A novel piecewise multivariate function approximation method via universal matrix representation

Tuna, Süha; Tunga, Burcu

doi:10.1007/s10910-013-0179-y

Cited by 17 publications

(11 citation statements)

References 8 publications

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“…According to the universal function approximation theorem [16][17][18][19][20], f MAML can also be represented as an approximator for functions on x * .…”

Section: Problem Formulationmentioning

confidence: 99%

EW‐CACTUs‐MAML: A Robust Metalearning System for Rapid Classification on a Large Number of Tasks

Wang

Zhang

2022

Complexity

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This study aims to develop a robust metalearning system for rapid classification on a large number of tasks. The model-agnostic metalearning (MAML) with the CACTUs method (clustering to automatically construct tasks for unsupervised metalearning) is improved as EW-CACTUs-MAML after integrated with the entropy weight (EW) method. Few-shot mechanisms are introduced in the deep network for efficient learning of a large number of tasks. The process of implementation is theoretically interpreted as “gene intelligence.” Validation of EW-CACTUs-MAML on a typical dataset (Omniglot) indicates an accuracy of 97.42%, performing better than CACTUs-MAML (validation accuracy = 97.22%). At the end of this paper, the availability of our thoughts to improve another metalearning system (EW-CACTUs-ProtoNets) is also preliminarily discussed based on a cross-validation on another typical dataset (Miniimagenet).

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“…According to the universal function approximation theorem [16][17][18][19][20], f MAML can also be represented as an approximator for functions on x * .…”

Section: Problem Formulationmentioning

confidence: 99%

EW‐CACTUs‐MAML: A Robust Metalearning System for Rapid Classification on a Large Number of Tasks

Wang

Zhang

2022

Complexity

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“…The 3-D EMPR expansion is a finite sum. Thus, it involves exactly 2 3 EMPR components [21][22][23][24] . The graphical expression of the EMPR decomposition is given through Fig.…”

Section: Enhanced Multivariance Products Representationmentioning

confidence: 99%

Gene Teams are on the Field: Evaluation of Variants in Gene-Networks Using High Dimensional Modelling

Tuna

Güleç

Yücesan

et al. 2022

Preprint

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Variation is a key concept in every biological aspect, particularly in medical genetics. In this field, each genetic variant is evaluated mostly as an independent entity in respect to its clinical importance. This approach may be sufficient to detect the pathogenic variants in single-gene disorders. However, in most of the complex diseases, the combination of the variants in specific gene networks, rather than the presence of a certain single variant predominates. Therefore, while considering a complex disease, the disease status can be evaluated as the success of a team composed of certain variants. To apply this approach, we tested the efficiency of high-dimensional modelling of gene-network restricted variants in distinguishing a disease status. To evaluate the proposed method, we select two gene networks, mTOR and TGF-β. For each pathway, we generate 400 control and 400 patient group samples. The considered mTOR and TGF-β pathways contain 31 and 93 genes of varying sizes, respectively. We performed Chaos Game Representation to each gene sequence to obtain 2-D binary patterns. Produced patterns are ordered successively, and a 3-D tensor structure is achieved for each gene network. Features for each data sample are acquired by exploiting Enhanced Multivariance Products Representation to 3-D data. The features are split as training and testing vectors. The training vectors are employed to train a Support Vector Machines classification model. We manage to achieve more than 96% and 99% classification accuracies for mTOR and TGF-β networks, respectively, using a limited amount of training samples.

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“…The properties are almost same as the case of continuous functions except the need to change continuity with discreteness. Curious readers can find sufficiently detailed resources in scientific literature [12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Block tridiagonal matrix enhanced multivariance products representation (BTMEMPR)

Gündoğar

Demіralp

2017

J Math Chem

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The basic aim of this work is to design a new tridiagonal matrix enhanced multivariance products representation (TMEMPR) which uses not Cartesian vectors but matrices as the support entities. What we obtain after the construction of the representation has been a singular value decomposition like structure where the core matrix becomes a block tridiagonal matrix in contrast to the diagonal and tridiagonal matrix structures of the singular value decomposition of matrices and TMEMPR respectively. We have used support matrices in the construction and not directly orthogonality of the constructed support matrices but block orthogonality which means the mutual ortho normality of the columns of produced support matrices. Certain confirmative implementations finalize the paper.

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A novel piecewise multivariate function approximation method via universal matrix representation

Cited by 17 publications

References 8 publications

EW‐CACTUs‐MAML: A Robust Metalearning System for Rapid Classification on a Large Number of Tasks

EW‐CACTUs‐MAML: A Robust Metalearning System for Rapid Classification on a Large Number of Tasks

Gene Teams are on the Field: Evaluation of Variants in Gene-Networks Using High Dimensional Modelling

Block tridiagonal matrix enhanced multivariance products representation (BTMEMPR)

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