Spiral Structure
QUANTIFYING STRUCTURAL TIME VARYING CHANGES IN HELICAL DATA Sameer Singh
Pattern Analysis and Neural Networks Group Department of Computing University of Exeter UK (s.singh@exeter.ac.uk)
ABSTRACT
Spiral structures are one of the most difficult patterns to classify. Spiral time series data has a helical movement with time that is both difficult to predict as well as classify. This paper focusses on how structural information about spirals can be useful in providing critical information to a neural network for their recognition. Results are presented on neural network solutions to the classical two-spiral problem by extracting structural and rotational information from the spiral training data. The results show that in both two and three dimension, the spirals can be easily recognised by neural networks if they are trained on the temporal structural changes.
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1. SPIRAL STRUCTURES
In our previous paper in Pattern Recognition Letters[11] it was highlighted that spiral classification is a difficult problem which can be reasonably well solved using a fuzzy nearest neighbour classifier. Our earlier reservation for not using a neural network was that neural networks have convergence problems with raw coordinate data as inputs for recognising spirals. The two spiral benchmark from Carnegie Mellon repository in particular has been highly researched and it has been found that sophisticated neural networks have difficulty in classifying spirals with reasonable accuracy. In this paper we summarise the problem in short again for new readers and develop an input selection method for neural networks that allows them to recognise spirals in two or more dimensions with relative ease.
Spiral data is found in several natural and physical domains. The classic double helix DNA, the motion of particles in cyclotrons, spiral feed in manufacturing, spiral galaxies and spiral movement of financial stocks are some of the well-known examples. Spirals are particularly
Pattern Analysis and Neural Networks Group Department of Computing University of Exeter UK (s.singh@exeter.ac.uk)
ABSTRACT
Spiral structures are one of the most difficult patterns to classify. Spiral time series data has a helical movement with time that is both difficult to predict as well as classify. This paper focusses on how structural information about spirals can be useful in providing critical information to a neural network for their recognition. Results are presented on neural network solutions to the classical two-spiral problem by extracting structural and rotational information from the spiral training data. The results show that in both two and three dimension, the spirals can be easily recognised by neural networks if they are trained on the temporal structural changes.
1
1. SPIRAL STRUCTURES
In our previous paper in Pattern Recognition Letters[11] it was highlighted that spiral classification is a difficult problem which can be reasonably well solved using a fuzzy nearest neighbour classifier. Our earlier reservation for not using a neural network was that neural networks have convergence problems with raw coordinate data as inputs for recognising spirals. The two spiral benchmark from Carnegie Mellon repository in particular has been highly researched and it has been found that sophisticated neural networks have difficulty in classifying spirals with reasonable accuracy. In this paper we summarise the problem in short again for new readers and develop an input selection method for neural networks that allows them to recognise spirals in two or more dimensions with relative ease.
Spiral data is found in several natural and physical domains. The classic double helix DNA, the motion of particles in cyclotrons, spiral feed in manufacturing, spiral galaxies and spiral movement of financial stocks are some of the well-known examples. Spirals are particularly
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