Optimal Dictionary for Least Squares Representation
Authors: Mohammed Rayyan Sheriff, Debasish Chatterjee
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Example 1. Let V ˆV1 V2 be a random vector taking values in R2... Elementary calculations lead to ΣV : Eρr V V Js ˆ17{6 20{9 20{9 11{6 . We employed the procedure described in Algorithm 2 for the given matrix ΣV and K 3 in matlab. An optimal dictionary ty 1, y 2, y 3u was obtained, with... the optimum value of the objective function was reported to be 1.8930. |
| Researcher Affiliation | Academia | Mohammed Rayyan Sheriff EMAIL Debasish Chatterjee EMAIL Systems and Control Engineering IIT Bombay Mumbai 400076, India |
| Pseudocode | Yes | Algorithm 1: Calculation of orthonormal bases à la Theorem 14 Algorithm 2: ℓ2-optimal dictionary for the case XV Rn. Algorithm 3: A procedure to obtain ℓ2-optimal dictionary. |
| Open Source Code | No | No explicit statement or link for open-source code is provided in the paper. |
| Open Datasets | No | Example 1 uses a custom defined distribution: Let V ˆV1 V2 be a random vector taking values in R2, with V1 and V2 being independent random variables. Let the density functions of V1 and V2 be ρV1pvq 2pv 1q1r1,2spvq and ρV2pvq 2p2 vq1r1,2spvq, respectively. |
| Dataset Splits | No | The paper does not use any specific dataset with defined splits for experiments. The numerical example relies on a mathematically defined random vector distribution, not a partitioned dataset. |
| Hardware Specification | No | The paper mentions the use of 'matlab' for a numerical example but provides no specific details about the hardware used for computations (e.g., CPU, GPU models, memory). |
| Software Dependencies | No | The paper mentions the use of 'matlab' in Example 1 but does not specify a version number or other software dependencies with version details. |
| Experiment Setup | Yes | Example 1. Let V ˆV1 V2 be a random vector taking values in R2... Elementary calculations lead to ΣV : Eρr V V Js ˆ17{6 20{9 20{9 11{6 . We employed the procedure described in Algorithm 2 for the given matrix ΣV and K 3 in matlab. |