Union of Low-Rank Tensor Spaces: Clustering and Completion
Authors: Morteza Ashraphijuo, Xiaodong Wang
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we provide a fundamental theoretical analysis for the two important mentioned problems. One of the main ideas behind our analysis for the tensor space clustering problem is to take advantage of the condition on the sampling rate that guarantees the unique completability for the tensor completion problem. Then, we use the unique completability property on each of the tensors to correctly identify whether a tensor space fits in that tensor. |
| Researcher Affiliation | Academia | Morteza Ashraphijuo EMAIL Columbia University New York, NY 10027, USA Xiaodong Wang EMAIL Columbia University New York, NY 10027, USA |
| Pseudocode | No | The paper presents mathematical formulations, lemmas, theorems, and proofs related to tensor analysis. It does not include any explicitly labeled pseudocode blocks or algorithms in a structured format. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing code or a link to a code repository for the methodology described. It mentions that "algorithms such as the one developed in (Ashraphijuo et al., 2019) can be developed" but this refers to other work or potential future development, not the immediate release of code for this paper's contributions. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical analysis of tensor spaces. It does not use specific datasets in empirical experiments, and therefore, no information about public datasets is provided. |
| Dataset Splits | No | The paper is a theoretical work that does not involve empirical experiments on specific datasets. Therefore, there is no mention of dataset splits (training, validation, test) in the text. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical analysis rather than computational experiments. As such, no specific hardware (e.g., GPUs, CPUs, or other computational resources) used for running experiments is mentioned. |
| Software Dependencies | No | The paper is a theoretical study and does not describe any software implementation or empirical experiments. Therefore, no specific software dependencies or version numbers are mentioned. |
| Experiment Setup | No | The paper provides a theoretical analysis of tensor clustering and completion problems. It does not include details of an experimental setup, hyperparameters, or training configurations, as it does not present empirical results. |