995 research outputs found
Geometrical complexity of data approximators
There are many methods developed to approximate a cloud of vectors embedded
in high-dimensional space by simpler objects: starting from principal points
and linear manifolds to self-organizing maps, neural gas, elastic maps, various
types of principal curves and principal trees, and so on. For each type of
approximators the measure of the approximator complexity was developed too.
These measures are necessary to find the balance between accuracy and
complexity and to define the optimal approximations of a given type. We propose
a measure of complexity (geometrical complexity) which is applicable to
approximators of several types and which allows comparing data approximations
of different types.Comment: 10 pages, 3 figures, minor correction and extensio
Data complexity measured by principal graphs
How to measure the complexity of a finite set of vectors embedded in a
multidimensional space? This is a non-trivial question which can be approached
in many different ways. Here we suggest a set of data complexity measures using
universal approximators, principal cubic complexes. Principal cubic complexes
generalise the notion of principal manifolds for datasets with non-trivial
topologies. The type of the principal cubic complex is determined by its
dimension and a grammar of elementary graph transformations. The simplest
grammar produces principal trees.
We introduce three natural types of data complexity: 1) geometric (deviation
of the data's approximator from some "idealized" configuration, such as
deviation from harmonicity); 2) structural (how many elements of a principal
graph are needed to approximate the data), and 3) construction complexity (how
many applications of elementary graph transformations are needed to construct
the principal object starting from the simplest one).
We compute these measures for several simulated and real-life data
distributions and show them in the "accuracy-complexity" plots, helping to
optimize the accuracy/complexity ratio. We discuss various issues connected
with measuring data complexity. Software for computing data complexity measures
from principal cubic complexes is provided as well.Comment: Computers and Mathematics with Applications, in pres
Multi-disciplinary shape optimization of an entry capsule integrated with custom neural network approximation and multi-delity approach
This paper describes a new integrated approach for the multi-disciplinary optimization of a entry capsule’s shape. Aerothermodynamics, Flight Mechanics and Thermal Protection System behaviour of a reference spaceship when crossing Martian atmosphere are considered, and several analytical, semi-empirical and numerical models are used. The multi-objective and multi-disciplinary optimization process implemented in Isight software environment allows finding a Pareto front of best shapes. The optimization process is integrated with a set of artificial neural networks, trained and updated by a multi-fidelity evolution control approach, to approximate the objective and constraint functions. Results obtained by means of the integrated approach with neural networks approximators are described and compared to the results obtained by a different optimization process, not using the approximators. The comparison highlights advantages and possible drawbacks of the proposed method, mainly in terms of calls to the true model and precision of the obtained Pareto front
An adaptive neuro-fuzzy propagation model for LoRaWAN
This article proposes an adaptive-network-based fuzzy inference system (ANFIS) model for accurate estimation of signal propagation using LoRaWAN. By using ANFIS, the basic knowledge of propagation is embedded into the proposed model. This reduces the training complexity of artificial neural network (ANN)-based models. Therefore, the size of the training dataset is reduced by 70% compared to an ANN model. The proposed model consists of an efficient clustering method to identify the optimum number of the fuzzy nodes to avoid overfitting, and a hybrid training algorithm to train and optimize the ANFIS parameters. Finally, the proposed model is benchmarked with extensive practical data, where superior accuracy is achieved compared to deterministic models, and better generalization is attained compared to ANN models. The proposed model outperforms the nondeterministic models in terms of accuracy, has the flexibility to account for new modeling parameters, is easier to use as it does not require a model for propagation environment, is resistant to data collection inaccuracies and uncertain environmental information, has excellent generalization capability, and features a knowledge-based implementation that alleviates the training process. This work will facilitate network planning and propagation prediction in complex scenarios
Neural Network Modelling of Constrained Spatial Interaction Flows
Fundamental to regional science is the subject of spatial interaction. GeoComputation - a new research paradigm that represents the convergence of the disciplines of computer science, geographic information science, mathematics and statistics - has brought many scholars back to spatial interaction modeling. Neural spatial interaction modeling represents a clear break with traditional methods used for explicating spatial interaction. Neural spatial interaction models are termed neural in the sense that they are based on neurocomputing. They are clearly related to conventional unconstrained spatial interaction models of the gravity type, and under commonly met conditions they can be understood as a special class of general feedforward neural network models with a single hidden layer and sigmoidal transfer functions (Fischer 1998). These models have been used to model journey-to-work flows and telecommunications traffic (Fischer and Gopal 1994, Openshaw 1993). They appear to provide superior levels of performance when compared with unconstrained conventional models. In many practical situations, however, we have - in addition to the spatial interaction data itself - some information about various accounting constraints on the predicted flows. In principle, there are two ways to incorporate accounting constraints in neural spatial interaction modeling. The required constraint properties can be built into the post-processing stage, or they can be built directly into the model structure. While the first way is relatively straightforward, it suffers from the disadvantage of being inefficient. It will also result in a model which does not inherently respect the constraints. Thus we follow the second way. In this paper we present a novel class of neural spatial interaction models that incorporate origin-specific constraints into the model structure using product units rather than summation units at the hidden layer and softmax output units at the output layer. Product unit neural networks are powerful because of their ability to handle higher order combinations of inputs. But parameter estimation by standard techniques such as the gradient descent technique may be difficult. The performance of this novel class of spatial interaction models will be demonstrated by using the Austrian interregional traffic data and the conventional singly constrained spatial interaction model of the gravity type as benchmark. References Fischer M M (1998) Computational neural networks: A new paradigm for spatial analysis Environment and Planning A 30 (10): 1873-1891 Fischer M M, Gopal S (1994) Artificial neural networks: A new approach to modelling interregional telecommunciation flows, Journal of Regional Science 34(4): 503-527 Openshaw S (1993) Modelling spatial interaction using a neural net. In Fischer MM, Nijkamp P (eds) Geographical information systems, spatial modelling, and policy evaluation, pp. 147-164. Springer, Berlin
Analogue neuromorphic systems.
