Proposed Distance Function Research Articles

Two Medoid-Based Algorithms for Clustering Sets

This paper proposes two algorithms for clustering data, which are variable-sized sets of elementary items. An example of such data occurs in the analysis of a medical diagnosis, where the goal is to detect human subjects who share common diseases to possibly predict future illnesses from previous medical history. The first proposed algorithm is based on K-medoids and the second algorithm extends the random swap algorithm, which has proven to be capable of efficient and careful clustering; both algorithms depend on a distance function among data objects (sets), which can use application-sensitive weights or priorities. The proposed distance function makes it possible to exploit several seeding methods that can improve clustering accuracy. A key factor in the two algorithms is their parallel implementation in Java, based on functional programming using streams and lambda expressions. The use of parallelism smooths out the O(N2) computational cost behind K-medoids and clustering indexes such as the Silhouette index and allows for the handling of non-trivial datasets. This paper applies the algorithms to several benchmark case studies of sets and demonstrates how accurate and time-efficient clustering solutions can be achieved.

Neural Joint Space Implicit Signed Distance Functions for Reactive Robot Manipulator Control

In this letter, we present an approach for learning a neural implicit signed distance function expressed in joint space coordinates, that efficiently computes distance-to-collisions for arbitrary robotic manipulator configurations. Computing such distances is a long standing problem in robotics as approximate representations of the robot and environment geometry can lead to overly conservative constraints, numerical instabilities and expensive computations – limiting real-time reactive control and task success. Leveraging GPU parallelization and the differentiable nature of the proposed distance function allows for fast calculation of gradients with respect to the neural network inputs, providing a continuous repulsive vector field directly in joint space. We show that the learned high-resolution collision representation can be used to achieve real-time reactive control by i) formulating it as a collision-avoidance constraint for a quadratic programming (QP) inverse kinematics (IK), and ii) introducing it as a collision cost in a sampling-based joint space model predictive controller (MPC). For a reaching benchmark task with a 7DoF robot and dynamic obstacles intentionally obstructing the robot's path we achieve average 250 Hz control frequency with QP-IK and 92 Hz with MPC, showing an accelerated performance of 15% for QP-IK and 40% for MPC over baseline distance computation techniques.

Comparative analysis of modified semi-supervised learning algorithms on a small amount of labeled data

The paper is devoted to improving semi-supervised clustering methods and comparing their accuracy and robustness. The proposed approach is based on expanding a clustering algorithm for using an available set of labels by replacing the distance function. Using the distance function considers not only spatial data but also available labels. Moreover, the proposed distance function could be adopted for working with ordinal variables as labels. An extended approach is also considered, based on a combination of unsupervised k-medoids methods, modified for using only labeled data during the medoids calculation step, supervised method of k nearest neighbor, and unsupervised k-means. The learning algorithm uses information about the nearest points and classes’ centers of mass. The results demonstrate that even a small amount of labeled data allows us to use semi-supervised learning, and proposed modifications improve accuracy and algorithm performance, which was found during experiments.

Reachable Distance Function for KNN Classification

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the affinity between data points. This paper proposes a reachable distance function for KNN classification. The reachable distance function is not a geometric direct-line distance between two data points. It gives a consideration to the class attribute of a training dataset when measuring the affinity between data points. Concretely speaking, the reachable distance between data points includes their class center distance and real distance. Its shape looks like “Z,” and we also call it a Z distance function. In this way, the affinity between data points in the same class is always stronger than that in different classes. Or, the intraclass data points are always closer than those interclass data points. We evaluated the reachable distance with experiments, and demonstrated that the proposed distance function achieved better performance in KNN classification.

Phylogenicity of B.1.1.7 surface glycoprotein, novel distance function and first report of V90T missense mutation in SARS-CoV-2 surface glycoprotein

Phylogenicity of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) B.1.1.7 surface glycoproteins reported from Europe to the National Center for Biotechnology Information (NCBI) virus database by the mid of April 2021 is analyzed. Novel function for computing phylogenetic distance is proposed for that purpose. Proposed distance function resulted in better-fitted clusters than Jaccard and Sorensen-Dice and accurate evolutionary links were predicted for B.1.1.7 spike variants. Most B.1.1.7 spike variants were linked to their likely direct predecessors at single amino acid change, that in many cases resulted in loss of the key mutations that are associated to the higher B.1.1.7 SARS-CoV-2 infectivity. There were also cases where second mutation was introduced to compensate for the missing mutation. Unreported V90T SARS-CoV-2 surface glycoprotein mutation was also identified, that contributes towards escaping 2–51 neutralizing antibody.

