Graph-based Similarity Measures Research Articles

Evaluating Quantitative Measures for Assessing Functional Similarity in Engineering Design

AbstractThe development of example-based design support tools, such as those used for design-by-analogy, relies heavily on the computation of similarity between designs. Various vector- and graph-based similarity measures operationalize different principles to assess the similarity of designs. Despite the availability of various types of similarity measures and the widespread adoption of some, these measures have not been tested for cross-measure agreement, especially in a design context. In this paper, several vector- and graph-based similarity measures are tested across two datasets of functional models of products to explore the ways in which they find functionally similar designs. The results show that the network-based measures fundamentally operationalize functional similarity in a different way than vector-based measures. Based upon the findings, we recommend a graph-based similarity measure such as NetSimile in the early stages of design when divergence is desirable and a vector-based measure such as cosine similarity in a period of convergence, when the scope of the desired function implementation is clearer.

Multi-View Graph Matching for 3D Model Retrieval

3D model retrieval has been widely utilized in numerous domains, such as computer-aided design, digital entertainment, and virtual reality. Recently, many graph-based methods have been proposed to address this task by using multi-view information of 3D models. However, these methods are always constrained by many-to-many graph matching for the similarity measure between pairwise models. In this article, we propose a multi-view graph matching method (MVGM) for 3D model retrieval. The proposed method can decompose the complicated multi-view graph-based similarity measure into multiple single-view graph-based similarity measures and fusion. First, we present the method for single-view graph generation, and we further propose the novel method for the similarity measure in a single-view graph by leveraging both node-wise context and model-wise context. Then, we propose multi-view fusion with diffusion, which can collaboratively integrate multiple single-view similarities w.r.t. different viewpoints and adaptively learn their weights, to compute the multi-view similarity between pairwise models. In this way, the proposed method can avoid the difficulty in the definition and computation of the traditional high-order graph. Moreover, this method is unsupervised and does not require a large-scale 3D dataset for model learning. We conduct evaluations on four popular and challenging datasets. The extensive experiments demonstrate the superiority and effectiveness of the proposed method compared against the state of the art. In particular, this unsupervised method can achieve competitive performances against the most recent supervised and deep learning method.

An Efficient Content-Based Image Retrieval System for the Diagnosis of Lung Diseases.

The main problem in content-based image retrieval (CBIR) systems is the semantic gap which needs to be reduced for efficient retrieval. The common imaging signs (CISs) which appear in the patient's lung CT scan play a significant role in the identification of cancerous lung nodules and many other lung diseases. In this paper, we propose a new combination of descriptors for the effective retrieval of these imaging signs. First, we construct a feature database by combining local ternary pattern (LTP), local phase quantization (LPQ), and discrete wavelet transform. Next, joint mutual information (JMI)-based feature selection is deployed to reduce the redundancy and to select an optimal feature set for CISs retrieval. To this end, similarity measurement is performed by combining visual and semantic information in equal proportion to construct a balanced graph and the shortest path is computed for learning contextual similarity to obtain final similarity between each query and database image. The proposed system is evaluated on a publicly available database of lung CT imaging signs (LISS), and results are retrieved based on visual feature similarity comparison and graph-based similarity comparison. The proposed system achieves a mean average precision (MAP) of 60% and 0.48 AUC of precision-recall (P-R) graph using only visual features similarity comparison. These results further improve on graph-based similarity measure with a MAP of 70% and 0.58 AUC which shows the superiority of our proposed scheme.

Minimax Bridgeness-Based Clustering for Hyperspectral Data

Hyperspectral (HS) imaging has been used extensively in remote sensing applications like agriculture, forestry, geology and marine science. HS pixel classification is an important task to help identify different classes of materials within a scene, such as different types of crops on a farm. However, this task is significantly hindered by the fact that HS pixels typically form high-dimensional clusters of arbitrary sizes and shapes in the feature space spanned by all spectral channels. This is even more of a challenge when ground truth data is difficult to obtain and when there is no reliable prior information about these clusters (e.g., number, typical shape, intrinsic dimensionality). In this letter, we present a new graph-based clustering approach for hyperspectral data mining that does not require ground truth data nor parameter tuning. It is based on the minimax distance, a measure of similarity between vertices on a graph. Using the silhouette index, we demonstrate that the minimax distance is more suitable to identify clusters in raw hyperspectral data than two other graph-based similarity measures: mutual proximity and shared nearest neighbours. We then introduce the minimax bridgeness-based clustering approach, and we demonstrate that it can discover clusters of interest in hyperspectral data better than comparable approaches.

