A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation and Recognition of Handwritten Digits Using Deformable Templates
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Classification Using the Inner-Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Dissimilarity Representation for Pattern Recognition: Foundations And Applications (Machine Perception and Artificial Intelligence)
A Riemannian approach to graph embedding
Pattern Recognition
Hyperbolic embedding of internet graph for distance estimation and overlay construction
IEEE/ACM Transactions on Networking (TON)
Sign Language Recognition by Combining Statistical DTW and Independent Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Inexact Graph Comparison Approach in Joint Eigenspace
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Non-Euclidean or non-metric measures can be informative
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Geometric characterisation of graphs
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Rectifying non-euclidean similarity data through tangent space reprojection
IbPRIA'11 Proceedings of the 5th Iberian conference on Pattern recognition and image analysis
Determining the cause of negative dissimilarity eigenvalues
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
The dissimilarity space: Bridging structural and statistical pattern recognition
Pattern Recognition Letters
The dissimilarity representation for structural pattern recognition
CIARP'11 Proceedings of the 16th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
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Most problems in pattern recognition can be posed in terms of using the dissimilarities between the set of objects of interest. A vector-space representation of the objects can be obtained by embedding them as points in Euclidean space. However many dissimilarities are non-Euclidean and cannot be represented accurately in Euclidean space. This can lead to a loss of information and poor performance. In this paper, we approach this problem by embedding the points in a non-Euclidean curved space, the hypersphere. This is a metric but non-Euclidean space which allows us to define a geometry and therefore construct geometric classifiers. We develop a optimisation-based procedure for embedding objects on hyperspherical manifolds from a given set of dissimilarities. We use the Lie group representation of the hypersphere and its associated Lie algebra to define the exponential map between the manifold and its local tangent space. We can then solve the optimisation problem locally in Euclidean space. This process is efficient enough to allow us to embed large datasets. We also define the nearest mean classifier on the manifold and give results for the embedding accuracy, the nearest mean classifier and the nearest-neighbor classifier on a variety of indefinite datasets.