestion but also consumes considerable sensor node resources. Data redundancy occurs due to the spatial and temporal correlations among the data gathered by the neighboring nodes. Data aggregation is a prominent technique that performs in-network filtering of the redundant data and accelerates knowledge extraction by eliminating the correlated data. However, most data aggregation techniques have low accuracy because they do not consider the presence of erroneous data from faulty nodes, which represents an open research challenge. To address this challenge, we have proposed a novel, lightweight, and energy-efficient function-based data aggregation approach for a cluster-based hierarchical WSN. Our proposed approach works at two levels: the node level and the cluster head level. At the node level, the data aggregation is performed using the exponential moving average (EMA), and a threshold-based mechanism is adopted to detect any outliers to improve the accuracy of data aggregation. At the cluster head level, we have employed a modified version of the Euclidean distance function to provide highly refined aggregated data to the base station. Our experimental results show that our approach reduces the communication cost, transmission cost, and energy consumption at the nodes and cluster heads and delivers highly refined, fused data to the base station.

Instability and mode transition analysis of a hydrogen-rich combustion in a model afterburner

Combustion instabilities were investigated experimentally for a hydrogen-rich combustion in a model afterburner installed at the end of a high-enthalpy wind tunnel. Air was supplied at 0.3 MPa and 950 K. The combustion instabilities were studied with the time-resolved measurements of a near-infrared (NIR) emission from water molecules over 780 nm using a high-speed video camera. Pressure was also measured in the combustor. The pressure and the NIR images were analyzed by data-driven approach, which include the fast Fourier transform (FFT), the wavelet transform, the dynamic mode decomposition (DMD) and the Gaussian process latent variable methods (GP-LVM). Thermoacoustic instability was observed under a rich condition, and the amplitude of the pressure oscillation was the maximum at the overall equivalence ratio of approximately 2.4 or 2.7 as a result of the FFT. The combustion dynamics were investigated in detail for an experimental run at the equivalence ratio of 2.4. A pressure spectrogram indicated a flame–vortex interaction with a Strouhal number of 0.5 (2300 Hz), thermoacoustic instability (560 Hz), and their transitions with the wavelet transform. For NIR images, the same tendency was also observed in the spectrogram of the modes obtained by the Gabor-filtered DMD, which could clearly resolve the high-order harmonic modes of the flame–vortex interaction and the thermoacoustic instability. Furthermore, NIR images were analyzed with GP-LVM to study the evolution of the combustion dynamics in a three-dimensional latent space. Recurrence plots with the Euclidean distance function were used to visualize the evolutions of the combustion dynamics. A limit cycle behavior of the flame–vortex interaction was clearly observed, whereas the limit cycle of the thermoacoustic instability showed more complicated behaviors. The transition behaviors of the instabilities were observed in the recurrence plots in detail, indicating that the flame–vortex interaction excited the fourth harmonic mode of the thermoacoustic instability, followed by the basic mode.

Effective K-Nearest Neighbor Algorithms Performance Analysis of Thyroid Disease

ABSTRACT Thyroid is an essential gland as its hormones are controlling the metabolism system of the human body. An abnormal amount of thyroid gland secretion causes two major types of diseases which are hyperthyroidism and hypothyroidism. In this research study, the implementation of K-Nearest neighbor (KNN) with its various distance functions is presented to detect thyroid disease. The proposed study consists of three phases, which are KNN without feature selection, KNN using L1-based feature selection, and KNN using chi-square-based feature selection techniques. Thyroid datasets from KEEL dataset repository and another from a registered hospital in Pakistan were used in this study. The new dataset was distinguished from existing datasets as it included three additional features, i.e., pulse rate, Body Mass Index (BMI), and Blood Pressure (BP). Various distance functions were used to analyze the performance of the KNN model on these two datasets. Performance evaluation metrics have been used to discuss the achievement of the classifier. The optimal range of k values from the results are described between 1 and 5. Euclidean and Cosine distance functions achieved the highest accuracy using chi-square-based feature selection technique for new dataset as compared to existing datasets.

