Tetsuo Furukawa

Modular network SOM

This study aims to develop a generalized framework of an SOM called a modular network SOM (mnSOM). The mnSOM has an array structure consisting of functional modules that are trainable neural networks, e.g., multi-layer perceptrons (MLPs), instead of the vector units of the conventional SOM. In the case of MLP-modules, an mnSOM learns a group of systems or functions in terms of the input-output relationships in parallel with generating a feature map of them. Thus an mnSOM with MLP modules is an SOM in function space rather than in vector space. In this paper, first, as an example, we focus on a class of mnSOM that consists of MLP modules and introduce the architecture and algorithm. Then, a more generalized framework is described. Finally, some simulation results of an MLP-module-mnSOM are presented.

SOM of SOMs: self-organizing map which maps a group of self-organizing maps

This paper aims to propose an extension of SOMs called an “SOM of SOMs,” or SOM2, in which the mapped objects are self-organizing maps themselves. In SOM2, each nodal unit of the conventional SOM is replaced by a function module of SOM. Therefore, SOM2 can be regarded as a variation of a modular network SOM (mnSOM). Since each child SOM module in SOM2 is trained to represent a manifold, the parent SOM in SOM2 generates a self-organizing map representing the distribution of the group of manifolds modeled by the child SOMs. This extension of SOM is easily generalized in the case of SOMn, such that “SOM2 as SOM of SOM2s.” In this paper, the algorithm of SOM2 is introduced, and some simulation results are reported.

Modular network SOM (mnSOM): from vector space to function space

Kohonens self-organizing map (SOM), which performs topology-preserving transformation from a high dimensional data vector space to a low-dimensional map space, provides a powerful tool for data analysis, classification and visualization in many application fields. Despite its power, SOM can only deal with vectorized data, although many expansions have been proposed for various data-type cases. This study aims to develop a novel generalization of SOM called modular network SOM (mnSOM), which enables users to deal with general data classes in a consistent manner. mnSOM has an array structure consisting of function modules that are trainable neural networks, e.g. multi-layer perceptrons (MLPs), instead of the vector units of the conventional SOM family. In the case of MLP-modules, mnSOM learns a group of systems or functions in terms of the input-output relationships, and at the same time, mnSOM generates a feature map that shows distances between the learned systems. Thus, mnSOM with MLP modules is an SOM in function space rather than in vector space. From this point of view, the conventional SOM of Kohonens can be regarded as a special case of mnSOM, the modules consisting of fixed-value bias units. In this paper, mnSOM with MLP modules is described along with some application examples.

Nitric oxide, 2-amino-4-phosphonobutyric acid and light/dark adaptation modulate short-wavelength-sensitive synaptic transmission to retinal horizontal cells.

Light-induced changes in the input resistance (Rin) of external, luminosity (i.e. H1) type horizontal cell (HC) perikarya were studied by the bridge-balance method in light-adapted and dark-adapted retinae of carp. Changes in input resistance (delta Rin) induced by short-(460 nm) and long-wavelength (674 nm) flashes, adjusted in intensity to elicit equal-amplitude membrane voltage responses (equal-voltage condition), were measured. In light-adapted retinae, long-wavelength stimuli increased Rin consistently; in contrast, the increase was much less with short-wavelength stimuli. This equal-voltage chromatic delta Rin difference was lost in dark-adapted retinae whereby the delta Rin (an increase) became the same for short- and long-wavelengths. The chromatic delta Rin difference could be recovered by light adaptation or application of sodium nitroprusside to the dark-adapted retinae. Conversely, the equal-voltage chromatic delta Rin difference was eliminated by injection of NG-monomethyl-L-arginine into H1HCs of the light-adapted retinae or by treating the retinae with 2-amino-4-phosphonobutyrate (APB). These results suggest that H1HCs of the carp retina possess distinct postsynaptic mechanisms which mediate short- and long-wavelength signal transmission. Furthermore, it appears that the short-wavelength-sensitive pathway is active only during the light-adapted state of the retina. Taken together, therefore, the short-wavelength transmission to H1HCs probably operates on an APB-sensitive glutamate receptor, with nitric oxide as a light-adaptive messenger.

