Competitive Hebbian Learning Rule Forms Perfectly Topology Preserving Maps

By Thomas Martinetz. 1993

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In Statistical Learning Theory

Citations in the corpus

Lifelong learning of human actions with deep neural network self-organization (2017, background): “In this case, the learning parameters are kept fixed and map topology develops through competitive Hebbian learning (Martinetz, 1993).”
A self-organizing neural network architecture for learning human-object interactions (2017, methodology): “such as the GNG [50] and the GWR networks [17] are characterized by a dynamic topological structure able to adapt toward the input data space through the mechanism of the competitive Hebbian learning [66]. Unlike the GNG, where the network grows at a constant rate, the GWR algorithm is equipped with”
Recent Advances of Continual Learning in Computer Vision: An Overview (2021, positive): “EHG is constructed based on competitive Heb-Recent bian learning [119] and represents the topology of the feature space.”
Few-Shot Class-Incremental Learning (2020, positive): “NG maps the feature space F to a finite set of feature vectors V = {vj}j=1 and preserves the topology of F by competitive Hebbian learning [28], as shown in Figure 2.”
Emergence of multimodal action representations from neural network self-organization (2017, background): “During the training, the network dynamically changes its topological structure to better match the input space following competitive Hebbian learning (Martinetz, 1993).”
Self-organizing neural integration of pose-motion features for human action recognition (2015, methodology): “During the training, Growing When Required networks (Marsland et al., 2002) dynamically change their topological structure through competitive Hebbian learning (Martinetz, 1993) to incrementally match the input space.”
An incremental growing neural gas learns topologies (2005, methodology): “Hebbian Learning [ Mar93 ] tobuild upatopology during self-organizatio n. Theprinciple oftheCompetitive Hebbian Learning (CHL)method issimply tocreate anedgebetween thewinning andthesecond winning unit ateachadaptation step.”
A Growing Neural Gas Network Learns Topologies (1994, methodology): “Then we propose a new network model which also makes use of CHL.”
Ltd Registered in England and Wales Registered Number : 1072954 Registered office : (2004, background): “That is, the case of the self-organizing map (SOM) [9], growing neural gas [9], growing cell structure (GCS) [11], or enhanced self-organizing incremental neuronal network (ESOINN) [6].”
Human motion assessment in real time using recurrent self-organization (2016, methodology): “A general approach for updating the weight and context vectors is using the competitive Hebbian learning rule [10].”
A self-organising network that grows when required (2002, methodology): “This has been formalised by Martinetz (1993) , through the definition of the perfectly topology-preserving map.”
Topology-Preserving Class-Incremental Learning (2020, methodology): “An eﬀective way to model the topology of a feature space is to perform Competitive Hebbian learning (CHL) [28] on the feature space manifold.”
Multi-modal integration of dynamic audiovisual patterns for an interactive reinforcement learning scenario (2016, background): “During the training, the network starts with two neurons and then dynamically changes its topological structure to better match the input space following competitive Hebbian learning [22].”
An incremental network for on-line unsupervised classification and topology learning (2006, methodology): “Martinetz and Schulten (1994) prove some theorems and reach the conclusion that the competitive Hebbian rule is suitable for forming a path preserving representations of a given manifold.”
Incremental Unsupervised Time Series Analysis Using Merge Growing Neural Gas (2009, background): “Connections between neurons are created by topology preserving Competitive Hebbian Learning [ 20 ].”
Incremental Learning in Biological and Machine Learning Systems (2002, background): “In Growing Neural Gas(54) the network topology is generated incrementally by competitive Hebbian learning.(89) The dimensionality depends on the input data and can be locally different.”
Class-Incremental Learning with Topological Schemas of Memory Spaces (2021, background): “Competitive Hebbian learning [37] (CHL) rule is an effective way to form perfectly topology preserving maps in the feature space.”
Clustering: A neural network approach (2010, unknown): “The induced Delaunay triangulation is optimally topologypreserving in a general sense (Martinetz, 1993).”