Tensor Synthetic Datasets | 100×100 ×100 | 500×500×500 | 800×800×800 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Initial dimension size (I=J=K) | 10 | 50 | 80 | 100 | 250 | 400 | 100 | 400 | 640 | ||
Initial Density 60% | Static | IM-PARAFAC | 1.76 | 1.62 | 2.66 | 126.84 | 131.49 | 270.04 | 540.79 | 543.60 | 1050.21 |
SamBaTen (CP-ALS) | 1.97 | 1.98 | 2.77 | 235.55 | 211.94 | 553.88 | 1398.33 | 1323.99 | 2416.36 | ||
InParTen2-Static | 0.74 | 0.77 | 1.08 | 36.94 | 48.28 | 72.14 | 180.63 | 177.64 | 357.48 | ||
Dynamic | SamBaTen (Incremental) | 1.16 | 1.13 | 1.21 | 42.97 | 66.47 | 89.53 | 351.21 | 477.21 | 652.03 | |
InParTen2 | |||||||||||
Initial Density 20% | Static | IM-PARAFAC | 1.76 | 1.27 | 1.39 | 125.80 | 98.03 | 110.03 | 570.94 | 397.80 | 459.99 |
SamBaTen (CP-ALS) | 1.97 | 1.98 | 2.72 | 264.09 | 194.66 | 265.96 | 1403.27 | 973.12 | 990.81 | ||
InParTen2-Static | 0.97 | 0.86 | 0.88 | 46.03 | 35.58 | 39.55 | 146.53 | 108.07 | 119.39 | ||
Dynamic | SamBaTen (Incremental) | 1.19 | 1.04 | 0.99 | 39.69 | 35.18 | 30.91 | 293.2 | 250.71 | 182.81 | |
InParTen2 |
Tensor Synthetic Datasets | 100 × 100 ×100 | 500× 500×500 | Tensor 800×800×800 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Initial size (I=J=K) | 10 | 50 | 80 | 100 | 250 | 400 | 100 | 400 | 640 | ||
Initial Density 60% | Static | IM-PARAFAC | 0.82 | 0.69 | 0.57 | 0.82 | 0.73 | 0.57 | 0.83 | 0.70 | 0.57 |
SamBaTen (CP-ALS) | 0.82 | 0.71 | 0.56 | 0.82 | 0.72 | 0.57 | 0.83 | 0.72 | 0.57 | ||
InParTen2-Static | 0.82 | 0.69 | 0.56 | 0.82 | 0.72 | 0.57 | 0.82 | 0.72 | 0.56 | ||
Dynamic | SamBaTen (Incremental) | 0.85 | 0.78 | 0.57 | 0.83 | 0.80 | 0.57 | 0.83 | 0.79 | 0.58 | |
InParTen2 | 0.82 | 0.69 | 0.56 | 0.82 | 0.71 | 0.57 | 0.83 | 0.72 | 0.56 | ||
Initial Density 20% | Static | IM-PARAFAC | 0.82 | 0.82 | 0.82 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
SamBaTen (CP-ALS) | 0.82 | 0.82 | 0.82 | 0.82 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | ||
InParTen2-Static | 0.82 | 0.82 | 0.82 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 | ||
Dynamic | SamBaTen (Incremental) | 0.84 | 0.85 | 0.83 | 0.85 | 0.98 | 0.87 | 1.02 | 0.88 | 0.86 | |
InParTen2 | 0.82 | 0.82 | 0.83 | 0.82 | 0.84 | 0.84 | 0.84 | 0.84 | 0.84 |
Execution Time(min) | Relative Error | ||||||
---|---|---|---|---|---|---|---|
YELP | MovieLens | Netflix | YELP | MovieLens | Netflix | ||
Static | IM-PARAFAC | 7.44 | 76.03 | 924.91 | 0.98 | 0.75 | 0.79 |
SamBaTen (CP-ALS) | 44.71 | 518.73 | N.A. | 0.98 | 0.99 | N.A. | |
InParTen2-Static | 2.047 | 29.03 | 893.33 | 0.96 | 0.76 | 0.79 | |
Dynamic | SamBaTen (incremental) | 36.42 | 36.65 | N.A. | 0.98 | 0.91 | N.A. |
InParTen2 | 1.94 | 23.50 | 246.63 | 0.97 | 0.80 | 0.80 |
