Geodesic Distance Function Learning via Heat Flow on Vector Fields
Authors: Binbin Lin, Ji Yang, Xiaofei He, Jieping Ye
ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm. In this section, we empirically evaluate the effectiveness of our proposed Geodesic Distance Learning (GDL) algorithm in comparison with three representative distance metric learning algorithms. |
| Researcher Affiliation | Academia | Binbin Lin BINBIN.LIN@ASU.EDU Ji Yang YANGJI9181@GMAIL.COM Xiaofei He XIAOFEIHE@CAD.ZJU.EDU.CN Jieping Ye JIEPING.YE@ASU.EDU Center for Evolutionary Medicine and Informatics, Arizona State University, Tempe, AZ 85287, USA State Key Lab of CAD&CG, College of Computer Science, Zhejiang University Hangzhou 310058, China |
| Pseudocode | Yes | Algorithm 1 GDL (Geodesic Distance Learning) Require: Data sample X = (x1, . . . , xn) Rm n and a base point xq, 1 q n. Ensure: f = (f1, . . . , fn) Rn for i = 1 to n do Compute the tangent space coordinates Ti Rm d by using PCA end for Set an initial vector field V 0 via Eq. (3) and construct sparse block matrices B and C Solve (I + t B)V = V 0 to obtain V Normalize each vector in V to obtain ˆV Solve 2Lf = CT ˆV to obtain f return f |
| Open Source Code | No | The paper does not provide any explicit statement or link for the open-sourcing of the code for its own methodology. |
| Open Datasets | Yes | The first one is from the CMU PIE face database (Sim et al., 2003), which contains 32 32 cropped face images of 68 persons. The second data set contains 5,000 images of 50 semantic categories, from the Corel database. |
| Dataset Splits | No | The paper mentions 'For real data, we perform cross-validation to choose d.' but does not provide specific percentages or counts for training, validation, and test splits, nor details on the cross-validation setup (e.g., number of folds). |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models, processor types, or memory amounts used for running its experiments. |
| Software Dependencies | No | The paper mentions using the 'LSQR package' but does not specify its version number or the versions of any other software dependencies used in their implementation. |
| Experiment Setup | Yes | We empirically set t = 1 for GDL in all experiments as GDL performs very stable when t varies. The dimension of the manifold d is set to 2 in the synthetic example. For real data, we perform cross-validation to choose d. Specifically, d = 9 for the CMU PIE data set and d = 2 for the Corel data set. We use the same nearest neighbor graph for all six algorithms. The number of nearest neighbors is set to 16 on both synthetic and real data sets and the weight is the simple 0 1 weight. |