A Unified Framework for Structured Graph Learning via Spectral Constraints
Authors: Sandeep Kumar, Jiaxi Ying, José Vinícius de M. Cardoso, Daniel P. Palomar
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we present a number of comprehensive experiments for the evaluation of the performance of the proposed algorithms, i.e., SGL, SGA, and SGLA. The advantage of incorporating spectral information in the proposed framework is clearly illustrated. First, we introduce the experimental settings in Subsection 6.1 and the benchmarks for comparison in 6.2. Then the experiments are organized in the following three parts: Subsection 6.3 evalu- A Unified Framework for Structured Graph Learning via Spectral Constraints ates SGL for learning the following graph structures: grid, modular, and multi-component graphs; Subsection 6.4 shows bipartite graph learning with SGA, and Subsection 6.4 shows multi-component bipartite graph learning via SGLA. |
| Researcher Affiliation | Academia | Sandeep Kumar EMAIL Department of Industrial Engineering and Data Analytics The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong Jiaxi Ying EMAIL Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong Jos e Vin ıcius de M. Cardoso EMAIL Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong Daniel P. Palomar EMAIL Department of Electronic and Computer Engineering Department of Industrial Engineering and Data Analytics The Hong Kong University of Science and Technology Clear Water Bay, Hong Kong |
| Pseudocode | Yes | Algorithm 1: Updating rule for λ Input: d1, d2, . . . , dq, β, c1, and c2; 2 if λ satisfies c1 λ1 λq c2 then 3 return λ1, . . . , λq; 4 while not c1 λ1 λq c2 do 5 if c1 λ1 λr with at least one inequality strict and r 1 then 6 λ1 = = λr = c1; 7 else if λs λq c2 with at least one inequality strict and s q then 8 λs = = λq = c2; 9 else if λi λm with at least one inequality strict and 1 i m q then 10 di m = 1 m i+1 Pm j=i dj; 11 λi = = λm = 1 d2 i m + 4/β ; Output: λ1, . . . , λq. |
| Open Source Code | Yes | An open source R package containing the code for all the experiments is available at https://CRAN.R-project.org/package=spectralGraphTopology. |
| Open Datasets | Yes | Herein, the animals data set (Osherson et al., 1991; Lake and Tenenbaum, 2010) is considered to learn weighted graphs. Every node denotes a unique animal and edge weights represent similarities among them. ... We now consider the RNA-Seq Cancer Genome Atlas Research Network (Weinstein et al., 2013) data set available at UC-Irvine Machine Learning Database (Dheeru and Karra Taniskidou, 2017). |
| Dataset Splits | No | The paper uses synthetic data generated from an IGMRF model where the number of samples (n) is varied relative to the number of nodes (p), but no explicit training/validation/test splits are defined for reproducibility. For real datasets like the 'animals data set' and 'Cancer Genome data set', the paper describes using the data for tasks like clustering or graph learning without specifying how the data was partitioned into distinct training, validation, or test sets. |
| Hardware Specification | No | The paper discusses computational complexity (e.g., O(p^3)) and states that the most computationally demanding steps are eigenvalue decompositions, but it does not specify any particular hardware (GPU, CPU models, memory, or cloud instances) used for conducting the experiments. |
| Software Dependencies | Yes | Problem (44) is a convex optimization problem, that can be solved via disciplined convex programming frameworks such as CVX (Grant and Boyd, 2014; Fu et al., 2017a). ... CVX: Matlab software for disciplined convex programming, version 2.1, 2014. |
| Experiment Setup | Yes | For the experiments involving synthetic data, we create several synthetic data sets based on different graph structures G. ... We set c1 = 10-5 and c2 = 104. We observed that the experimental performances of the algorithms are not sensitive to different values of c1 and c2 as long as they are reasonably small and large, respectively. The choice for the hyperparameters β, γ, and α are discussed for each case separately. ... We use α = 0.0015 for both SGL and CGL. In addition, we fix β = 20 for SGL. ... In the case of SGL, we fix β = 10 for n/p <= 100, otherwise we fix β = 100. Additionally, we set α = 0. ... For the Cancer Genome data set: We apply SGL with k = 5 and β = 5. We also compare the SGL performance against the existing state-of-the-art methods for graph learning algorithms namely GLasso with α = 1.71 and GGL with α = 1.71. We also include in the performance comparison the graph-based clustering algorithm CLR with k = 5 and m = 10, where m is the number of neighbors taken into the consideration when creating an initial affinity matrix. Additionally, we conducted experiments with CLR for different choices of m = 3, 5, 7. |