Efficient Pairwise Penetrating-rank Similarity Retrieval

Many web applications demand a measure of similarity between two entities, such as collaborative filtering, web document ranking, linkage prediction, and anomaly detection. P-Rank (Penetrating-Rank) has been accepted as a promising graph-based similarity measure, as it provides a comprehensive way of encoding both incoming and outgoing links into assessment. However, the existing method to compute P-Rank is iterative in nature and rather cost-inhibitive. Moreover, the accuracy estimate and stability issues for P-Rank computation have not been addressed. In this article, we consider the optimization techniques for P-Rank search that encompasses its accuracy, stability, and computational efficiency. (1) The accuracy estimation is provided for P-Rank iterations, with the aim to find out the number of iterations, k , required to guarantee a desired accuracy. (2) A rigorous bound on the condition number of P-Rank is obtained for stability analysis. Based on this bound, it can be shown that P-Rank is stable and well-conditioned when the damping factors are chosen to be suitably small. (3) Two matrix-based algorithms, applicable to digraphs and undirected graphs, are, respectively, devised for efficient P-Rank computation, which improves the computational time from O ( kn 3 ) to O (υ n 2 +υ 6 ) for digraphs, and to O (υ n 2 ) for undirected graphs, where n is the number of vertices in the graph, and υ (≪ n ) is the target rank of the graph. Moreover, our proposed algorithms can significantly reduce the memory space of P-Rank computations from O ( n 2 ) to O (υ n +υ 4 ) for digraphs, and to O (υ n ) for undirected graphs, respectively. Finally, extensive experiments on real-world and synthetic datasets demonstrate the usefulness and efficiency of the proposed techniques for P-Rank similarity assessment on various networks.

A saliency-weighted orthogonal regression-based similarity measure for entropic graphs

Various measures are used to determine similarity ratios among images before and after image registration. Image registration methods are based on finding the translation, rotation, and scaling parameters that maximize the similarity between two images by taking advantage of the feature points and densities that are found. While the similarity criterion is calculated, it is possible and advantageous to use approximation methods on the graphs based on information theory. The current study proposes a new similarity measure based on saliency-weighted orthogonal regression derived from the weighted sums of the saliency map of the orthogonal regression residuals formed on the entropic graph. It is evaluated in terms of both quantitative and qualitative methods and compared with other graph-based similarity measures.

Graph-based context-aware collaborative filtering

Context-aware recommender systems (CARS) are specially designed to take into account the contextual conditions under which a user experiences an item, with the goal of generating improved recommendations. A known difficulty when constructing recommender systems is data sparseness, which reduces the effectiveness of collaborative filtering algorithms. While using contextual information provides fine-grained signals for the recommendation process, it makes the data even sparser and increases the computational complexity. In this paper, we present a method for making context-aware recommendations, which is less sensitive to data sparseness. The proposed method exploits the transitivity of the interactions between users and items on the user-item graph to augment the direct interactions, thus reducing the negative effect of sparse data. Based on graph transitivity we introduce a new graph-based association measure that we use as a measure of similarity between two users or two items in nearest neighbor recommendation methods. This combination of graph-based similarity measure with nearest neighbor methods allows considering more contextual conditions at a lower risk of being affected by data sparseness caused by additional contextual dimensions. We experimentally evaluated the proposed method on three contextually-tagged data sets. The results show that our method outperforms several baselines and state-of-the-art context-aware recommendation methods.

Heterogeneous Graph Based Similarity Measure for Categorical Data Unsupervised Learning

Different from numerical attributes, measuring the similarity between categorical attributes is more complex due to their non-inherently ordered characteristic, especially in an unsupervised scheme. This work, therefore, presents a new method, Heterogeneous Graph-based Similarity measure (HGS), to measure the similarity between categorical data for unsupervised learning. In order to capture the possible complex relationships hidden among attributes, a heterogeneous weighted graph is creatively constructed by extracting the information from categorical data. Both objects and attribute values are represented as nodes and their occurrence and co-occurrence relationships are shown as edges. Based on a derived node-pair graph, three rules are used to iteratively update the similarity scores between object pairs and attribute-value pairs until the scores converge. We also analyze its complexities and validate the metric properties and convergence. In experiment validation, five state-of-the-art measures are compared with HGS based on 20 UCI datasets and 6 high-dimensional datasets in the medical domain in both k-modes and spectral clustering and similarity search experiments. The results show although no measure can outperform all other measures on all datasets, HGS can perform better in both clustering and similarity search tasks on the whole. Finally, six studies further discuss the convergence, time cost, and parameter sensitivity of the HGS, explore its application to imbalanced class distribution, and compare it with its variants by different initialization and graph construction.

New Graph Based Trust Similarity Measure

Trust network in social networks can be considered as graph which trustors and trustees are graph vertices and edges present trust between them with measured values. To evaluate trust between trustors and trustees there is some similarity measures to measure similarity between trustors together or trustees together and then by using evaluated values predict trust value between them. Similarity measure has important effect on final accuracy. In this paper we propose graph based similarity measure. Similarity between two users is computed by connection between them on graph then this computed similarity used with k- nearest neighbors method to evaluate(predict) trust between users. To the best of our knowledge this is the first work introduces graph based similarity measure, empirical results on two real datasets show accuracy of predicted trust using proposed similarity measure outperforms accuracy of method without it.