Mining Shift Work Operation from Event Logs

Event logs are records of events that are generally used in process mining to determine the manner in which various processes are practically implemented. Previous studies on process mining attempted to combine the results based on different perspectives such as control flow, data, performance, and resources (organizational) to create a simulation model. This study focuses on the resource perspective. A prior study from the resource perspective focused on clustering the resources into organizational units. Implementing the results of the above study in a simulation model will yield inaccurate results because the resources are assumed to always be available if no task is performed. In a practical scenario, resources (particularly humans) tend to work based on shifts. Thus, we propose mining the shift work operation of resources from event logs to tackle this issue. We utilized a self-organizing map and k-means clustering to incorporate the shift work information from the event logs into the simulation model. Moreover, we introduce a distance function and weight-centroid updating rule in the clustering technique to realize our objective. We conducted extensive experiments with artificial data sets to assess the effectiveness of the proposed method. The simulation shows that introducing the shift work operation time of resources can yield more accurate results. Furthermore, the proposed distance function can capture the shift work operation of the resources more precisely compared with the general distance function.

Multiple Photon Sampling Technique Based on Stochastic Progressive Photon Mapping

This paper introduces a multiple photon sampling technique based on stochastic progressive photon mapping. We use the image space concept to divide the scene into continuous sub-blocks and then we calculate our proposed distance function and photon number function in each of the sub-blocks. The distance function is used to calculate the distance error of the hit point and to determine whether each sub-block is located at a boundary between different objects. The photon number function is used to calculate the photon number error and to determine whether the photon distribution in each sub-block is uniform. Based on the values of the distance error and the photon number error, the multiple photon sampling technique is used to acquire multiple samples of the hit point in each sub-block. Instead of using a single radius for the radiance estimate, we use three different radii and compute the final radiance estimate as a weighted average of the three values. When compared with the existing stochastic progressive photon mapping method, our method provides a better solution to the photon distribution problem and can also reduce bias and noise, especially in the scene with drastic changes in light and dark.

On Variational and PDE-Based Methods for Accurate Distance Function Estimation

A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and $$p$$-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

An ADMM-based scheme for distance function approximation

A novel variational problem for approximating the distance function (to a domain boundary) is proposed. It is shown that this problem can be efficiently solved by ADMM. A review of several other variational and PDE-based methods for distance function estimation is presented. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments. Applications of the method to the problems of surface curvature estimation and computing the skeleton of a binary image are shown.

Optimal Distance Function for Locally Weighted Average Prediction of Just‐in‐Time Methods

AbstractThis paper discusses the optimal distance function for Just‐in‐Time prediction. We focus on the standard Locally Weighted Average (LWA) prediction with Mahalanobis distance, and find the optimal distance which minimizes the prediction error. The key idea of this work is to introduce an integral which works as a model of the LWA prediction. This integral approximates the LWA prediction, and it becomes easier to discuss analytically. The main result of this paper is to show that the optimal distance function for such integral is constructed through a convex optimization. A numerical example and an experiment with a motor are shown to demonstrate the validity of the proposed distance function.

Distance function design and Lyapunov techniques for the stability of hybrid trajectories

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.

Multiple Attribute Group Decision Analysis for Intuitionistic Triangular and Trapezoidal Fuzzy Numbers

Solving Multiple Attribute Group Decision Making (MAGDM) problems has become one of the most important researches in recent days. In situations where the information or the data is of the form of an Intuitionistic Triangular Fuzzy Number (ITrFN) or Intuitionistic Trapezoidal Fuzzy Number (ITzFN), a new distance function is defined for ranking the alternatives in the decision making process. After processing the decision information through a sequence of arithmetic aggregation operators, namely, the Intuitionistic Triangular Fuzzy Weighted Arithmetic Averaging (ITrFWAA), Intuitionistic Triangular Fuzzy Ordered Weighted Averaging (ITrFOWA) operator and the Intuitionistic Triangular Fuzzy Hybrid Aggregation (ITrFHA) operator, the proposed distance function is utilized to rank the best alternative. A model is proposed to solve MAGDM problems using the developed distance formula defined for ITrFNs. Numerical illustration is provided and comparisons are made with some of the existing MAGDM models and ranking procedures.

A tree-matching algorithm: Application to airways in CT images of subjects with the acute respiratory distress syndrome.

To match anatomical trees such as airways, we propose a graph-based strategy combined with an appropriate distance function. The strategy was devised to cope with topological and geometrical differences that may arise between trees corresponding to the same subject, but extracted from images acquired in different conditions. The proposed distance function, called father/family distance, combines topological and geometrical information in a single measure, by calculating a sum of path-to-path distances between sub-trees of limited extent. To use it successfully, the branches of these sub-trees need to be brought closer, which is obtained by successively translating the roots of these sub-trees prior to their actual matching. The work herein presented contributes to a study of the acute respiratory distress syndrome, where a series of pulmonary CT images from the same subject is acquired at varying settings (pressure and volume) of the mechanical ventilation. The method was evaluated on 45 combinations of synthetic trees, as well as on 15 pairs of real airway trees: nine corresponding to end-expiration and end-inspiration with the same pressure, and six corresponding to end-inspiration with significantly different pressures. It achieved a high rate of successful matches with respect to a hand-made reference containing a total of 2391 matches in real data: sensitivity of 94.3% and precision of 92.8%, when using the basic parameter settings of the algorithm.

