Extending stability through hierarchical clusters in Echo State Networks
Echo State Networks (ESN) are reservoir networks that satisfy well-established criteria for stability when constructed as feedforward networks. Recent evidence suggests that stability criteria are altered in the presence of reservoir substructures, such as clusters. Understanding how the reservoir a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2010-07-01
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| Series: | Frontiers in Neuroinformatics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fninf.2010.00011/full |
| _version_ | 1818566081940291584 |
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| author | Sarah Jarvis Sarah Jarvis Stefan Rotter Stefan Rotter Ulrich Egert Ulrich Egert |
| author_facet | Sarah Jarvis Sarah Jarvis Stefan Rotter Stefan Rotter Ulrich Egert Ulrich Egert |
| author_sort | Sarah Jarvis |
| collection | DOAJ |
| description | Echo State Networks (ESN) are reservoir networks that satisfy well-established criteria for stability when constructed as feedforward networks. Recent evidence suggests that stability criteria are altered in the presence of reservoir substructures, such as clusters. Understanding how the reservoir architecture affects stability is thus important for the appropriate design of any ESN. To quantitatively determine the influence of the most relevant network parameters, we analysed the impact of reservoir substructures on stability in hierarchically clustered ESNs (HESN), as they allow a smooth transition from highly structured to increasingly homogeneous reservoirs. Previous studies used the largest eigenvalue of the reservoir connectivity matrix (spectral radius) as a predictor for stable network dynamics. Here, we evaluate the impact of clusters, hierarchy and intercluster connectivity on the predictive power of the spectral radius for stability. Both hierarchy and low relative cluster sizes extend the range of spectral radius values, leading to stable networks, while increasing intercluster connectivity decreased maximal spectral radius. |
| first_indexed | 2024-12-14T01:49:11Z |
| format | Article |
| id | doaj.art-31c7f3a8757942bf81c61574d5b5eb5f |
| institution | Directory Open Access Journal |
| issn | 1662-5196 |
| language | English |
| last_indexed | 2024-12-14T01:49:11Z |
| publishDate | 2010-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Neuroinformatics |
| spelling | doaj.art-31c7f3a8757942bf81c61574d5b5eb5f2022-12-21T23:21:26ZengFrontiers Media S.A.Frontiers in Neuroinformatics1662-51962010-07-01410.3389/fninf.2010.00011559Extending stability through hierarchical clusters in Echo State NetworksSarah Jarvis0Sarah Jarvis1Stefan Rotter2Stefan Rotter3Ulrich Egert4Ulrich Egert5University of FreiburgBernstein Center FreiburgUniversity of FreiburgBernstein Center FreiburgUniversity of FreiburgBernstein Center FreiburgEcho State Networks (ESN) are reservoir networks that satisfy well-established criteria for stability when constructed as feedforward networks. Recent evidence suggests that stability criteria are altered in the presence of reservoir substructures, such as clusters. Understanding how the reservoir architecture affects stability is thus important for the appropriate design of any ESN. To quantitatively determine the influence of the most relevant network parameters, we analysed the impact of reservoir substructures on stability in hierarchically clustered ESNs (HESN), as they allow a smooth transition from highly structured to increasingly homogeneous reservoirs. Previous studies used the largest eigenvalue of the reservoir connectivity matrix (spectral radius) as a predictor for stable network dynamics. Here, we evaluate the impact of clusters, hierarchy and intercluster connectivity on the predictive power of the spectral radius for stability. Both hierarchy and low relative cluster sizes extend the range of spectral radius values, leading to stable networks, while increasing intercluster connectivity decreased maximal spectral radius.http://journal.frontiersin.org/Journal/10.3389/fninf.2010.00011/fullclustered networksfeedforwardreservoir networks |
| spellingShingle | Sarah Jarvis Sarah Jarvis Stefan Rotter Stefan Rotter Ulrich Egert Ulrich Egert Extending stability through hierarchical clusters in Echo State Networks Frontiers in Neuroinformatics clustered networks feedforward reservoir networks |
| title | Extending stability through hierarchical clusters in Echo State Networks |
| title_full | Extending stability through hierarchical clusters in Echo State Networks |
| title_fullStr | Extending stability through hierarchical clusters in Echo State Networks |
| title_full_unstemmed | Extending stability through hierarchical clusters in Echo State Networks |
| title_short | Extending stability through hierarchical clusters in Echo State Networks |
| title_sort | extending stability through hierarchical clusters in echo state networks |
| topic | clustered networks feedforward reservoir networks |
| url | http://journal.frontiersin.org/Journal/10.3389/fninf.2010.00011/full |
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