Semantic sensitive tensor factorization

Nakatsuji, Makoto; Toda, Hiroyuki; Sawada, Hiroshi; Zheng, Jin; Hendler, James A.

doi:10.1016/j.artint.2015.09.001

Cited by 16 publications

(15 citation statements)

References 13 publications

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“…Since the damping factor is 0 ≤ λ < 1, as described in (18). Consequently, it is clear that Equation (8) gives the upper estimate for the responsibilities in the iterations.…”

Section: Definitionmentioning

confidence: 96%

“…If rt(xi, xj) > 0 or rt−1(xi, xj) > 0, the subset j , which includes data point pair (xi, xj), is added to the availability set of the (t + 1)-th iteration t+1, from the first condition of Definition 7 (lines [15][16]. As for availability, if at(xj, xi) = at−1(xj, xi) for a data point pair such that (xj, xi) ∈ t, i is added to the availability set of the (t+1)-th iteration t+1, from the second condition of Definition 7 (lines [18][19]. In addition, j is added to the responsibility set of the (t + 1)-th iteration t+1 when xj ∈ {x t−1 , x t−1 }, from the second condition of Definition 6 (lines [20][21].…”

Section: Clustering Algorithmmentioning

confidence: 99%

“…In order to obtain the clustering results, Affinity Propagation performs iterative computations the same as other approaches in machine learning [11,17,18]. Affinity Propagation is derived from a standard inference technique on a factor graph, and uses the max-product algorithm to perform maximum a posteriori inference [13].…”

Section: Preliminariesmentioning

confidence: 99%

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Adaptive Message Update for Fast Affinity Propagation

Fujiwara¹,

Nakatsuji

Shiokawa³

et al. 2015

Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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Affinity Propagation is a clustering algorithm used in many applications. It iteratively updates messages between data points until convergence. The message updating process enables Affinity Propagation to have higher clustering quality compared with other approaches. However, its computation cost is high; it is quadratic in the number of data points. This is because it updates the messages of all data point pairs. This paper proposes an efficient algorithm that guarantees the same clustering results as the original algorithm. Our approach, F-AP, is based on two ideas: (1) it computes upper and lower estimates to limit the messages to be updated in each iteration, and (2) it dynamically detects converged messages to efficiently skip unneeded updates. Experiments show that F-AP is much faster than previous approaches with no loss in clustering performance.

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“…Since the damping factor is 0 ≤ λ < 1, as described in (18). Consequently, it is clear that Equation (8) gives the upper estimate for the responsibilities in the iterations.…”

Section: Definitionmentioning

confidence: 96%

Section: Clustering Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Message Update for Fast Affinity Propagation

Fujiwara¹,

Nakatsuji

Shiokawa³

et al. 2015

Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Self Cite

View full text Add to dashboard Cite

show abstract

“…The patternoriented tensor decomposition method is used to decompose these tensors, and the obtained core tensors are used in the subsequent deep neural network classification model. A tensor is a data structure similar to a vector or matrix [18,19]. Tensor decomposition is a dimensionality reduction operation on the tensor [20,21].…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…where { } is a set of factor matrices, ∈ R × . The factor matrices are all column orthogonal ones [19]. Furthermore, is the core tensor, ∈ R 1 × 2 ×⋅⋅⋅× .…”

Section: Definition 8 (Frobenius Norm Of a Tensor) Given An -Mode Tementioning

confidence: 99%

Learning Users’ Intention of Legal Consultation through Pattern-Oriented Tensor Decomposition with Bi-LSTM

Guo

Zhang

2019

Wireless Communications and Mobile Computing

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Online legal consultation plays an increasingly important role in the modern rule-of-law society. This study aims to understand the intention of legal consultation of users with different language expressions and legal knowledge background. A critical issue is a method through which users’ legal consultation data are classified and the feature of each category is extracted. Traditional classification methods rely considerably on lexical and syntactic features and frequently require strict sentence formatting, which eliminates substantial energy and may not be universally applicable. We aim to extract the patterns of users’ consultation on different categories, which minimally depend on lexical, syntax, and sentence formatting. However, research in this area has rarely been conducted in previous legal advisory service studies. In this study, a classification approach for multiclass users’ intention based on pattern-oriented tensor decomposition and Bi-LSTM is proposed, and each user’s legal consulting statement is expressed as a tensor. Moreover, we propose a pattern-oriented tensor decomposition method that can obtain a core tensor that approximates the patterns of users’ consultation. These patterns can improve the accuracy of classifying users’ intention of legal consultation. We use Bi-LSTM to automatically learn and optimize these patterns. Evidently, Bi-LSTM with a pattern-oriented tensor decomposition layer performs better than a recurrent neural network only. Results show that our method is more accurate than the previous work, and the factor matrix and core tensor calculated by the pattern-oriented tensor decomposition are interpretable.

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Multi‐view side information‐incorporated tensor completion

Tian

Xia

2022

Numerical Linear Algebra App

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Tensor completion originates in numerous applications where data utilized are of high dimensions and gathered from multiple sources or views. Existing methods merely incorporate the structure information, ignoring the fact that ubiquitous side information may be beneficial to estimate the missing entries from a partially observed tensor. Inspired by this, we formulate a sparse and low‐rank tensor completion model named SLRMV. The ‐norm instead of its relaxation is used in the objective function to constrain the sparseness of noise. The CP decomposition is used to decompose the high‐quality tensor, based on which the combination of Schatten ‐norm on each latent factor matrix is employed to characterize the low‐rank tensor structure with high computation efficiency. Diverse similarity matrices for the same factor matrix are regarded as multi‐view side information for guiding the tensor completion task. Although SLRMV is a nonconvex and discontinuous problem, the optimality analysis in terms of Karush‐Kuhn‐Tucker (KKT) conditions is accordingly proposed, based on which a hard‐thresholding based alternating direction method of multipliers (HT‐ADMM) is designed. Extensive experiments remarkably demonstrate the efficiency of SLRMV in tensor completion.

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Semantic sensitive tensor factorization

Cited by 16 publications

References 13 publications

Adaptive Message Update for Fast Affinity Propagation

Adaptive Message Update for Fast Affinity Propagation

Learning Users’ Intention of Legal Consultation through Pattern-Oriented Tensor Decomposition with Bi-LSTM

Multi‐view side information‐incorporated tensor completion

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