Linear Dimensionality Reduction: Survey, Insights, and Generalizations
Authors: John P. Cunningham, Zoubin Ghahramani
JMLR 2015 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Section 4 validates this claim by applying this generic solver without change to different objectives f X( ), both classic and novel. We require only the condition that f X( ) be differentiable in M to enable simple gradient descent methods. ... Figure 2: Performance comparison between heuristic solvers and direct optimization of linear dimensionality reduction objectives. |
| Researcher Affiliation | Academia | John P. Cunningham EMAIL Department of Statistics Columbia University New York City, USA Zoubin Ghahramani EMAIL Department of Engineering University of Cambridge Cambridge, UK |
| Pseudocode | Yes | Algorithm 1 gives pseudocode for a projected gradient method over the Stiefel manifold. |
| Open Source Code | Yes | We implemented these methods in MATLAB, both natively for first order methods, and using the excellent manopt software library (Boumal et al., 2014) for first and second order methods (all code is available at http://github.com/cunni/ldr). |
| Open Datasets | No | In each panel (A and B), we simulated data of dimensionality d = 3, with n = 3000 points, corresponding to 1000 points in each of 3 clusters (shown in black, blue, and red). Data in each cluster were normally distributed with random means (normal with standard deviation 5/2) and random covariance (uniformly distributed orientation and exponentially distributed eccentricity with mean 5). We ran PCA on 20 random data sets for each dimensionality d {4, 8, 16, ..., 1024}, each time projecting onto r = 3 dimensions. Data were normally distributed with random covariance (exponentially distributed eccentricity with mean 2). |
| Dataset Splits | No | The paper describes generating synthetic data and testing methods on it, but does not mention specific training, validation, or test splits. The focus is on optimizing objectives for dimensionality reduction. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU, GPU models, or memory specifications used for running the experiments. |
| Software Dependencies | No | We implemented these methods in MATLAB, both natively for first order methods, and using the excellent manopt software library (Boumal et al., 2014) for first and second order methods (all code is available at http://github.com/cunni/ldr). While MATLAB and Manopt are mentioned, specific version numbers are not provided for either. |
| Experiment Setup | Yes | We ran PCA on 20 random data sets for each dimensionality d {4, 8, 16, ..., 1024}, each time projecting onto r = 3 dimensions. Data were normally distributed with random covariance (exponentially distributed eccentricity with mean 2). ... We generated data with 1000 data points in each of d classes, where within class data was generated according to a normal distribution with random covariance (uniformly distributed orientation and exponentially distributed eccentricity with mean 5), and each class mean vector was randomly chosen (normal with standard deviation 5/d). |