A New Approach to Task Segmentation in Mobile Robots by mnSOM

Proposed is a new task segmentation method in navigation of mobile robots by a modular network SOM (mnSOM). mnSOM is an extension of SOM in that a function module instead of a vector unit is used to increase its representation capability. It has the ability of both segmentation and interpolation. During learning, modules in mnSOM compete with each other to become an expert for a subset of data. To increase temporal continuity of winner modules, winner decision algorithms using an MSE based threshold are proposed to improve standard mnSOM. We also propose methods for labeling modules based on MSE. The resulting mnSOM demonstrates good segmentation performance of 89.3% for a novel dataset.

Tensor SOM and tensor GTM

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures.

Effects of nitric oxide, light adaptation and APB on spectral characteristics of H1 horizontal cells in carp retina

The spectral characteristics of cone-driven horizontal cells of H1 subtype (H1 HCs) receiving main synaptic input from red-sensitive cones were studied in light- and dark-adapted retinae of carp. The spectral sensitivity profile of H1 HCs in dark-adapted retinae was practically the same as the absorption spectrum of red-sensitive cones. Light-adaptation decreased the sensitivity preferentially in the short-wavelength (blue/green) region, resulting in a relative enhancement of the 617 nm peak. Application of nitric oxide (NO) donors, sodium nitroprusside (SNP) and S-nitrosoglutathione (SNOG or GSNO), or dopamine to dark-adapted retinae decreased the sensitivity preferentially in blue/green region, an effect similar to that of light-adaptation. Application of haemoglobin (Hb, an NO scavenger) or 2-amino-4-phosphonobutyrate (APB, a metabotropic glutamate receptor agonist), to light-adapted retinae increased the sensitivity preferentially in the blue/green region, an effect similar to dark-adaptation. The photoresponses of H1 HCs were univariant in dark-adapted retinae as well as Hb-treated light-adapted retinae. In light-adapted retinae with normal Ringer, however, the univariance did not hold. These results suggested that the photoresponses of H1 HCs to short-wavelength stimuli contain a depolarising (sign-reversing) component, which can be activated by light-adaptation or application of NO and dopamine, and inactivated by dark-adaptation or deprivation of NO or application of APB.

Task Segmentation in a Mobile Robot by mnSOM and Clustering with Spatio-temporal Contiguity

In our previous study, task segmentation by mnSOM implicitly assumes that winner modules corresponding to subsequences in the same class share the same label. This paper proposes to do task segmentation by applying various clustering methods to the resulting mnSOM without using the above assumption. Firstly we use the conventional hierarchical clustering. It assumes that the distances between any pair of modules are provided with precision, but this is not exactly true. Accordingly, this is followed by a clustering based on only the distance between spatially adjacent modules with modification by their temporal contiguity. This clustering with spatio-temporal contiguity provides superior performance to the conventional hierarchical clustering and comparable performance with mnSOM using the implicit assumption.

An online adaptation control system using mnSOM

Autonomous Underwater Vehicles (AUVs) are attractive tools to survey earth science and oceanography, however, there exists a lot of problems to be solved such as motion control, acquisition of sensor data, decision-making, navigation without collision, self-localization and so on. In order to realize useful and practical robots, underwater vehicles should take their action by judging the changing condition from their own sensors and actuators, and are desirable to make their behavior, because of features caused by the working environment. We have been investigated the application of brain-inspired technologies such as Neural Networks (NNs) and Self-Organizing Map (SOM) into AUVs. A new controller system for AUVs using Modular Network SOM (mnSOM) proposed by Tokunaga et al. is discussed in this paper. The proposed system is developed using recurrent NN type mnSOM. The efficiency of the system is investigated through the simulations.

Requirements for the learning of multiple dynamics

The aim of this work is to discover the principles of learning a group of dynamical systems. The learning mechanism, which is referred to as the Learning Algorithm of Multiple Dynamics (LAMD), is expected to satisfy the following four requirements. (i) Given a set of time-series sequences for training, estimate the dynamics and their latent variables. (ii) Order the dynamical systems according to the similarities between them. (iii) Interpolate intermediate dynamics from the given dynamics. (iv) After training, the LAMD should be able to identify or classify new sequences. For this purpose several algorithms have been proposed, such as the Recurrent Neural Network with Parametric Bias and the modular network SOM with recurrent network modules. In this paper, it is shown that these types of algorithms do not satisfy the above requirements, but can be improved by normalization of estimated latent variables. This confirms that the estimation process of latent variables plays an important role in the LAMD. Finally, we show that a fully latent space model is required to satisfy the requirements, for which purpose a SOM with a higher-rank, such as a SOM2, is best suited.