Learning matrix quantization and relevance learning based on Schatten-p-norms

Bohnsack, Andrea; Domaschke, Kristin; Kaden, Marika; Lange, Mandy; Villmann, Thomas

doi:10.1016/j.neucom.2015.12.109

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…This concept allows to think about new processing steps inside and between capsules and hence to go beyond vectorial operations. This is however not a new concept in machine learning, but rather a well established property of PBs: a simple example is to use a matrix as the input to a VQ network, then the prototypes are matrices as well and hence, a respective matrix dissimilarity has to be chosen [88]. However, using more complex dissimilarity measures it is also possible to model prototypes as affine subspaces of the input space [89,90].…”

Section: Arbitrary Input Dimensions and Structured Data For Nns And V...mentioning

confidence: 99%

Prototype-based Neural Network Layers: Incorporating Vector Quantization

Saralajew,

Holdijk,

Rees

et al. 2018

Preprint

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Neural networks currently dominate the machine learning community and they do so for good reasons. Their accuracy on complex tasks such as image classification is unrivaled at the moment and with recent improvements they are reasonably easy to train. Nevertheless, neural networks are lacking robustness and interpretability. Prototype-based vector quantization methods on the other hand are known for being robust and interpretable. For this reason, we propose techniques and strategies to merge both approaches. This contribution will particularly highlight the similarities between them and outline how to construct a prototype-based classification layer for multilayer networks. Additionally, we provide an alternative, prototypebased, approach to the classical convolution operation. Numerical results are not part of this report, instead the focus lays on establishing a strong theoretical framework. By publishing our framework and the respective theoretical considerations and justifications before finalizing our numerical experiments we hope to jumpstart the incorporation of prototype-based learning in neural networks and vice versa.

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Section: Arbitrary Input Dimensions and Structured Data For Nns And V...mentioning

confidence: 99%

Prototype-based Neural Network Layers: Incorporating Vector Quantization

Saralajew,

Holdijk,

Rees

et al. 2018

Preprint

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“…21 However, the LVQ neural network cannot easily obtain ideal recognition accuracy and low computational complexity when the sample space is relatively large. 24 Therefore, an I-LVQ neural network is considered and applied to recognize driving cycle online.…”

Section: Dcr Model Based On the I-lvq Neural Networkmentioning

confidence: 99%

A strategy of electrical energy management for internal combustion engine vehicle based on driving cycle recognition and electrical load perception

Wang

Zhang

et al. 2018

Advances in Mechanical Engineering

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Electrical energy consumption is an important component of energy consumption for internal combustion engine vehicle, which directly affects the fuel economy. A bus-based electrical energy management system is built, and an electrical energy management strategy based on driving cycle recognition and electrical load perception is presented to achieve the refined management of vehicle energy. Six typical driving cycles are selected to establish an improved learning vector quantization neural network model for driving cycle recognition. The corresponding model training algorithm is designed by utilizing a similar driving cycle classification and the gradient optimization so that the better recognition accuracy and the less computation intensity can be obtained. An online recognition mechanism based on sliding time window is devised, and the optimal time window length is determined. To minimize fuel consumption, a dynamic optimal regulation strategy for the output power of the alternator and battery, which considers driving cycle recognition and electrical load perception, is proposed. Experimental results show that the strategy can effectually improve the vehicle fuel economy according to the driving cycle and the electrical load change and decrease the fuel consumption per 100 miles of vehicle.

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“…Hofmann et al (2015) propose kernel robust soft LVQ (RSLVQ) which is capable of classifying complex data sets [23]. They describe a general gram matrix including low rank approximations and how the models could be implemented in this approach.…”

Section: Some Variants Of Learning Vector Quantizationmentioning

confidence: 99%

“…They describe a general gram matrix including low rank approximations and how the models could be implemented in this approach. Bohnsack et al (2016) improve LVQ method in order to get the classification of matrix data based on matrix norms [24]. In general learning algorithms are based on vectorial approach, the contribution of the article is to work for matrix norms.…”

Section: Some Variants Of Learning Vector Quantizationmentioning

confidence: 99%

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Geometrical Modification of Learning Vector Quantization Method for Solving Classification Problems

Günel¹,

Aşlıyan²,

Gör³

2016

SDÜ Fen Bil Enst Der

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Abstract:In this paper, a geometrical scheme is presented to show how to overcome an encountered problem arising from the use of generalized delta learning rule within competitive learning model. It is introduced a theoretical methodology for describing the quantization of data via rotating prototype vectors on hyper-spheres.The proposed learning algorithm is tested and verified on different multidimensional datasets including a binary class dataset and two multiclass datasets from the UCI repository, and a multiclass dataset constructed by us. The proposed method is compared with some baseline learning vector quantization variants in literature for all domains. Large number of experiments verify the performance of our proposed algorithm with acceptable accuracy and macro f 1 scores. Sınıflandırma Problemlerinin Çözümü için Destekleyici Ögrenmeli Vektör NicemlemeMetodunun Geometrik Modifikasyonu Anahtar KelimelerMakine ögrenmesi, Destekleyici ögrenmeli vektör nicemleme, Geometrik ögrenme yaklaşımı Özet: Bu çalışmada yarışmacı ögrenme modelinde kullanılan genelleştirilmiş delta ögrenme kuralı ile ortaya çıkan problemin üstesinden gelmek için geometrik bir yaklaşım önerilmiştir. Veri nicemlemesinin izah edilebilmesi için prototip vektörlerinin hiper-küreler üzerinde döndürülmesi esasına dayalı teorik bir metodoloji geliştirilmiştir. Önerilen ögrenme algoritması UCI veri havuzundan alınmış bir tanesi ikili sınıflandırma veri seti ve iki tanesi çok sınıflı olan veri setleri ile bir tanesi tarafımızdan hazırlanan çoklu sınıf veriseti üzerinde test edilmiş ve geçerliligi denetlenmiştir. Önerilen metot, literatürde referans alınan bazı destekleyici ögrenmeli vektör nicemleme ag varyasyonları ile farklı alanlarda karşılaştırılmıştır. Çok sayıdaki deneysel çalışmalar, makul dogruluk degerleri ve makro f 1 skorları ile önerilen algoritmanın performansını dogrulamaktadır.

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Learning matrix quantization and relevance learning based on Schatten-p-norms

Cited by 6 publications

References 25 publications

Prototype-based Neural Network Layers: Incorporating Vector Quantization

Prototype-based Neural Network Layers: Incorporating Vector Quantization

A strategy of electrical energy management for internal combustion engine vehicle based on driving cycle recognition and electrical load perception

Geometrical Modification of Learning Vector Quantization Method for Solving Classification Problems

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