Masahiro Kimura

Surface deformation with differential geometric structures

This paper considers the deformation of a given surface to a surface that smoothly connects to previously designed surfaces while reflecting the overall shape of the initial surface. We introduce deformation energy using a Laplacian-based functional, which is defined by the global differential geometric structures of the initial surface. It is shown that the proposed deformation energy does not depend on representations of the initial surface, and relates to the mean curvature vector, a geometric quantity correlated to overall surface shape, and also has a good computational property. An example is presented to demonstrate the effectiveness of our method.

Multinomial PCA for extracting major latent topics from document streams

We propose a new unsupervised learning method called multinomial PCA (MuPCA) for efficiently extracting the major latent topics from a document stream based on the bag-of-words (BOW) representation of a document. Unlike PCA, MuPCA follows a suitable probabilistic generative model for the document stream represented as time-series of word-frequency vectors. Using real data of document streams on the Web, we experimentally demonstrate the effectiveness of the proposed method.

Modeling of growing networks with communities

We propose a growing network model and its learning algorithm. Unlike the conventional scale-free models, we incorporate community structure, which is an important characteristic of many real-world networks including the Web. In our experiments, we confirmed that the proposed model exhibits a degree distribution with a power-law tail, and our method can precisely estimate the probability of a new link creation from data without community information. Moreover, by introducing a measure of dynamic hub-degrees, we could predict the change of hub-degrees between communities.

On unique representations of certain dynamical systems produced by continuous-time recurrent neural networks

This article extends previous mathematical studies on elucidating the redundancy for describing functions by feedforward neural networks (FNNs) to the elucidation of redundancy for describing dynamical systems (DSs) by continuous-time recurrent neural networks (RNNs). In order to approximate a DS on Rn using an RNN with n visible units, an ndimensional affine neural dynamical system (A-NDS) can be used as the DS actually produced by the above RNN under an affine map from its visible state-space Rn to its hidden state-space. Therefore, we consider the problem of clarifying the redundancy for describing A-NDSs by RNNs and affine maps. We clarify to what extent a pair of an RNN and an affine map is uniquely determined by its corresponding A-NDS and also give a nonredundant sufficient search set for the DS approximation problem based on A-NDS.

Critical Link Identification Based on Bridge Detection for Network with Uncertain Connectivity

Efficiently identifying critical links that substantially degrade network performance if they fail to function is challenging for a large complex network. In this paper, we tackle this problem under a more realistic situation where each link is probabilistically disconnected as if a road is blocked in a natural disaster than assuming that any road is never blocked in a disaster. To solve this problem, we utilize the bridge detection technique in graph theory and efficiently identify critical links in case the node reachability is taken as the performance measure, which corresponds to the number of people who can reach at least one evacuation facility in a disaster. Using two real-world road networks, we empirically show that the proposed method is much more efficient than the other methods that are based on traditional centrality measures and the links our method detected are substantially more critical than those by the others.

Tracking and Visualization of Cluster Dynamics by Sequence-based SOM

Since events and physical phenomena change with time, it is important to capture the main transitions and elements of such events and phenomena. Such transitions can be seen to occur in the World Wide Web (Levene & Poulovassilis, 2004), news topics (Allan, 2002), a person’s health condition, and the state of an instrument or a plant. Transition, or change, refers to a sequential increase/decrease or generation/extinction of the feature of the object. Visualization of such transitions of dynamic clusters is helpful in understanding such phenomena instinctively and plays a useful role in many application domains, such as fault diagnosis and medial examinations. Although a number of clustering methods have been proposed (Jain et al., 1999), most conventional clustering methods deal with static data and cannot handle sequential changes of the cluster explicitly. Tracing the trajectory within clusters that have been collectively processed and a sliding window-based method to generate separate clusters can be considered as simple methods. Although the former method cannot trace changes of clusters, it can trace changes in the number of data that belong to each cluster. The latter method can handle changes of clusters to a certain degree. However, there are some problems, such as setting an appropriate window size, the inevitable decrease in the number of data within a window, and the correspondence relationships of clusters between windows. The present study considers a window-based approach using the temporal neighborhood to address the above-described problems. Kohonens Self-Organizing Map (SOM) (Kohonen, 2000) is considered to be an appropriate technique for visualizing clusters and their similarity relationships. The SOM is an unsupervised neural network learning technique that produces clusters and subsequently projects them onto a low-dimensional (normally two-dimensional) topology map. The conventional SOM deals with static data. However, we have extended the SOM learning model by introducing the Sequencing Weight Function (SWF), so that the model can visualize the transition of dynamics clusters. This model is referred to herein as the Sequence-based SOM (SbSOM) (Fukui et al., 2008). A SOM-based method was selected because the SOM has a neuron topology in the feature space and that is associated with topology (visualization) space. The introduction of temporal order into the topology is natural. The proposed method mitigates the problems of appropriate 7