Graph Embedding Using Dissimilarities with Applications in Classification

2013 ◽  
pp. 363-380
Author(s):  
Horst Bunke ◽  
Kaspar Riesen
Keyword(s):  
Pattern Recognition ◽  
Nearest Neighbor ◽  
Graph Matching ◽  
Graph Embedding ◽  
Mathematical Structure ◽  
Object Representations ◽  
Mathematical Concepts ◽  
Novel Approach ◽  
Representational Power ◽  
Mathematical Operations

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, commonly referred to as graph matching. Yet, distance-based pattern recognition is basically limited to nearest-neighbor classification. The present chapter reviews a novel approach for graph embedding in vector spaces built upon the concept of graph matching. The key-idea of the proposed embedding method is to use the distances of an input graph to a number of training graphs, termed prototypes, as vectorial description of the graph. That is, all graph matching procedures proposed in the literature during the last decades can be employed in this embedding framework. The rationale for such a graph embedding is to bridge the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. Hence, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.

Graph Embedding Using Dissimilarities with Applications in Classification

2012 ◽  
pp. 156-173
Author(s):  
Horst Bunke ◽  
Kaspar Riesen
Keyword(s):  
Pattern Recognition ◽  
Nearest Neighbor ◽  
Graph Matching ◽  
Graph Embedding ◽  
Mathematical Structure ◽  
Object Representations ◽  
Mathematical Concepts ◽  
Novel Approach ◽  
Representational Power ◽  
Mathematical Operations

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, commonly referred to as graph matching. Yet, distance-based pattern recognition is basically limited to nearest-neighbor classification. The present chapter reviews a novel approach for graph embedding in vector spaces built upon the concept of graph matching. The key-idea of the proposed embedding method is to use the distances of an input graph to a number of training graphs, termed prototypes, as vectorial description of the graph. That is, all graph matching procedures proposed in the literature during the last decades can be employed in this embedding framework. The rationale for such a graph embedding is to bridge the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. Hence, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.

scholarly journals A new variational approach for the thermodynamic topology optimization of hyperelastic structures

2020 ◽  
Author(s):  
Philipp Junker ◽  
Daniel Balzani
Keyword(s):  
Topology Optimization ◽  
Variational Approach ◽  
Large Deformations ◽  
Mathematical Structure ◽  
Detailed Model ◽  
Novel Approach ◽  
Extremal Principles ◽  
Model Derivation ◽  
Numerical Discretization ◽  
Total Structure

AbstractWe present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.

scholarly journals Novel metric for hyperbolic phylogenetic tree embeddings

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Hirotaka Matsumoto ◽  
Takahiro Mimori ◽  
Tsukasa Fukunaga
Keyword(s):  
Phylogenetic Tree ◽  
Hyperbolic Space ◽  
Nearest Neighbor ◽  
Cancer Genomics ◽  
Geometric Approach ◽  
Artificial Intelligence Research ◽  
Phylogenetic Methods ◽  
Novel Approach ◽  
Multiple Trees ◽  
Euclidean Embeddings

Abstract Advances in experimental technologies, such as DNA sequencing, have opened up new avenues for the applications of phylogenetic methods to various fields beyond their traditional application in evolutionary investigations, extending to the fields of development, differentiation, cancer genomics, and immunogenomics. Thus, the importance of phylogenetic methods is increasingly being recognized, and the development of a novel phylogenetic approach can contribute to several areas of research. Recently, the use of hyperbolic geometry has attracted attention in artificial intelligence research. Hyperbolic space can better represent a hierarchical structure compared to Euclidean space, and can therefore be useful for describing and analyzing a phylogenetic tree. In this study, we developed a novel metric that considers the characteristics of a phylogenetic tree for representation in hyperbolic space. We compared the performance of the proposed hyperbolic embeddings, general hyperbolic embeddings, and Euclidean embeddings, and confirmed that our method could be used to more precisely reconstruct evolutionary distance. We also demonstrate that our approach is useful for predicting the nearest-neighbor node in a partial phylogenetic tree with missing nodes. Furthermore, we proposed a novel approach based on our metric to integrate multiple trees for analyzing tree nodes or imputing missing distances. This study highlights the utility of adopting a geometric approach for further advancing the applications of phylogenetic methods.

scholarly journals Two Stepped Majority Voting for Efficient EEG based Emotion Classification

2020 ◽  
Author(s):  
aras Masood Ismael ◽  
Ömer F Alçin ◽  
Karmand H Abdalla ◽  
Abdulkadir k sengur
Keyword(s):  
Emotion Recognition ◽  
Nearest Neighbor ◽  
Noise Removal ◽  
Majority Voting ◽  
Emotion Classification ◽  
K Nearest Neighbor ◽  
Discrimination Accuracy ◽  
Novel Approach ◽  
Knn Classifier ◽  
Low Pass

Abstract In this paper, a novel approach that is based on two-stepped majority voting is proposed for efficient EEG based emotion classification. Emotion recognition is important for human-machine interactions. Facial-features and body-gestures based approaches have been generally proposed for emotion recognition. Recently, EEG based approaches become more popular in emotion recognition. In the proposed approach, the raw EEG signals are initially low-pass filtered for noise removal and band-pass filters are used for rhythms extraction. For each rhythm, the best performed EEG channels are determined based on wavelet-based entropy features and fractal dimension based features. The k-nearest neighbor (KNN) classifier is used in classification. The best five EEG channels are used in majority voting for getting the final predictions for each EEG rhythm. In the second majority voting step, the predictions from all rhythms are used to get a final prediction. The DEAP dataset is used in experiments and classification accuracy, sensitivity and specificity are used for performance evaluation metrics. The experiments are carried out to classify the emotions into two binary classes such as high valence (HV) vs low valence (LV) and high arousal (HA) vs low arousal (LA). The experiments show that 86.3% HV vs LV discrimination accuracy and 85.0% HA vs LA discrimination accuracy is obtained. The obtained results are also compared with some of the existing methods. The comparisons show that the proposed method has potential in the use of EEG based emotion classification.

