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Tatsuro Kawamoto

Publications and source records attributed to Tatsuro Kawamoto.

At least 19 recordsLinked to original sources
arXiv2023

Entropy of microcanonical finite-graph ensembles

The entropy of random graph ensembles has gained widespread attention in the field of graph theory and network science. We consider microcanonical ensembles of simple graphs with prescribed degree sequences. We demonstrate that the mean-field approximations of the generating function using the Chebyshev-Hermite polynomials provide estimates for the entropy of finite-graph ensembles. Our estimate reproduces the Bender-Canfield formula in the limit of large graphs.

cond-mat.stat-mech↗
arXiv2023

Finding community structure using the ordered random graph model

Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a particularly important feature, and the structure can be identified through the adjacency matrix when it is close to a block-diagonal form. However, classical ordering algorithms for matrices fail to align matrix elements such that the community structure is visible. In this study, we propose an ordering algorithm based on the maximum-likelihood estimate of the ordered random graph model. We show that the proposed method allows us to more clearly identify community structures than the existing ordering algorithms.

physics.soc-ph↗
arXiv2023

Single-trajectory map equation

Community detection, the process of identifying module structures in complex systems represented on networks, is an effective tool in various fields of science. The map equation, which is an information-theoretic framework based on the random walk on a network, is a particularly popular community detection method. Despite its outstanding performance in many applications, the inner workings of the map equation have not been thoroughly studied. Herein, we revisit the original formulation of the map equation and address the existence of its ``raw form,'' which we refer to as the single-trajectory map equation. This raw form sheds light on many details behind the principle of the map equation that are hidden in the steady-state limit of the random walk. Most importantly, the single-trajectory map equation provides a more balanced community structure, naturally reducing the tendency of the overfitting phenomenon in the map equation.

physics.soc-ph↗
arXiv2023

Consistency between ordering and clustering methods for graphs

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has been studied much more actively than the latter, particularly for the data represented as graphs. This study fills this gap by investigating methodological relationships between several clustering and ordering methods, focusing on spectral techniques. Furthermore, we evaluate the resulting performance of the clustering and ordering methods. To this end, we propose a measure called the label continuity error, which generically quantifies the degree of consistency between a sequence and partition for a set of elements. Based on synthetic and real-world datasets, we evaluate the extents to which an ordering method identifies a module structure and a clustering method identifies a banded structure.

cs.LG↗
arXiv2023

Sequential locality of graphs and its hypothesis testing

The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically affected by the ordering of rows and columns, or vertex ordering, statistical assessment of graphs together with their vertex sequences is important in identifying the characteristic structures of graphs. In this paper, we propose a hypothesis testing framework that assesses how locally vertices are connected to each other along a specified vertex sequence, which provides a statistical foundation for an optimization problem called envelope reduction or minimum linear arrangement. The proposed tests are particularly suitable for moderately small data and formulated based on a combinatorial approach and a block model with intrinsic vertex ordering.

cs.SI↗
arXiv2022

Contribution of directedness in graph spectra

In graph analyses, directed edges are often approximated to undirected ones so that the adjacency matrices may be symmetric. However, such simplification has not been thoroughly verified. In this study, we investigate how directedness affects the graph spectra by introducing random directization, which is an opposite operation of neglecting edge directions. We analytically reveal that uniformly random directization typically conserves the relative spectral structure of the adjacency matrix in the perturbative regime. The result of random directization implies that the spectrum of the adjacency matrix can be conserved after the directedness is ignored.

physics.soc-ph↗
arXiv2021

Graph-based open-ended survey on concerns related to COVID-19

The COVID-19 pandemic is an unprecedented public health crisis with broad social and economic consequences. We conducted four surveys between April and August 2020 using the graph-based open-ended survey (GOS) framework, and investigated the most pressing concerns and issues for the general public in Japan. The GOS framework is a hybrid of the two traditional survey frameworks that allows respondents to post their opinions in a free-format style, which can subsequently serve as one of the choice items for other respondents, just as in a multiple-choice survey. As a result, this framework generates an opinion graph that relates opinions and respondents. We can also construct annotated opinion graphs to achieve a higher resolution. By clustering the annotated opinion graphs, we revealed the characteristic evolution of the response patterns as well as the interconnectedness and multi-faceted nature of opinions. Substantively, our notable finding is that "social pressure," not "infection risk," was one of the major concerns of our respondents. Social pressure refers to criticism and discrimination that they anticipate receiving from others should they contract COVID-19. It is possible that the collectivist nature of Japanese culture coupled with the government's policy of relying on personal responsibility to combat COVID-19 explains some of the above findings, as the latter has led to the emergence of vigilantes. The presence of mutual surveillance can contribute to growing skepticism toward others as well as fear of ostracism, which may have negative consequences at both the societal and individual levels.

