GTM: A principled alternative to the self-organizing map

The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.

Understanding policy implementation processes as self-organizing systems

Implementation studies and related research in organizational theory can be enhanced by drawing on the field of complex systems to understand better and, as a consequence, more successfully manage change. This article reinterprets data previously published in the British Journal of Management to reveal a new contribution, that policy implementation processes should be understood as a self-organizing system in which adaptive abilities are extremely important for stakeholders. In other words, national policy is reinterpreted at the local level, with each local organization uniquely mixing elements of national policy with their own requirements making policy implementation unpredictable and more sketchy. The original article explained different paces and directions of change in terms of traditional management processes: leadership, politics, implementation and vision. By reinterpreting the data, it is possible to reveal that deeper level processes, which are more emergent, are also at work influencing change, which the authors label possibility space. Implications for theory, policy and practice are identified.

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

The power of the powerless:neighbourhood based self-help networks of the poor in Istanbul

Recent poverty research focuses on the household responses to poverty through structure vs. agency perspectives. The human agency perspective, however, provides us important insights for looking beyond these simplistic tendencies which assume poor people as inherently passive, or envision them as helpless victims. In Turkey, politicians view poverty as a temporary and manageable problem which can be dealt with the provision of more charity or community support. Migrant networks, informal sector work and social assistance are considered to be important mechanisms that would provide resources for the poor. This paper argues that for some of the poor households none of these mechanisms provide sufficient resources. Instead, neighbourhood-based small-group solidarities and self-help networks enable those poor to develop collective capabilities and make ends meet. The paper also reveals that in Turkey, the implementation of social policies for poverty reduction could bring about relationships of patronage and in some cases contribute to existing inequalities.

Self-organising zooms for decentralised redundancy management in visual sensor networks

When visual sensor networks are composed of cameras which can adjust the zoom factor of their own lens, one must determine the optimal zoom levels for the cameras, for a given task. This gives rise to an important trade-off between the overlap of the different cameras’ fields of view, providing redundancy, and image quality. In an object tracking task, having multiple cameras observe the same area allows for quicker recovery, when a camera fails. In contrast having narrow zooms allow for a higher pixel count on regions of interest, leading to increased tracking confidence. In this paper we propose an approach for the self-organisation of redundancy in a distributed visual sensor network, based on decentralised multi-objective online learning using only local information to approximate the global state. We explore the impact of different zoom levels on these trade-offs, when tasking omnidirectional cameras, having perfect 360-degree view, with keeping track of a varying number of moving objects. We further show how employing decentralised reinforcement learning enables zoom configurations to be achieved dynamically at runtime according to an operator’s preference for maximising either the proportion of objects tracked, confidence associated with tracking, or redundancy in expectation of camera failure. We show that explicitly taking account of the level of overlap, even based only on local knowledge, improves resilience when cameras fail. Our results illustrate the trade-off between maintaining high confidence and object coverage, and maintaining redundancy, in anticipation of future failure. Our approach provides a fully tunable decentralised method for the self-organisation of redundancy in a changing environment, according to an operator’s preferences.

Self-aware and self-expressive camera networks

Smart cameras perform on-board image analysis, adapt their algorithms to changes in their environment, and collaborate with other networked cameras to analyze the dynamic behavior of objects. A proposed computational framework adopts the concepts of self-awareness and self-expression to more efficiently manage the complex tradeoffs among performance, flexibility, resources, and reliability. The Web extra at http://youtu.be/NKe31-OKLz4 is a video demonstrating CamSim, a smart camera simulation tool, enables users to test self-adaptive and self-organizing smart-camera techniques without deploying a smart-camera network.

Learning to be different:heterogeneity and efficiency in distributed smart camera networks

In this paper we study the self-organising behaviour of smart camera networks which use market-based handover of object tracking responsibilities to achieve an efficient allocation of objects to cameras. Specifically, we compare previously known homogeneous configurations, when all cameras use the same marketing strategy, with heterogeneous configurations, when each camera makes use of its own, possibly different marketing strategy. Our first contribution is to establish that such heterogeneity of marketing strategies can lead to system wide outcomes which are Pareto superior when compared to those possible in homogeneous configurations. However, since the particular configuration required to lead to Pareto efficiency in a given scenario will not be known in advance, our second contribution is to show how online learning of marketing strategies at the individual camera level can lead to high performing heterogeneous configurations from the system point of view, extending the Pareto front when compared to the homogeneous case. Our third contribution is to show that in many cases, the dynamic behaviour resulting from online learning leads to global outcomes which extend the Pareto front even when compared to static heterogeneous configurations. Our evaluation considers results obtained from an open source simulation package as well as data from a network of real cameras. © 2013 IEEE.