Evaluation of Distance Functions for the Comparison of Gradient Orientation Histograms

Local features of an image are used in many computer vision applications such as object detection and scene matching. The gradient orientation histogram is used by many local features such as Scale Invariant Feature Transform (SIFT), a widely used image local feature. This paper discusses various distance functions that can be used to measure the similarity between the local features described by the gradient orientation histogram. A distance function, based on the quadratic form is proposed for the SIFT descriptor. The state of the art distance functions - Euclidean, Chi-square, Manhattan and the proposed quadratic form based distance function are calculated between the features extracted from the images. Nearest neighborhood ratio strategy is used to find the corresponding features based on the distance measure. Correct matches are estimated using the ground truth transformation function between the images, present in the form of homograph matrix. It is experimentally found that the proposed distance function has an execution time reduced by 21% compared to the Euclidean distance for a similar accuracy performance. The proposed distance retrieves more number of correct matches compared to the modified Earth Mover distance which is fastest among the evaluated distance functions. The future work will be aimed at improving the time taken for computing the distance matrix between the feature sets and a better strategy for computing the matches.

A similarity assessment technique for effective grouping of documents

Document clustering refers to the task of grouping similar documents and segregating dissimilar documents. It is very useful to find meaningful categories from a large corpus. In practice, the task to categorize a corpus is not so easy, since it generally contains huge documents and the document vectors are high dimensional. This paper introduces a hybrid document clustering technique by combining a new hierarchical and the traditional k-means clustering techniques. A distance function is proposed to find the distance between the hierarchical clusters. Initially the algorithm constructs some clusters by the hierarchical clustering technique using the new distance function. Then k-means algorithm is performed by using the centroids of the hierarchical clusters to group the documents that are not included in the hierarchical clusters. The major advantage of the proposed distance function is that it is able to find the nature of the corpora by varying a similarity threshold. Thus the proposed clustering technique does not require the number of clusters prior to executing the algorithm. In this way the initial random selection of k centroids for k-means algorithm is not needed for the proposed method. The experimental evaluation using Reuter, Ohsumed and various TREC data sets shows that the proposed method performs significantly better than several other document clustering techniques. F-measure and normalized mutual information are used to show that the proposed method is effectively grouping the text data sets.

A generalized distance function for preferential choices

Many cognitive theories of judgement and decision making assume that choice options are evaluated relative to other available options. The extent to which the preference for one option is influenced by other available options will often depend on how similar the options are to each other, where similarity is assumed to be a decreasing function of the distance between options. We examine how the distance between preferential options that are described on multiple attributes can be determined. Previous distance functions do not take into account that attributes differ in their subjective importance, are limited to two attributes, or neglect the preferential relationship between the options. To measure the distance between preferential options it is necessary to take the subjective preferences of the decision maker into account. Accordingly, the multi-attribute space that defines the relationship between options can be stretched or shrunk relative to the attention or importance that a person gives to different attributes describing the options. Here, we propose a generalized distance function for preferential choices that takes subjective attribute importance into account and allows for individual differences according to such subjective preferences. Using a hands-on example, we illustrate the application of the function and compare it to previous distance measures. We conclude with a discussion of the suitability and limitations of the proposed distance function.

Extended Subtree: A New Similarity Function for Tree Structured Data

Although several distance or similarity functions for trees have been introduced, their performance is not always satisfactory in many applications, ranging from document clustering to natural language processing. This research proposes a new similarity function for trees, namely Extended Subtree (EST), where a new subtree mapping is proposed. EST generalizes the edit base distances by providing new rules for subtree mapping. Further, the new approach seeks to resolve the problems and limitations of previous approaches. Extensive evaluation frameworks are developed to evaluate the performance of the new approach against previous proposals. Clustering and classification case studies utilizing three real-world and one synthetic labeled data sets are performed to provide an unbiased evaluation where different distance functions are investigated. The experimental results demonstrate the superior performance of the proposed distance function. In addition, an empirical runtime analysis demonstrates that the new approach is one of the best tree distance functions in terms of runtime efficiency.

A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

We are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using α-cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach.

A composite kernel for named entity recognition

In this paper, we propose a novel kernel function for support vector machines (SVM) that can be used for sequential labeling tasks like named entity recognition (NER). Machine learning methods like support vector machines, maximum entropy, hidden Markov model and conditional random fields are the most widely used methods for implementing NER systems. The features used in machine learning algorithms for NER are mostly string based features. The proposed kernel is based on calculating a novel distance function between the string based features. In tasks like NER, the similarity between the contexts as well as the semantic similarity between the words play an important role. The goal is to capture the context and semantic information in NER like tasks. The proposed distance function makes use of certain statistics primarily derived from the training data and hierarchical clustering information. The kernel function is applied to the Hindi and biomedical NER tasks and the results are quite promising.

Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using α-cuts

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using α -cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers, we present a dynamic programming method for finding a shortest path in the network. Examples are worked out to illustrate the applicability of the proposed model.