This thesis addresses a new area of science and technology, that of neuromorphic
systems, namely the problems and prospects of analogue neuromorphic systems. The
subject is subdivided into three chapters.
Chapter 1 is an introduction. It formulates the oncoming problem of the creation
of highly computationally costly systems of nonlinear information processing (such as
artificial neural networks and artificial intelligence systems). It shows that an analogue
technology could make a vital contribution to the creation such systems. The basic principles
of creation of analogue neuromorphic systems are formulated. The importance
will be emphasised of the principle of orthogonality for future highly efficient complex
information processing systems.
Chapter 2 reviews the basics of neural and neuromorphic systems and informs on
the present situation in this field of research, including both experimental and theoretical
knowledge gained up-to-date. The chapter provides the necessary background for
correct interpretation of the results reported in Chapter 3 and for a realistic decision on
the direction for future work.
Chapter 3 describes my own experimental and computational results within the
framework of the subject, obtained at De Montfort University. These include: the
building of (i) Analogue Polynomial Approximator/lnterpolatoriExtrapolator, (ii) Synthesiser
of orthogonal functions, (iii) analogue real-time video filter (performing the
homomorphic filtration), (iv) Adaptive polynomial compensator of geometrical distortions
of CRT- monitors, (v) analogue parallel-learning neural network (backpropagation
algorithm).
Thus, this thesis makes a dual contribution to the chosen field: it summarises the
present knowledge on the possibility of utilising analogue technology in up-to-date and
future computational systems, and it reports new results within the framework of the
subject. The main conclusion is that due to its promising power characteristics, small
sizes and high tolerance to degradation, the analogue neuromorphic systems will playa
more and more important role in future computational systems (in particular in systems
of artificial intelligence)
A Nonparametric Ensemble Binary Classifier and its Statistical Properties
In this work, we propose an ensemble of classification trees (CT) and
artificial neural networks (ANN). Several statistical properties including
universal consistency and upper bound of an important parameter of the proposed
classifier are shown. Numerical evidence is also provided using various real
life data sets to assess the performance of the model. Our proposed
nonparametric ensemble classifier doesn't suffer from the `curse of
dimensionality' and can be used in a wide variety of feature selection cum
classification problems. Performance of the proposed model is quite better when
compared to many other state-of-the-art models used for similar situations
A methodology for neural spatial interaction modelling
This paper presents a methodology for neural spatial interaction modelling. Particular emphasis is laid on design, estimation and performance issues in both cases, unconstrained and singly constrained spatial interaction. Families of classical neural network models, but also less classical ones such as product unit neural network models are considered. Some novel classes of product unit and summation unit models are presented for the case of origin or destination constrained spatial interaction flows. The models are based on a modular connectionist architecture that may be viewed as a linked collection of functionally independent neural modules with identical feedforward topologies, operating under supervised learning algorithms. Parameter estimation is viewed as Maximum Likelihood (ML) learning. The nonconvex nature of the loss function makes the Alopex procedure, a global search procedure, an attractive and appropriate optimising scheme for ML learning. A benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained, neural network model versions in terms of generalization performance measured by Kullback and Leibler`s information criterion. Hereby, the authors make use of the bootstrapping pairs approach to overcome the largely neglected problem of sensitivity to the specific splitting of the data into training, internal validation and testing data sets, and to get a better statistical picture of prediction variability of the models. Keywords: Neural spatial interaction models, origin constrained or destination constrained spatial interaction, product unit network, Alopex procedure, boostrapping, benchmark performance tests.
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