Illumination Robust Loop Closure Detection with the Constraint of Pose

Background: Loop closure detection is a crucial part in robot navigation and simultaneous location and mapping (SLAM). Appearance-based loop closure detection still faces many challenges, such as illumination changes, perceptual aliasing and increasing computational complexity. Methods: In this paper, we proposed a visual loop closure detection algorithm that combines illumination robust descriptor DIRD and odometry information. In this algorithm, a new distance function is built by fusing the Euclidean distance function and Mahalanobis distance function, which integrates the pose uncertainty of body and can dynamically adjust the threshold of potential loop closure locations. Then, potential locations are verified by calculating the similarity of DIRD descriptors. Results: The proposed algorithm is evaluated on KITTI and EuRoC datasets, and is compared with SeqSLAM algorithm, which is one of the state of the art loop closure detection algorithms. The results show that the proposed algorithm could effectively reduce the computing time and get better performance on P-R curve. Conclusion: The new loop closure detection method makes full use of odometry information and image appearance information. The application of the new distance function can effectively reduce the missed detection caused by odometry error accumulation. The algorithm does not require extracting image features or learning stage, and can realize real-time detection and run on the platform with limited computational power.

Intra-Treatment PET/MRI Separates Intermediate Risk p16-Positive Oropharynx Cancer Patients into Favorable and Unfavorable Cohorts

Although patients with low risk p16-positive oropharynx squamous cell carcinoma (LR p16+OPSCC) exhibit superior clinical outcomes than patients with p16+OPSCC and intermediate risk factors (T4, >N2b, and > 10 pack-years), there exists overlap in outcomes between the two groups. Metrics to define patients with IR p16+OPSCC that exhibit favorable outcomes remain to be defined. We evaluated the utility of early tumor response to definitive radiotherapy assessed by intra-treatment PET/MRI to define favorable and unfavorable IR p16+OPSCC cohorts. Patients with p16+OPSCC underwent pre-treatment PET/MRI and repeat imaging two weeks into definitive radiotherapy. Changes in volume, metabolic activity, and diffusion of the primary tumor and largest large lymph were evaluated. Standard T-test was used to assess the significance of observed changes. K-means clustering with Euclidean distance function and silhouette width were used to establish clusters. Thirteen patients were prospectively enrolled, 5 low risk and 8 intermediate risk. There was no significant difference in the intra-treatment response within the LR cohort. The IR group clustered into 2 groups. Five IR p16+OPSCC patients exhibited radiographic changes that were similar to the LR cohort and 3 IR patients exhibited changes that were significantly different from the LR cohort and the similarly responding IR cohort. All patients were disease free by PET/MRI at 3 months. We demonstrate the ability of intra-treatment PET/MRI responses to identify patients with IR p16+OPSCC that exhibit similar and dissimilar responses to definitive radiotherapy when compared to patients with LR disease. These data may provide a mechanism to determine in real-time the appropriateness for therapy escalation and de-intensification of IR p16+OPSCC undergoing definitive radiotherapy.

Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

Detection of Road Surface Changes from Multi-Temporal Unmanned Aerial Vehicle Images Using a Convolutional Siamese Network

Road quality commonly decreases due to aging and deterioration of road surfaces. As the number of roads that need to be surveyed increases, general maintenance—particularly surveillance—can be quite costly if carried out using traditional methods. Therefore, using unmanned aerial vehicles (UAVs) and deep learning to detect changes via surveys is a promising strategy. This study proposes a method for detecting changes on road surfaces using pairs of UAV images captured at different times. First, a convolutional Siamese network is introduced to extract the features of an image pair and a Euclidean distance function is applied to calculate the distance between two features. Then, a contrastive loss function is used to enlarge the distance between changed feature pairs and reduce the distance between unchanged feature pairs. Finally, the initial change map is improved based on the preliminary differences between the two input images. Our experimental results confirm the effectiveness of this approach.

On critical points of quadratic low-rank matrix optimization problems

AbstractThe absence of spurious local minima in certain nonconvex low-rank matrix recovery problems has been of recent interest in computer science, machine learning and compressed sensing since it explains the convergence of some low-rank optimization methods to global optima. One such example is low-rank matrix sensing under restricted isometry properties (RIPs). It can be formulated as a minimization problem for a quadratic function on the Riemannian manifold of low-rank matrices, with a positive semidefinite Riemannian Hessian that acts almost like an identity on low-rank matrices. In this work new estimates for singular values of local minima for such problems are given, which lead to improved bounds on RIP constants to ensure absence of nonoptimal local minima and sufficiently negative curvature at all other critical points. A geometric viewpoint is taken, which is inspired by the fact that the Euclidean distance function to a rank-$k$ matrix possesses no critical points on the corresponding embedded submanifold of rank-$k$ matrices except for the single global minimum.

