'Neural-gas' network for vector quantization and its application to time-series prediction

By Thomas Martinetz, Stanislav G. Berkovich, Klaus Schulten. 1993

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Citations in the corpus

Continual Lifelong Learning with Neural Networks: A Review (2018, background): “of basic biological findings on Hebbian-like learning and plasticity (Kohonen, 1982; Martinetz et al., 1993; Fritzke, 1992; Marsland et al., 2002), demonstrating that neural map organization results from unsupervised, statistical learning with nonlinear approximations of the input distribution.”
A Comprehensive Study of Class Incremental Learning Algorithms for Visual Tasks (2020, neutral): “n. Self-Organizing Maps (SOMs) are online unsupervised learning algorithms that rely on approximate stochastic gradient technique, and can be adapted to Incremental Learning. Neural Gas (NG) networks [43] and its growing NG variant [18] are related to SOMs which are often exploited for incremental l”
Nonlinear Time Series Analysis by Using Gamma Growing Neural Gas (2012, methodology): “As this type of context does not depend on the lattice architecture, it can be combined with other self-organizing neural networks such as Neural Gas (NG) [5] and Growing Neural Gas (GNG) [6], to produce the Merge Neural Gas (MNG) [7] and the Merge Growing Neural Gas (MGNG) [8], respectively.”
Control of multistability (2014, methodology): “The finite set W is taken as a finite approximation of the true state space X using a vector quantization technique [263].”
A self-organising network that grows when required (2002, methodology): “This network has a lot in common with the Neural Gas model of Martinetz, Berkovich, and Schulten (1993) .”
Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data (2017, methodology): “• Neural Gas — Artificial neural network clustering method, based on self-organizing maps [12, 31].”
Neural network-based clustering using pairwise constraints (2015, methodology): “Among these tasks, clustering has received less attention recently and neural approaches are usually addressed in an unsupervised fashion using techniques such as self-organizing maps (Kohonen, 1982), neural gas (Martinetz et al., 1993), or adaptive resonance theory (Grossberg, 1976).”
Prototype-based models in machine learning. (2016, background): “Therefore, the name Neural Gas Algorithm has been coined for this particular VQ scheme.(5) It is frequently used for the faithful representation of datasets by a relatively large number of prototypes, the positions of which represent the density of observations in feature space.”
A novel kernel method for clustering (2005, methodology): “K-Means shares this limitation with other clustering algorithms, like SOM [12], [13] and Neural Gas [15].”
Dynamic self-organising map (2011, methodology): “Vector quantisation can be achieved using several methods such as variations of the k -means method [1], Linde–Buzo–Gray (LBG) algorithm [2] or neural network models such as the self-30 organising map (SOM) [3], neural gas (NG) [4] and growing neural gas (GNG) [5].”
Mathematical Aspects of Divergence Based Vector Quantization Using Fr´ echet-Derivatives (2009, background): “[ 33 ]. The cost function of NG to be minimized writes as”
Local and Piecewise Affine Approaches to System Identification (2003, methodology): “The approaches described in [26, 76, 78, 82, 103, 148, 152, 154] fall into this category.”
Merge SOM for temporal data (2005, methodology): “Key words: Self-organizing map, temporal Kohonen map, sequence processing, recurrent models, neural gas, fractal encoding, finite automata, speaker identification, DNA splice site detection.”
Applying LSTM to Time Series Predictable through Time-Window Approaches (2000, methodology): “Neural Gas [17] : The Neural Gas algorithm for a Vector Quantization approach.”
A survey of kernel and spectral methods for clustering (2008, methodology): “Another technique that tries to minimize the distortion error is the neural gas algorithm [54], based on a soft adaptation rule.”