A survey of self-awareness and its application in computing systems

Novel computing systems are increasingly being composed of large numbers of heterogeneous components, each with potentially different goals or local perspectives, and connected in networks which change over time. Management of such systems quickly becomes infeasible for humans. As such, future computing systems should be able to achieve advanced levels of autonomous behaviour. In this context, the system's ability to be self-aware and be able to self-express becomes important. This paper surveys definitions and current understanding of self-awareness and self-expression in biology and cognitive science. Subsequently, previous efforts to apply these concepts to computing systems are described. This has enabled the development of novel working definitions for self-awareness and self-expression within the context of computing systems.

Static, dynamic, and adaptive heterogeneity in distributed smart camera networks

We study heterogeneity among nodes in self-organizing smart camera networks, which use strategies based on social and economic knowledge to target communication activity efficiently. We compare homogeneous configurations, when cameras use the same strategy, with heterogeneous configurations, when cameras use different strategies. Our first contribution is to establish that static heterogeneity leads to new outcomes that are more efficient than those possible with homogeneity. Next, two forms of dynamic heterogeneity are investigated: nonadaptive mixed strategies and adaptive strategies, which learn online. Our second contribution is to show that mixed strategies offer Pareto efficiency consistently comparable with the most efficient static heterogeneous configurations. Since the particular configuration required for high Pareto efficiency in a scenario will not be known in advance, our third contribution is to show how decentralized online learning can lead to more efficient outcomes than the homogeneous case. In some cases, outcomes from online learning were more efficient than all other evaluated configuration types. Our fourth contribution is to show that online learning typically leads to outcomes more evenly spread over the objective space. Our results provide insight into the relationship between static, dynamic, and adaptive heterogeneity, suggesting that all have a key role in achieving efficient self-organization.

Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

A modelling and simulation environment for self-aware and self-expressive systems

Self-awareness and self-expression are promising architectural concepts for embedded systems to be equipped with to match them with dedicated application scenarios and constraints in the avionic and space-flight industry. Typically, these systems operate in largely undefined environments and are not reachable after deployment for a long time or even never ever again. This paper introduces a reference architecture as well as a novel modelling and simulation environment for self-aware and self-expressive systems with transaction level modelling, simulation and detailed modelling capabilities for hardware aspects, precise process chronology execution as well as fine timing resolutions. Furthermore, industrial relevant system sizes with several self-aware and self-expressive nodes can be handled by the modelling and simulation environment.

CamSim:a distributed smart camera network simulator

Smart cameras allow pre-processing of video data on the camera instead of sending it to a remote server for further analysis. Having a network of smart cameras allows various vision tasks to be processed in a distributed fashion. While cameras may have different tasks, we concentrate on distributed tracking in smart camera networks. This application introduces various highly interesting problems. Firstly, how can conflicting goals be satisfied such as cameras in the network try to track objects while also trying to keep communication overhead low? Secondly, how can cameras in the network self adapt in response to the behavior of objects and changes in scenarios, to ensure continued efficient performance? Thirdly, how can cameras organise themselves to improve the overall network's performance and efficiency? This paper presents a simulation environment, called CamSim, allowing distributed self-adaptation and self-organisation algorithms to be tested, without setting up a physical smart camera network. The simulation tool is written in Java and hence allows high portability between different operating systems. Relaxing various problems of computer vision and network communication enables a focus on implementing and testing new self-adaptation and self-organisation algorithms for cameras to use.

Self-adaptive probabilistic roadmap generation for intelligent virtual agents

Agents inhabiting large scale environments are faced with the problem of generating maps by which they can navigate. One solution to this problem is to use probabilistic roadmaps which rely on selecting and connecting a set of points that describe the interconnectivity of free space. However, the time required to generate these maps can be prohibitive, and agents do not typically know the environment in advance. In this paper we show that the optimal combination of different point selection methods used to create the map is dependent on the environment, no point selection method dominates. This motivates a novel self-adaptive approach for an agent to combine several point selection methods. The success rate of our approach is comparable to the state of the art and the generation cost is substantially reduced. Self-adaptation therefore enables a more efficient use of the agent's resources. Results are presented for both a set of archetypal scenarios and large scale virtual environments based in Second Life, representing real locations in London.

GTM: the generative topographic mapping

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.