Exploration of 3D Activity Cliffs on the Basis of Compound Binding Modes and Comparison of 2D and 3D Cliffs

Activity cliffs are formed by pairs or groups of structurally similar compounds having large differences in potency and are focal points of structure-activity relationship (SAR) analysis. The choice of molecular representations is a critically important aspect of activity cliffs analysis. Thus far, activity cliffs have predominantly been defined on the basis of molecular graph or fingerprint representations. Herein we introduce 3D activity cliffs derived from comparisons of experimentally determined compound binding modes. The analysis of 3D activity cliffs is generally applicable to target proteins for which structures of multiple ligand complexes are available. For two popular targets, β-secretase 1 (BACE1) and factor Xa (FXa), public domain X-ray structures with bound inhibitors were collected. Crystallographic binding modes of inhibitors were systematically compared using a 3D similarity method taking conformational, positional, and atomic property differences into account. In addition, standard 2D similarity relationships were also determined. SAR information associated with individual compounds substantially changed when either bioactive conformations or 2D molecular graphs were used for similarity evaluation. 3D activity cliffs were identified for BACE1 and FXa inhibitor sets and systematically compared to 2D cliffs. It was found that less than 40% of 3D activity cliffs were conserved when 2D similarity was applied. The limited conservation of 3D and 2D cliffs provides further evidence for the strong molecule representation dependence of activity cliffs. Moreover, 3D cliffs represent a new class of activity cliffs that convey SAR information in ways that differ from graph-based similarity measures. In cases where sufficient structural information is available, the comparison of 3D and 2D cliffs is expected to aid in SAR analysis and mapping of critical binding determinants.

Data mining in an engineering design environment: OR applications from graph matching

Abstract Data mining has been making inroads into the engineering design environment—an area that generates large amounts of heterogeneous data for which suitable mining methods are not readily available. For instance, an unsupervised data mining task (clustering) requires an accurate measure of distance or similarity. This paper focuses on the development of an accurate similarity measure for bills of materials (BOM) that can be used to cluster BOMs into product families and subfamilies. The paper presents a new problem called tree bundle matching (TBM) that is identified as a result of the research, gives a non-polynomial formulation, a proof that the problem is NP-hard, and suggests possible heuristic approaches. In a typical life cycle of an engineering project or product, enormous amounts of diverse engineering data are generated. Some of these include BOM, product design models in CAD, engineering drawings, manufacturing process plans, quality and test data, and warranty records. Such data contain information crucial for efficient and timely development of new products and variants; however, this information is often not available to designers. Our research employs data mining methods to extract this design information and improve its accessibility to design engineers. This paper focuses on one aspect of the overall research agenda, clustering BOMs into families and subfamilies. It extends previous work on a graph-based similarity measure for BOMs (a class of unordered trees) by presenting a new TBM problem, and proves the problem to be NP-hard. The overall contribution of this work is to demonstrate the OR applications from graph matching, stochastic methods, optimization, and others to data mining in the engineering design environment.

A novel graph-based similarity measure for 2D chemical structures.

In this paper, we propose a graph-based method to measure the similarity between chemical compounds described by 2D form. Our main idea is to measure the similarity between two compounds based on edges, nodes, and connectivity of their common subgraphs. We applied the proposed similarity measure in combination with a clustering method to more than eleven thousand compounds in the chemical compound database KEGG/LIGAND and discovered that compound clusters with highly similar structure compounds that share common names, take part in the same pathways, and have the same requirement of enzymes in reactions. Furthermore, we discovered the surprising sameness between pathway modules identified by clusters of similar structure compounds and that identified by genomic contexts, namely, operon structures of enzyme genes.

Information

Data mining has been making inroads into the engineering design environment—an area that generates large amounts of heterogeneous data for which suitable mining methods are not readily available. For instance, an unsupervised data mining task (clustering) requires an accurate measure of distance or similarity. This paper focuses on the development of an accurate similarity measure for bills of materials (BOM) that can be used to cluster BOMs into product families and subfamilies. The paper presents a new problem called tree bundle matching (TBM) that is identified as a result of the research, gives a non-polynomial formulation, a proof that the problem is NP-hard, and suggests possible heuristic approaches.In a typical life cycle of an engineering project or product, enormous amounts of diverse engineering data are generated. Some of these include BOM, product design models in CAD, engineering drawings, manufacturing process plans, quality and test data, and warranty records. Such data contain information crucial for efficient and timely development of new products and variants; however, this information is often not available to designers. Our research employs data mining methods to extract this design information and improve its accessibility to design engineers. This paper focuses on one aspect of the overall research agenda, clustering BOMs into families and subfamilies. It extends previous work on a graph-based similarity measure for BOMs (a class of unordered trees) by presenting a new TBM problem, and proves the problem to be NP-hard. The overall contribution of this work is to demonstrate the OR applications from graph matching, stochastic methods, optimization, and others to data mining in the engineering design environment.