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
Overview
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 Granger causality in 128 freqCausality summarized by 4 bands
Step 3: Learn L1 regularized regression Input : 16M 2 Granger causality features Output : action category label Sparse regression coefficient W for each action Common causality pattern within each class Positive coefficient W ij edge i → j have high causality Negative coefficient W ij 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 Deposit on the floor w/ R handPunch front w/ L hand Jumping JackPunch front w/ R hand Kick front w/ R legSquat Kick side w/ R legWalk two steps
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
Example of Sparse Granger Causality Graph Model DEPOSIT FLOOR RIGHT HANDKICK RIGHT SIDE
Example of Sparse Granger Causality Graph Model PUNCH LEFT FRONTPUNCH RIGHT FRONT
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