cs.SI↗
arXiv2020

Identifying macroscopic features in foreign visitor travel pathways

Human travel patterns are commonly studied as networks in which the points of departure and destination are encoded as nodes and the travel frequency between two points is recorded as a weighted edge. However, because travelers often visit multiple destinations, which constitute pathways, an analysis incorporating pathway statistics is expected to be more informative over an approach based solely on pairwise frequencies. Hence, in this study, we apply a higher-order network representation framework to identify characteristic travel patterns from foreign visitor pathways in Japan. We expect that the results herein are mainly useful for marketing research in the tourism industry.

physics.soc-ph↗
arXiv2020

Fragility of spectral clustering for networks with an overlapping structure

Communities commonly overlap in real-world networks. This is a motivation to develop overlapping community detection methods, because methods for non-overlapping communities may not perform well. However, deterioration mechanism of the detection methods used for non-overlapping communities have rarely been investigated theoretically. Here, we analyze an accuracy of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics. Our analysis on an overlapping stochastic block model reveals how the structural information is lost from the leading eigenvector because of the overlapping structure.

cs.SI↗
arXiv2020

Spectral clustering of annotated graphs using a factor graph representation

Graph-structured data commonly have node annotations. A popular approach for inference and learning involving annotated graphs is to incorporate annotations into a statistical model or algorithm. By contrast, we consider a more direct method named scotch-taping, in which the structural information in a graph and its node annotations are encoded as a factor graph. Specifically, we establish the mathematical basis of this method in the spectral framework.

cs.SI↗
arXiv2020

Democratic summary of public opinions in free-response surveys

Social surveys have been widely used as a method of obtaining public opinion. Sometimes it is more ideal to collect opinions by presenting questions in free-response formats than in multiple-choice formats. Despite their advantages, free-response questions are rarely used in practice because they usually require manual analysis. Therefore, classification of free-format texts can present a formidable task in large-scale surveys and can be influenced by the interpretations of analysts. In this study, we propose a network-based survey framework in which responses are automatically classified in a statistically principled manner. This can be achieved because in addition to the texts, similarities among responses are also assessed by each respondent. We demonstrate our approach using a poll on the 2016 US presidential election and a survey taken by graduates of a particular university. The proposed approach helps analysts interpret the underlying semantics of responses in large-scale surveys.

cs.SI↗
arXiv2019

Evaluating network partitions through visualization

Network clustering requires making many decisions manually, such as the number of groups and a statistical model to be used. Even after filtering using an information criterion or regularizing with a nonparametric framework, we are commonly left with multiple candidates with reasonable partitions. In the end, the user has to decide which inferred groups should be regarded as informative. Here we propose a visualization method that efficiently represents network partitioning based on statistical inference algorithms. Our non-statistical assessment procedure based on visualization helps users extract informative groups when they cannot uniquely determine significant groups on the basis of statistical assessments. The proposed visualization is also effective for use as a benchmark test of different clustering algorithms.

cs.SI↗
arXiv2019

Counting the number of metastable states in the modularity landscape: Algorithmic detectability limit of greedy algorithms in community detection

Modularity maximization using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of implementation, this approach is persistently popular because, presumably, its risk of algorithmic failure is not well understood. This Rapid Communication provides insight into this issue by estimating the algorithmic performance limit of modularity maximization. This is achieved by counting the number of metastable states under a local update rule. Our results offer a quantitative insight into the level of sparsity at which a greedy algorithm typically fails.

physics.soc-ph↗
arXiv2018

Mean-field theory of graph neural networks in graph partitioning

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.

cs.LG↗
arXiv2018

Comparative analysis on the selection of number of clusters in community detection

We conduct a comparative analysis on various estimates of the number of clusters in community detection. An exhaustive comparison requires testing of all possible combinations of frameworks, algorithms, and assessment criteria. In this paper we focus on the framework based on a stochastic block model, and investigate the performance of greedy algorithms, statistical inference, and spectral methods. For the assessment criteria, we consider modularity, map equation, Bethe free energy, prediction errors, and isolated eigenvalues. From the analysis, the tendency of overfit and underfit that the assessment criteria and algorithms have, becomes apparent. In addition, we propose that the alluvial diagram is a suitable tool to visualize statistical inference results and can be useful to determine the number of clusters.

cs.SI↗
arXiv2018

Algorithmic detectability threshold of the stochastic block model

The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation--maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure, but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.

cs.SI↗
arXiv2017

Algorithmic infeasibility of community detection in higher-order networks

In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an algorithm that assumes a high-dimensional model and such an algorithm may perform poorly or be extremely sensitive to the initial estimate of the model parameters. Herein, we address this problem of community detection through a detectability analysis. We focus on the expectation-maximization (EM) algorithm with belief propagation (BP), and analytically derive its algorithmic detectability threshold, i.e., the limit of the modular structure strength below which the algorithm can no longer detect any modular structures. The results indicate the existence of a phase in which the community detection of a lower-order network outperforms its higher-order counterpart.

cs.SI↗