Grouping interdependent tasks: Using spectral graph partitioning to study complex systems

Lee, Chi Hyon; Hoehn‐Weiss, Manuela N.; Karim, Samina

doi:10.1002/smj.2455

“…Spectral clustering algorithms based on similarity provide a stronger and more stable approach for finding the global optimum [18], [25], especially for nonconvex datasets [9], and are well suited for application to real problems [7]. The spectral clustering algorithm maximizes intercluster similarity and minimizes intercluster similarity [18].…”

Section: B Sna and Spectral Clusteringmentioning

confidence: 99%

“…A challenge in developing an organizational architecture concerns modularization-parsing the set of organizational elements (e.g., teams) into subsets, groups, or modules, such that the elements' intragroup relationships outweigh those across groups [5], [7]. Assigning elements to groups is also known as finding communities [8], partitioning [9], and clustering [10], [11], [40], [44].…”

mentioning

confidence: 99%

“…Next, we incorporate teams' attributes and relationships (structural similarity) to develop an integrated similarity matrix, more comprehensively and accurately than other similarity measurement methods. This article also presents an approach integrating the modularity index Q and an improved Silhouette index S using node attribute differences (ADs) (intacluster and interclister) to determine the optimal number of clusters, which is a particular challenge for spectral clustering algorithms [7]. Finally, we use centrality indices of intracluster and intercluster, with Q and S indices, to evaluate the clustering results.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Clustering Product Development Project Organization From the Perspective of Social Network Analysis

Yang

¹

,

Yang

²

,

Browning

³

et al. 2022

IEEE Trans. Eng. Manage.

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In product development (PD) organizations, coordinating technical dependencies among teams with different expertise in overlapping processes is a fundamental challenge. This article takes a more sophisticated approach than prior methodologies to improve coordination via organizational clustering, by accounting for both team structural and attribute similarity from the perspective of social network analysis. We built models to quantify the impact of the overlapping processes on the interaction strength among PD teams, which we then used to construct structural similarity by combining tie strength and social cohesion among teams via the design structure matrix. To evaluate the organization network, we propose social embeddedness-related centrality indices within (intracluster) and across (intercluster) team groupings. To facilitate knowledge sharing, we base team attribute similarity on product-and process-related expertise among teams. We integrate the modularity index and an improved silhouette index to find an optimal number of clusters, which we then incorporate with team similarity measures as inputs to a spectral clustering algorithm. An industrial example illustrates the proposed model. The clustering results reinforce several managerial practices but also yield new insights, such as how to measure similarity among teams based on organizational network characteristics and how structural and attribute similarities impact the optimal organizational structure.

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“…Clustering over graphs is a classical problem with applications in systems biology, social sciences, and other fields (Girvan and Newman 2002;Art, Sergiy, and others 2009;Mishra et al 2007;Lee, Hoehn-Weiss, and Karim 2016). Although most formulations of the clustering problem are NP-hard (Šíma and Schaeffer 2006), several approaches have yielded useful approximate algorithms.…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Embedding of Logistic Random Dot Product Graphs

O’Connor

¹

,

Médard

²

,

Feizi³

2020

AAAI

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A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.

show abstract

“…C LUSTERING over graphs is a classical problem with applications in systems biology, social sciences, and other fields [1], [2], [3], [4]. Although most formulations of the clustering problem are NP-hard [5], several approaches have yielded useful approximate algorithms.…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Latent Space Embedding of Logistic Random Dot Product Graphs

O'Connor,

Médard,

Feizi

2015

Preprint

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A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.

show abstract

Grouping interdependent tasks: Using spectral graph partitioning to study complex systems

Cited by 8 publications

References 89 publications

Clustering Product Development Project Organization From the Perspective of Social Network Analysis

Clustering Product Development Project Organization From the Perspective of Social Network Analysis

Maximum Likelihood Embedding of Logistic Random Dot Product Graphs

Maximum Likelihood Latent Space Embedding of Logistic Random Dot Product Graphs

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