JCaS (Joint Categorization and Segmentation)
GPCA (Generalized Principal Component Analysis)
GPCA (Generalized Principal Component Analysis) is an algebraic, non-iterative algorithm for segmenting points lying in an union of subspaces. For more information, please visit the corresponding GPCA research page.
We provide a MATLAB implementation of GPCA with Polynomial Differentiation and spectral clustering for subspace classification.
Download Code for GPCA PDA with Spectral Clustering.
Sparse Representation Theory
Sparce Subspace Clustering (SSC) is a subspace clustering algorithm that uses sparse vector representation, convex optimization, and spectral clustering. There are two implementations of the SSC algorithm, one based on the CVX package (http://cvxr.com/cvx), and the other based on ADMM, which can be downloaded from the following links below.
Please visit the corresponding SSC research page for more information.
Download Code for SSC using CVX.
Download Code for SSC using ADMM
Sparse Manifold Clustering and Embedding (SMCE) is an algorithm based on sparse representation theory for clustering and dimensionality reduction of data lying in a union of nonlinear manifolds. The MATLAB code can be downloaded using the following link:
Download Code for SMCE.
Sparse Modeling Representative Selection (SMRS) is an algorithm based on sparse multiple-measurement-vector recovery theory for selecting a subset of data points as the representatives.
Download Code for SMRS.
Structured-Sparse Subspace Classification is an algorithm based on block-sparse representation techniques (also known as Block Sparse Subspace Clustering (BSSC)) for classifying multi-subspace data, where the training data in each class lie in a union of subspaces.
Download Code for BSSC.
Please contact Ehsan Elhamifar ( ehsan [at] cis [dot] jhu [dot] edu ) for questions and comments regarding the code.
For more information please visit Ehsan's research page .
Other subspace clustering algorithms
Motion segmentation algorithms
The problem of segmenting features tracked in a video with multiple objects can be viewed as the problem of segmenting points lying in an union of subspaces. Many machine learning algorithms can therefore be used to solve this problem (see the Motion Segmentation research page for more information on this topic).
We provide MATLAB implementation of three subspace separation and motion segmentation algorithms:
- GPCA with spectral clustering
- RANSAC (RANdom SAmple Consensus)
- Local Subspace Affinity (LSA)
Download Code for motion segmentation with GPCA, RANSAC and LSA
These algorithms can be tested on the Hopkins 155 dataset, which can be downloaded from the Data page.
Additional code for the Hopkins 155 dataset
The sequences contained in the Hopkins 155
dataset are outlier-free. In order to test the robustness to outliers of segmentation algorithms, one can add synthetically generated outliers to the trajectories in each sequence of the Hopkins 155 dataset. We provide MATLAB code that generates these outlying trajectories for any sequence of the Hopkins 155 datasets
Download Code for generating synthetic outliers
Histograms of Oriented Optical Flow (HOOF) and Binet-Cauchy Kernels for Non-Linear Dynamical Systems (NLDS)
We provide code for computing Histograms of Oriented Optical Flow (HOOF) - which are features computed at each time instant from a frame of optical-flow vectors to model dynamic phenomena such as human activities. Once a time-series of HOOF is extracted from a video sequence, these can be modeled as Non-Linear Dynamical Systems (NLDS). Kernel PCA is used to learn the parameters of these NLDS and the Binet-Cauchy kernels for NLDS can be used to compute a distance between pairs of such NLDS. This code was applied to the problem of human activity recognition and published in . Please contact rizwanch [at] cis [dot] jhu [dot] edu for questions and comments regarding the code.
Code HOOF and BC kernels for NLDS
Dynamic Texture Toolbox
The dynamic texture toolbox contains implementation of methods for identifying and comparing video sequences by representing them as Linear Dynamical Systems (LDSs). All code is currently implemented in MATLAB with some code depending on the MATLAB control systems toolbox. A set of tutorials on how to use the toolbox can be found here
and the complete documentation can be found here
. The code is licensed under the Lesser GPL and is provided for academic purposes. If you use this toolbox for a publication we would be grateful if you cite this toolbox as . In case of questions, comments, bugs or errors, please contact Avinash Ravichandran (avinash at cis dot jhu dot edu) or Rizwan Chaudhry (rizwanch at cis dot jhu dot edu).
Download Dynamic Texture Toolbox
Distances Between Linear Dynamical Systems
This is the code for computing the alignment distances between linear dynamical systems as described in reference . The code is implemented in MATLAB but also uses compiled MATLAB executed files (.mex files). Instructions for compiling .mex files from C++ source code is provided in README.odt. Note that the computation of f1 corresponds to the computation of the distance squared as described in reference . The stochastic alignment distances f2 and f3 are described in reference .
In case of questions, comments, bugs or errors, please contact Nicolas D. Jimenez at nicodjimenez (at) gmail (dot) com
Download Code for Dynamical Systems Distances
Low-Rank Subspace Clustering (LRSC)
The code below is the low-rank subspace clustering code used in our experiments for our CVPR 2011 publication . We note that if your objective is subspace clustering, then you will also need some clustering algorithm. We found that spectral clustering from Ng, Jordan et. al. performed the best.
Download Code for Low-Rank Subspace Clustering
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit (SSC-OMP)
We provide the code for subspace clustering using the orthogonal matching pursuit as described in our CVPR 2016 publication.
Download Code for SSC-OMP
Elastic net Subspace Clustering (EnSC)
The package contains code used in our CVPR 2016 publication. It contains a standalone elastic net solver which is very efficient for large scale problems. It also contains code for testing EnSC on four large scale databases.
Download Code for EnSC
Self-Representation based outlier detection in a union of subspaces
We provide the code for outlier detection in a union of subspaces as described in our CVPR 2017 publication.
Download Code for R-graph
Exemplar based subspace clustering for class-imbalanced data
IEEE Conference on Computer Vision and Pattern Recognition, June 2009.
Dynamic Texture Toolbox
European Control Conference, 2013.
IEEE Conference on Computer Vision and Pattern Recognition, 2012.
IEEE Conference on Computer Vision and Pattern Recognition, 2011.
ChaLearn Looking at People Workshop, 2015.
European Conference in Computer Vision (ECCV), 2018.