Fast and Memory-Efficient Tucker Decomposition for Answering Diverse Time Range Queries

Jang, Jun-Gi; Kang, U

doi:10.1145/3447548.3467290

Cited by 16 publications

(11 citation statements)

References 19 publications

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“…The property of the vectorization (i.e., vec(AB) = (B T ⊗ I)vec(A)) is used. Then, G (3) = Y (3) (V H) is expressed as follows:…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…T ED T V(:, r) ⊗ H(:, r) according to the above equation. We compute G (3) = Y (3) (V H) row by row. Fig.…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…Fig. 7 shows how we compute G (3) (k, r). In computing G (3) , we first compute ED T V, and then obtain G (3) (k, :) for all k (line 18 in Algorithm 3).…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…7 shows how we compute G (3) (k, r). In computing G (3) , we first compute ED T V, and then obtain G (3) (k, :) for all k (line 18 in Algorithm 3). After computing G (3) , we update W by computing G (3) (V T V * H T H) † where † denotes the Moore-Penrose pseudoinverse (line 19 in Algorithm 3).…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…In computing G (3) , we first compute ED T V, and then obtain G (3) (k, :) for all k (line 18 in Algorithm 3). After computing G (3) , we update W by computing G (3) (V T V * H T H) † where † denotes the Moore-Penrose pseudoinverse (line 19 in Algorithm 3). We obtain S k whose diagonal elements correspond to the kth row vector of W (line 21 in Algorithm 3).…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

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DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors

Jang¹,

Kang²

2022

Preprint

Self Cite

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Given an irregular dense tensor, how can we efficiently analyze it? An irregular tensor is a collection of matrices whose columns have the same size and rows have different sizes from each other. PARAFAC2 decomposition is a fundamental tool to deal with an irregular tensor in applications including phenotype discovery and trend analysis. Although several PARAFAC2 decomposition methods exist, their efficiency is limited for irregular dense tensors due to the expensive computations involved with the tensor.In this paper, we propose DPAR2, a fast and scalable PARAFAC2 decomposition method for irregular dense tensors. DPAR2 achieves high efficiency by effectively compressing each slice matrix of a given irregular tensor, careful reordering of computations with the compression results, and exploiting the irregularity of the tensor. Extensive experiments show that DPAR2 is up to 6.0× faster than competitors on real-world irregular tensors while achieving comparable accuracy. In addition, DPAR2 is scalable with respect to the tensor size and target rank.

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“…The property of the vectorization (i.e., vec(AB) = (B T ⊗ I)vec(A)) is used. Then, G (3) = Y (3) (V H) is expressed as follows:…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…T ED T V(:, r) ⊗ H(:, r) according to the above equation. We compute G (3) = Y (3) (V H) row by row. Fig.…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

“…Fig. 7 shows how we compute G (3) (k, r). In computing G (3) , we first compute ED T V, and then obtain G (3) (k, :) for all k (line 18 in Algorithm 3).…”

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

Section: Next We Need To Obtain Left and Right Singular Vectors Ofmentioning

confidence: 99%

See 3 more Smart Citations

DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors

Jang¹,

Kang²

2022

Preprint

Self Cite

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Compact lossy compression of tensors via neural tensor-train decomposition

Kwon,

Ko,

Jung

et al. 2024

Knowl Inf Syst

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Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor compression algorithms are available, many of them rely on strong data assumptions regarding its order, sparsity, rank, and smoothness. In this work, we propose TensorCodec, a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions.TensorCodec incorporates three key ideas. The first idea is neural tensor-train decomposition (NTTD) where we integrate a recurrent neural network into Tensor-Train Decomposition to enhance its expressive power and alleviate the limitations imposed by the low-rank assumption. Another idea is to fold the input tensor into a higher-order tensor to reduce the space required by NTTD. Finally, the mode indices of the input tensor are reordered to reveal patterns that can be exploited by NTTD for improved approximation. In addition, we extend TensorCodec to enable the lossy compression of tensors with missing entries, often found in real-world datasets. Our analysis and experiments on 8 real-world datasets demonstrate that TensorCodec is (a) Concise: it gives up to $$7.38 \times $$ 7.38 × more compact compression than the best competitor with similar reconstruction error, (b) Accurate: given the same budget for compressed size, it yields up to $$3.33\times $$ 3.33 × more accurate reconstruction than the best competitor, (c) Scalable: Its empirical compression time is linear in the number of tensor entries, and it reconstructs each entry in logarithmic time. Our code and datasets are available at https://github.com/kbrother/TensorCodec.

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