Essential Theory, Algorithms and Applications
نویسندگان
چکیده
Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.
منابع مشابه
Near Pole Polar Diagram of Points and its Duality with Applications
In this paper we propose a new approach to plane partitioning with similar features to those of Polar Diagram, but we assume that the pole is close to the sites. The result is a new tessellation of the plane in regions called Near Pole Polar Diagram NPPD. Here we define the (NPPD) of points, the dual and the Contracted dual of it, present an optimal algorithms to draw them and discuss the appli...
متن کاملfinding influential individual in Social Network graphs using CSCS algorithm and shapley value in game theory
In recent years, the social networks analysis gains great deal of attention. Social networks have various applications in different areas namely predicting disease epidemic, search engines and viral advertisements. A key property of social networks is that interpersonal relationships can influence the decisions that they make. Finding the most influential nodes is important in social networks b...
متن کاملImproving LNMF Performance of Facial Expression Recognition via Significant Parts Extraction using Shapley Value
Nonnegative Matrix Factorization (NMF) algorithms have been utilized in a wide range of real applications. NMF is done by several researchers to its part based representation property especially in the facial expression recognition problem. It decomposes a face image into its essential parts (e.g. nose, lips, etc.) but in all previous attempts, it is neglected that all features achieved by NMF ...
متن کاملClassification of encrypted traffic for applications based on statistical features
Traffic classification plays an important role in many aspects of network management such as identifying type of the transferred data, detection of malware applications, applying policies to restrict network accesses and so on. Basic methods in this field were using some obvious traffic features like port number and protocol type to classify the traffic type. However, recent changes in applicat...
متن کاملSolving Data Clustering Problems using Chaos Embedded Cat Swarm Optimization
In this paper, a new method is proposed for solving the data clustering problem using Cat Swarm Optimization (CSO) algorithm based on chaotic behavior. The problem of data clustering is an important section in the field of the data mining, which has always been noted by researchers and experts in data mining for its numerous applications in solving real-world problems. The CSO algorithm is one ...
متن کاملSolving Data Clustering Problems using Chaos Embedded Cat Swarm Optimization
In this paper, a new method is proposed for solving the data clustering problem using Cat Swarm Optimization (CSO) algorithm based on chaotic behavior. The problem of data clustering is an important section in the field of the data mining, which has always been noted by researchers and experts in data mining for its numerous applications in solving real-world problems. The CSO algorithm is one ...
متن کامل