Tensor Synthetic Datasets | 100 × 100 ×100 | 500× 500×500 | 800×800×800 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Density(%) | 5% | 10% | 20% | 5% | 10% | 20% | 5% | 10% | 20% | ||
Initial Density 60% | Static | IM-PARAFAC | 1.19 | 1.37 | 1.62 | 78.5 | 95.5 | 131.5 | 318.9 | 402.3 | 543.6 |
SamBaTen (CP-ALS) | 1.55 | 1.74 | 1.98 | 134.9 | 183.8 | 211.9 | 657.6 | 836.2 | 1323.9 | ||
InParTen2-Static | |||||||||||
Dynamic | SamBaTen | 1.07 | 1.07 | 1.13 | 35.5 | 45.7 | 66.5 | 301.5 | 354.2 | 477.2 | |
InParTen2 | |||||||||||
Initial Density 20% | Static | IM-PARAFAC | 0.87 | 0.99 | 1.27 | 40.9 | 58.5 | 98.03 | 167.9 | 246.3 | 397.8 |
SamBaTen (CP-ALS) | 1.42 | 1.48 | 1.98 | 41.9 | 116.2 | 194.66 | 345.6 | 554.3 | 973.1 | ||
InParTen2-Static | |||||||||||
Dynamic | SamBaTen | 0.92 | 0.96 | 1.04 | 18.3 | 24.9 | 35.2 | 87.7 | 125.9 | 250.7 | |
InParTen2 |
Tensor Synthetic Datasets | 100 × 100 ×100 | 500× 500×500 | 800×800×800 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Density | 5% | 10% | 20% | 5% | 10% | 20% | 5% | 10% | 20% | ||
Initial Density 60% | Static | IM-PARAFAC | 0.63 | 0.67 | 0.69 | 0.64 | 0.72 | 0.73 | 0.62 | 0.70 | 0.70 |
SamBaTen (CP-ALS) | 0.65 | 0.70 | 0.69 | 0.66 | 0.71 | 0.72 | 0.66 | 0.71 | 0.72 | ||
InParTen2-Static | 0.63 | 0.67 | 0.71 | 0.60 | 0.73 | 0.72 | 0.61 | 0.69 | 0.72 | ||
Dynamic | SamBaTen (Incremental) | 0.67 | 0.69 | 0.78 | 0.67 | 0.75 | 0.80 | 0.67 | 0.74 | 0.79 | |
InParTen2 | 0.61 | 0.67 | 0.69 | 0.65 | 0.73 | 0.71 | 0.63 | 0.72 | 0.72 | ||
Initial Density 20% | Static | IM-PARAFAC | 0.87 | 0.87 | 0.82 | 0.90 | 0.89 | 0.83 | 0.89 | 0.88 | 0.83 |
SamBaTen (CP-ALS) | 0.88 | 0.87 | 0.82 | 0.89 | 0.89 | 0.83 | 0.89 | 0.89 | 0.83 | ||
InParTen2-Static | 0.87 | 0.87 | 0.82 | 0.87 | 0.89 | 0.83 | 0.90 | 0.88 | 0.83 | ||
Dynamic | SamBaTen (Incremental) | 0.88 | 0.89 | 0.85 | 0.91 | 0.93 | 0.98 | 0.89 | 0.93 | 0.88 | |
InParTen2 | 0.86 | 0.89 | 0.82 | 0.91 | 0.90 | 0.84 | 0.87 | 0.90 | 0.86 |
Static tensor decomposition | Incremental (Single-aspect) | Incremental (Multi-aspect) | Distributed | Scalability | |
---|---|---|---|---|---|
√ | |||||
√ | |||||
√ | √ | ||||
√ | √ | √ | |||
√ | √ | ||||
√ | √ | ||||
InParTen2 | √ | √ | √ | √ | √ |
Data Name | Data type | Total Dimension | Initial Dimension | Non-zero | File size |
---|---|---|---|---|---|
YELP | User×Location×Time | 70,817×15,579×108 | 70,815×15,572×20 | 334,166 | 5.6MB |
MovieLens | User×Movie×Time | 71,567×10,681×157 | 71,559×9,717×5 | 10,000,054 | 187MB |
Netflix | User×Movie×Time | 2,649,429×17,770 ×2,182 | 2,648,623×17,764×50 | 98,754,343 | 1.8GB |
Symbols | Definitions |
---|---|
Tensor | |
Mode-n unfolding matrix of tensor | |
|| | Frobenius norm of tensor |
nnz( | Number of non-zero elements in tensor |
⊗ | Kronecker product |
⊙ | Khatri-Rao product |
* | Hadamard product (Element-wise product) |
† | Pseudo inverse |