ZEMCH 2015 - International Conference Proceedings | Page 247

Figure 2: Example of annotation for Dataset 2 3.2 Activity Pattern Modelling Based On Machine Learning Approaches The purpose of this work is to accurately model and detect daily activities in two datasets D1 and D2 as described in Section 3.1. 3.2.1 Feature Extraction In the feature extraction process, we built two different matrices: a feature matrix and a label matrix. The feature matrix presents sensor firings timeseries. The rows represent each sensor and the columns a moment in time (sample). As we are only working with binary sensors, each feature cell fxy must contain either a 0 or a 1 depending on the state of the sensor sx at the time ty. The label matrix has only just one row corresponding to ADL labels and again one column for each moment in time. Each label cell ly will consist on a number representing a class, therefore the range will be between 1 and the maximum number of activities (1-num_act) found in the activity or label matrix. Table I has a representation for both matrices. Table I: Feature and Label Matrices. fxy represent the features while ay contain the labels. Sensors range from s1 to sn, activities from 1 to num_act and samples are distributed from t1 to tm, which represent each unit of time, timeslice or sampling time. fxy t1 t2 t3 … tm s1 0/1 0/1 0/1 … 0/1 s2 0/1 0/1 0/1 … 0/1 s3 0/1 0/1 0/1 … 0/1 … … … … … . sn 0/1 0/1 0/1 … 0/1 1-num_act 1-num_act 1-num_act … 1-num_act Features ay Labels 3.2.2 The Proposed Approach based on a Non-linear Multi-class SVM We modelled activity patterns using a one vs. one (Pal, 2005) approach multi-class SVM classifier to perform supervised learning from labelled data as explained above. Due to non-linear unbalanced data, a non-linear SVM have been used for this purpose, which uses different kernels to separate different labelled points using hyperplanes. By using multidimensional planes, non-linear problems can be solved as linear ones, therefore allowing creating functions that maximize the separation between points of different classes. We evaluated the SVM performance using the most popular kernels: linear, polynomial, radial basis and sigmoid. For parameter estimation, we followed the guidelines published by the libsvm creator (Chang and Lin, 2011).The mathematical representation can be described as follows: Modelling occupant activity patterns for energy saving in buidings 245