The Novel Approach

2017 ◽  
pp. 1-12
Keyword(s):  
Risk Management ◽  
Project Management ◽  
Quality Management ◽  
Portfolio Management ◽  
Six Sigma ◽  
The Novel ◽  
Mathematical Concepts ◽  
Process Flow ◽  
Novel Approach ◽  
Generic Algorithms

This chapter presents the novel Six Sigma DMAIC generic approach to Risk Management. The method is introduced first. In The Generic Approach and Algorithms section, generic mathematical concepts are elaborated. Also, four generic classes of applications of the proposed method are identified including: 1) Portfolio Management; 2) Quality Management; 3) Project Management; and 4) Income Management. Furthermore, four generic algorithms are elaborated for the respective four classes of application of the method. The generic algorithms include description and process flow of the applications. Finally, the modelling tools used in the book's elaborations are detailed, as well as references for how to use these tools and run Simulation and Stochastic Optimisation step-by-step.

A Novel Algorithm for Sentiment Analysis of Online Movie Reviews

2018 ◽  
pp. 106-140
Author(s):  
Bisma Shah ◽  
Farheen Siddiqui
Keyword(s):  
Sentiment Analysis ◽  
Nearest Neighbor ◽  
Supervised Machine Learning ◽  
Learning Approaches ◽  
World Knowledge ◽  
K Nearest Neighbor ◽  
Customer Feedback ◽  
Novel Approach ◽  
The One ◽  
Novel Algorithm

Others' opinions can be decisive while choosing among various options, especially when those choices involve worthy resources like spending time and money buying products or services. Customers relying on their peers' past reviews on e-commerce websites or social media have drawn a considerable interest to sentiment analysis due to realization of its commercial and business benefits. Sentiment analysis can be exercised on movie reviews, blogs, customer feedback, etc. This chapter presents a novel approach to perform sentiment analysis of movie reviews given by users on different websites. Also, challenges like presence of thwarted words, world knowledge, and subjectivity detection in sentiments are addressed in this chapter. The results are validated by using two supervised machine learning approaches, k-nearest neighbor and naive Bayes, both on method of sentiment analysis without addressing aforementioned challenges and on proposed method of sentiment analysis with all challenges addressed. Empirical results show that proposed method outperformed the one that left challenges unaddressed.

Pattern Synthesis for Nonparametric Pattern Recognition

2011 ◽  
pp. 1511-1516
Author(s):  
P. Viswanath ◽  
Narasimha M. Murty ◽  
Bhatnagar Shalabh
Keyword(s):  
Pattern Recognition ◽  
Density Estimation ◽  
Nearest Neighbor ◽  
Curse Of Dimensionality ◽  
Parametric Methods ◽  
Pattern Synthesis ◽  
Parzen Window ◽  
Pattern Recognition Methods ◽  
The Given ◽  
Non Parametric

Parametric methods first choose the form of the model or hypotheses and estimates the necessary parameters from the given dataset. The form, which is chosen, based on experience or domain knowledge, often, need not be the same thing as that which actually exists (Duda, Hart & Stork, 2000). Further, apart from being highly error-prone, this type of methods shows very poor adaptability for dynamically changing datasets. On the other hand, non-parametric pattern recognition methods are attractive because they do not derive any model, but works with the given dataset directly. These methods are highly adaptive for dynamically changing datasets. Two widely used non-parametric pattern recognition methods are (a) the nearest neighbor based classification and (b) the Parzen-Window based density estimation (Duda, Hart & Stork, 2000). Two major problems in applying the non-parametric methods, especially, with large and high dimensional datasets are (a) the high computational requirements and (b) the curse of dimensionality (Duda, Hart & Stork, 2000). Algorithmic improvements, approximate methods can solve the first problem whereas feature selection (Isabelle Guyon & André Elisseeff, 2003), feature extraction (Terabe, Washio, Motoda, Katai & Sawaragi, 2002) and bootstrapping techniques (Efron, 1979; Hamamoto, Uchimura & Tomita, 1997) can tackle the second problem. We propose a novel and unified solution for these problems by deriving a compact and generalized abstraction of the data. By this term, we mean a compact representation of the given patterns from which one can retrieve not only the original patterns but also some artificial patterns. The compactness of the abstraction reduces the computational requirements, and its generalization reduces the curse of dimensionality effect. Pattern synthesis techniques accompanied with compact representations attempt to derive compact and generalized abstractions of the data. These techniques are applied with (a) the nearest neighbor classifier (NNC) which is a popular non-parametric classifier used in many fields including data mining since its conception in the early fifties (Dasarathy, 2002) and (b) the Parzen-Window based density estimation which is a well known non-parametric density estimation method (Duda, Hart & Stork, 2000).

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