
Sparse Granger Causality Graphs for Human Action Classification Saehoon Yi and Vladimir Pavlovic Rutgers, The State University of New Jersey
Outline • Objective and challenges • Previous work • Sparse Granger Causality Graph Model • Analysis and result • Conclusion
Objective • Classify human action time series data Challenges • High dimensional time series data • Dimensionality reduction • Difficulties in interpretation • Idiosyncratic patterns of same action • Need to find commonality within an action
Previous work • Learning dynamics of joints • Each action is modeled as Linear Dynamic System • C. Bregler, CVPR 97 • Align time series data • Dynamic Time Warping • Canonical Time Warping • F. Zhou and F. De la Torre, NIPS 2009 • Need to tune parameter for each pair of sequence • Isotonic Canonical Correlation Analysis • S. Shariat and V. Pavlovic, ICCV 2011
Our approach • Robust representation of continuous joint movements using micro event point processes. • Models salient and sparse temporal relations among skeletal joints movements
Step 1: Generate micro event point processes Continuous time series Joint angles on knees Detect maximal/minimal extreme points as events Micro event point processes
Step 2: Estimate Granger Causality Graph • Granger causality in time • Given two AR time series X, Y • Granger causality
Granger causality in frequency • Given two point processes , • Estimate power spectrum • Decompose spectrum using Wilson’s algorithm • Granger causality • [A. Nedungadi, G. Rangarajan, N. Jain, and M. Ding ’09]
Granger causality graph representation • Estimate Granger causality • for each pair of micro events • f frequencies → summarized to 4 bands
Step 3: Learn L1 regularized regression • Input : 16M2 Granger causality features • Output : action category label • Sparse regression coefficient W for each action • Common causality pattern within each class • Positive coefficient Wij • edge i→ j have high causality • Negative coefficient Wij • edge i→ j have low causality
Experiments • HDM05 dataset • Motion capture sequence of 29 skeletal joints • Each action is performed by 5 subjects • 8 action classes are chosen
Experiment settings • Two different cross validation settings • Cut 1 • Randomly partition training / testing across all subjects • Cut 2 • Test set subjects different from training subjects • To show classification accuracy on unseen data
Comparative result Confusion matrix of SGCGM
Conclusion • Learn common structure within an action • The sparse regression model chose which pairwise relationship is important for the action • Interpretability of the model • Granger causal graph describes temporal relationship between two joints
Thanks you. Q & A