Discriminative Recurring Signal Detection and Localization Zeyu You, Raviv Raich*, Xiaoli Z. Fern, and Jinsub Kim School of EECS, Oregon State University, Corvallis, OR 97331-5501

Organization Introduction Related work and our contribution Motivation Problem formulation Maximum likelihood estimation(MLE) Synthetic data experimental Results Real-world data experimental Results

Introduction What is a recurring pattern? Pattern characteristics: DNA motifs Music motifs Home appliance activations Pattern characteristics: Sharing same structure Recurring in nature

Applications Motifs Air-conditioning activation signals D'haeseleer, Patrik. "How does DNA sequence motif discovery work?." Nature biotechnology 24.8 (2006): 959-961. From Fee Lab Research in http://web.mit.edu/feelab/research.html Air-conditioning activation signals From Pecan Street dataset (Source: Pecan Street Research Institute)

Related work and our contribution Previous works [1-5] focus on: discover recurrent patterns from data finding the fundamental characteristics of the signal pattern Our contribution: a novel formulation of auto-detecting recurring signal patterns a maximum likelihood estimation (MLE) solution for the problem an increased detection performance on a real-world data

Generative vs. Discriminative

Motivation for our approach Flavor in discriminative for two reasons Robust to variations with in the pattern Robust to low signal to noise ratio

Problem formulation System diagram: System description: System target: Observed data: a collection of M signals Hidden data: System target: To learn a convolutional kernel w. y(t) w(t)* x(t) x(t) Signal Labeler w LR Y

The graphical model Instance labeler Signal labeler xmt ymt Ym T M w

The probabilistic model Instance labeler (logistic regression): Signal labeler: Condition model:

The data likelihood Data likelihood: Maximum likelihood estimation (MLE): Minimizing the negative log likelihood: Independence Data distribution Difference of convex

Convex-concave procedure (CCCP) Solution with CCCP [6]: Upper bound function (linearization): Gradient descent: Prior Posterior

Synthetic data experiment Setup: Train on M=160; Test on 40; Setting kernel size to be F=10, T0=7; 10 MC runs of different initialization. Data generation: Generate a rectangular pattern; Create an empty spectrogram with F=10, T=50; Random placing the pattern with varying magnitude into one time index out of 50; Add gaussian noise.

Synthetic results Discriminative vs. generative approach: True pattern Learned kernel Data Generative Discriminative localization localization ROC

Real world experiment Setup: Data generation: Four home ps-025,029,046,051, 25 days of disaggregated, time-sampled electricity usage data from the Pecan Street dataset ({Source: Pecan Street Research Institute}) Training period 11/17/2012-11/25/2012 meter reading; Test period 11/26/2012-12/11/2012; Validating kernel size and compared with general approach with window size set to be T0=700; Data generation: Extract activations based on power ground truth; Extract negative data by random selecting the time where the power has no significant increase; Remove DC offset and Despike large spike noise by median filter;

Experiment results Tuning T0 Fridge activation and data sample Generative detection Discriminative detection

Detection accuracy Performance: Discriminative is better at localization Discriminative is more Invariant to the slight variations of activation signals Discriminative has higher AUC than generative in general AUC table for both generative and discriminative

Discussion Can we extent our model to multi-class to give more discrimination between different activation patterns? Can we speedup the algorithm by converging quicker? Can we find more applicable real-world application areas for the algorithm?

References [1]  Zeyu You, Raviv Raich, and Yonghong Huang, “An inference framework for detection of home appliance activation from voltage measurements,” in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014, pp. 6033–6037. [2]  Alex S Park and James R Glass, “Unsupervised pat- tern discovery in speech,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 16, no. 1, pp. 186–197, 2008. [3]  Aline Cabasson and Olivier Meste, “Time delay estimation: a new insight into the woody’s method,” IEEE signal processing letters, vol. 15, pp. 573–576, 2008. [4]  Yoshiki Tanaka, Kazuhisa Iwamoto, and Kuniaki Uehara, “Discovery of time-series motif from multi-dimensional data based on mdl principle,” Machine Learning, vol. 58, no. 2-3, pp. 269–300, 2005. [5]  Jessica Lin, Eamonn Keogh, Stefano Lonardi, and Pranav Patel, “Finding motifs in time series,” in Proc. of the 2nd Workshop on Temporal Data Mining, 2002, pp. 53–68. [6]  Alan L Yuille and Anand Rangarajan, “The concave- convex procedure (cccp),” Advances in neural information processing systems, vol. 2, pp. 1033–1040, 2002.

Questions? Thank You!