An Analysis of Tensor Models for Learning on Structured Data

Nickel, Maximilian; Tresp, Volker

doi:10.1007/978-3-642-40991-2_18

Cited by 12 publications

(13 citation statements)

References 22 publications

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“…The reason for feature construction is that the training data determines the highest accuracy that can be achieved. Appropriate feature construction can increase the useful information in the data, which helps to improve the classification accuracy of the model [44][45][46]. Therefore, based on the original features, the accuracy of the classification algorithm is improved by constructing new features.…”

Section: Feature Construction Methodsmentioning

confidence: 99%

Research on a Mixed Gas Classification Algorithm Based on Extreme Random Tree

Zhao

Chen

et al. 2019

Applied Sciences

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Because of the low accuracy of the current machine olfactory algorithms in detecting two mixed gases, this study proposes a hybrid gas detection algorithm based on an extreme random tree to greatly improve the classification accuracy and time efficiency. The method mainly uses the dynamic time warping algorithm (DTW) to perform data pre-processing and then extracts the gas characteristics from gas signals at different concentrations by applying a principal component analysis (PCA). Finally, the model is established by using a new extreme random tree algorithm to achieve the target gas classification. The sample data collected by the experiment was verified by comparison experiments with the proposed algorithm. The analysis results show that the proposed DTW algorithm improves the gas classification accuracy by 26.87%. Compared with the random forest algorithm, extreme gradient boosting (XGBoost) algorithm and gradient boosting decision tree (GBDT) algorithm, the accuracy rate increased by 4.53%, 5.11% and 8.10%, respectively, reaching 99.28%. In terms of the time efficiency of the algorithms, the actual runtime of the extreme random tree algorithm is 66.85%, 90.27%, and 81.61% lower than that of the random forest algorithm, XGBoost algorithm, and GBDT algorithm, respectively, reaching 103.2568 s.

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Section: Feature Construction Methodsmentioning

confidence: 99%

Research on a Mixed Gas Classification Algorithm Based on Extreme Random Tree

Zhao

Chen

et al. 2019

Applied Sciences

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“…This allows us to define, in a conceptually simple way, the hypothesis class H G corresponding to the family of linear models whose weights are represented using an arbitrary TN structure G. We then proceed to deriving upper bounds on the VC/pseudodimension and generalization error of the class H G . These bounds follow from a classical result from Warren [64] which was previously used to obtain generalization bounds for neural networks [3], matrix completion [52] and tensor completion [39]. The bounds we derive naturally relate the capacity of H G to the underlying graph structure G through the number of nodes and effective number of parameters of the TN.…”

Section: Introductionmentioning

confidence: 90%

“…Related work Machine learning models using low-rank parametrization of the weights have been investigated (mainly from a practical perspective) for various decomposition models, including low-rank matrices [34,47,65], CP [1,35,6], Tucker [33,15,25,48], tensor train [46,9,42,54,17,51,10,63,66] and PEPS [11]. From a more theoretical perspective, generalization bounds for matrix and tensor completion have been derived in [52,39] (based on the Tucker format for the tensor case). A bound on the VC-dimension of low-rank matrix classifiers was derived in [65] and a bound on the pseudo-dimension of regression functions whose weights have low Tucker rank was given in [48] (for both these cases, we show that our results improve over these previous bounds, see Section 4.2).…”

Section: Introductionmentioning

confidence: 99%

Lower and Upper Bounds on the VC-Dimension of Tensor Network Models

Khavari,

Rabusseau

2021

Preprint

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Tensor network (TN) methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. TN methods can for example be used to efficiently learn linear models in exponentially large feature spaces [54]. In this work, we derive upper and lower bounds on the VC-dimension and pseudo-dimension of a large class of TN models for classification, regression and completion. Our upper bounds hold for linear models parameterized by arbitrary TN structures, and we derive lower bounds for common tensor decomposition models (CP, Tensor Train, Tensor Ring and Tucker) showing the tightness of our general upper bound. These results are used to derive a generalization bound which can be applied to classification with low-rank matrices as well as linear classifiers based on any of the commonly used tensor decomposition models. As a corollary of our results, we obtain a bound on the VC-dimension of the matrix product state classifier introduced in [54] as a function of the so-called bond dimension (i.e. tensor train rank), which answers an open problem listed by Cirac, Garre-Rubio and Pérez-García in [12].Preprint. Under review.

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“…Thus tensor factorizations can easily integrate multiple data modalities, reduce dimensionality and identify latent groups in each mode for meaningful summarization of both features and instances as propounded by [36] in medical data analysis. According to Nickel et al [37] tensor as a factorization tool has a collective entity for filtering hidden factors related to massive data. In Reference [38], it is proven that, tensor-based methods is ideal for mitigating personalized tagging and link prediction recommendation.…”

Section: General Frameworkmentioning

confidence: 99%

“…In the Google's wide and deep model [44], a generalized linear model was used to capture latent features in the wide perspective. In this paper, tensor factorization model which is non-linear in nature is chosen to be a platform model as a result of the fact that it has appealing property to efficiently impose structure on the vector space representation of the data as propounded by [37]. We will regard an array of numbers with more than 2 dimensions as a tensor.…”

Section: Multi-task Tensor Factorizationmentioning

confidence: 99%

Simple and Efficient Computational Intelligence Strategies for Effective Collaborative Decisions

Aboagye

Kumar

2019

Future Internet

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We approach scalability and cold start problems of collaborative recommendation in this paper. An intelligent hybrid filtering framework that maximizes feature engineering and solves cold start problem for personalized recommendation based on deep learning is proposed in this paper. Present e-commerce sites mainly recommend pertinent items or products to a lot of users through personalized recommendation. Such personalization depends on large extent on scalable systems which strategically responds promptly to the request of the numerous users accessing the site (new users). Tensor Factorization (TF) provides scalable and accurate approach for collaborative filtering in such environments. In this paper, we propose a hybrid-based system to address scalability problems in such environments. We propose to use a multi-task approach which represent multiview data from users, according to their purchasing and rating history. We use a Deep Learning approach to map item and user inter-relationship to a low dimensional feature space where item-user resemblance and their preferred items is maximized. The evaluation results from real world datasets show that, our novel deep learning multitask tensor factorization (NeuralFil) analysis is computationally less expensive, scalable and addresses the cold-start problem through explicit multi-task approach for optimal recommendation decision making.

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An Analysis of Tensor Models for Learning on Structured Data

Cited by 12 publications

References 22 publications

Research on a Mixed Gas Classification Algorithm Based on Extreme Random Tree

Research on a Mixed Gas Classification Algorithm Based on Extreme Random Tree

Lower and Upper Bounds on the VC-Dimension of Tensor Network Models

Simple and Efficient Computational Intelligence Strategies for Effective Collaborative Decisions

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