Using cognition to resolve duplicacy issues in socially connected healthcare for smart cities

Social web has transformed healthcare communication as patients reach out to seek support and advice by connecting with other patients, caregivers and healthcare professionals. The influx of health-related queries and the volume of answers within the medical forums is a testimony to this adaption. The scalability, natural interaction and dynamism of the continuously collected and connected user-generated social big data can support health assessment, intervention and provisioning to produce the best kind of cognitive smart city. On the flip side the use of social media for healthcare communication suffers from data deluge, lack of reliability and quality, confidentiality and privacy (location/personal) issues. Duplicate questions, that is, queries with similar semantics (meaning) corrupt the filtering mechanism, increase the response time and compromise with the quality of the answer too. This research puts forward solutions to resolve the key challenge of duplicacy within the medical community Question-Answering sites (Medical CQAs). We propose to solve the semantic question matching problem for duplicate question pair detection, using a hybrid deep learning model, which combines a Co-attention based Bi-Directional Long Short-Term Memory (Bi-LSTM) Siamese neural network and a Multi-layer perceptron classifier to output the probability of a similarity match between the two questions. Euclidean distance function is then used to compute the similarity between questions. The proposed model is validated on 100 question pairs which are scrapped from three featured groups, namely, ‘Irritable Bowel Syndrome’, ‘Anxiety Disorder’ and ‘Menopause’ of Patient.info community forum and an accuracy of 86.375% is observed. The results obtained are comparable to that of the Quora’s state-of-the-art results for duplicate detection.

Parameter tuning in KNN for software defect prediction: an empirical analysis

Software Defect Prediction (SDP) provides insights that can help software teams to allocate their limited resources in developing software systems. It predicts likely defective modules and helps avoid pitfalls that are associated with such modules. However, these insights may be inaccurate and unreliable if parameters of SDP models are not taken into consideration. In this study, the effect of parameter tuning on the k nearest neighbor (k-NN) in SDP was investigated. More specifically, the impact of varying and selecting optimal k value, the influence of distance weighting and the impact of distance functions on k-NN. An experiment was designed to investigate this problem in SDP over 6 software defect datasets. The experimental results revealed that k value should be greater than 1 (default) as the average RMSE values of k-NN when k>1(0.2727) is less than when k=1(default) (0.3296). In addition, the predictive performance of k-NN with distance weighing improved by 8.82% and 1.7% based on AUC and accuracy respectively. In terms of the distance function, kNN models based on Dilca distance function performed better than the Euclidean distance function (default distance function). Hence, we conclude that parameter tuning has a positive effect on the predictive performance of k-NN in SDP.

Design and Development of Machine Learning Algorithm for Forecasting Crime Rate

Controlling crime is one of the necessary things for a peaceful life. Forecasting the crime helps in planning the strategies in this task. Modern data analysis techniques like classification and prediction may be utilized for this purpose. Classification is a data mining approach that allocates items in a group to target categories or classes. It also may be used to label a target item into any one of the classes identified.Among many available classification techniques, clustering is one of the unsupervised machine learning approaches that could be used for creating clusters as features to enhance classification models. There are various clustering algorithm available like K-mean clustering, Kernel K-mean algorithm etc.PCA algorithm is used to reduce the dimension of the huge amount of data used so that the data can be represented in smaller database with reduced noise in the dataset. In general, mode is a set of values which occurs frequently. Hence, instead of k-mean which is an average value, frequent values may produce better result.K-Mean algorithm creates clusters and groups data properly. But randomly assuming centroid for clusters in the initial stage leads to too much of computational cost. So, in this work, K mode Clustering algorithm was used for clustering asit replaces the Euclidean distance function with the simple matching dissimilarity measure. Once the clusters were formed, a new algorithm was used to forecast the crime rate or future values of the data in the cluster.The proposed approach was tested on crime dataset and found efficient in this domain while comparing with some existing approaches