188 X Liang et aL Building and Environment 102 (2016)179-192 Table 3 Characteristics of occupant presence patterns. Pattern Occupancy rate Working time Going to work time Going home time Noon break time Pattern 1 Lowest Shortest Latest Earliest NA Pattern 2 Highest Longest Earliest Later 12 pm Pattern 3 Medium Medium Later Latest 2 pm Pattern 4 Medium Medium Earlier Earlier 1 pm by the attributes.Any samples can be classified to different patterns 100% top down along the path of the tree.The first decision level is 90% season.If season is winter,the branch is to the terminal node.If not, 80% the process will reach to the second decision level,namely week- 70% day.After split by the weekday nodes,the final decisions can be generated.It needs to be noted that the DST is not included in the 60% ■Pattern4 decision tree,which means DST cannot contribute enough infor- 50% ■Pattern3 mation to reach the threshold of gain radio.Namely,DST is not a 4% ■Pattern2 key attribute in the classification of patterns. 30% Pattern 1 Not only the classification,but also the probability of the clas- sification can be provided by the decision tree.In Fig.13,the lengths 10% of different colors represent the probability of different patterns. For example,if the season is winter,the decision is Pattern 3. MON UE WEN Behind this decision,there is more information of probability:the Weekday Pattern 3 is of the highest probability,Patterns 1 and 2 are of lower 100% probabilities,and the probability of Pattern 4 is zero.Table 4 shows 90% the rules of patterns in detail.80%of all the training samples are correctly classified based on these rules.The result of the decision tree model shows relatively good performance to be further applied 70% to prediction in the next step ■Pattern4 50% ■Pattern3 0% ■Pattern2 3.4.Prediction of occupancy schedule ■Pattern1 Based on the rules deduced by decision tree,the occupancy schedule can be predicted.Three prediction methods are compared 10% in this study.The first is the mean-day method.The predictions 0% WINTER SPWG SUMMER AUTUMN depend only on the time of day.The method is presented by Eq.(7). Season where t denotes the time of the day (e.g.3 pm)and Mday denotes the mean value of all days.For example,the prediction for 3 pm is 100% the average of all of the data for 3 pm in history.Therefore,there is 90% no different profile for each day of the week,for different seasons or 820% for other factors.This prediction method is simple and can be compared as a baseline R 70% 60% ■Pattern4 Prdiction(t)=Mday(t) (7) 50% Pattern 3 The second method is mean-week method.The method is 40% ■Pattern2 presented by Eq.(8).where day denotes the day of samples and 30% ■Pattern1 Mweekday denotes the mean value of the assigned weekday.For 20% example,the prediction of 3 pm on a Monday in spring is the 10% average of all historical data for 3 pm on Monday. 0% NO YES Prdiction(weekday,t)=Mweekday(t) (8) Daylight Saving Time The third method is the proposed method in this study,which is based on the probability of decision tree.The method is presented Fig.12.Relationship between occupancy patterns and weekdays,seasons and DST. by Eq.(9).where Mpi(i=1,2,3,4)denotes the mean value of the Pattern i and Ppi denotes the probability of Pattern i.For example, the prediction of 3 pm on a Monday in spring is the expectation of 3.5.Validation all historical data for 3 pm based on probability of patterns. Several statistical performance metrics are used to evaluate Prdiction(day,t)=Mp1(t).Pp1+Mp2(t)-Pp2 +Mp3(t)-Pp3 prediction.The definitions are described below. +Mp4(t)-Pp4 (9) The root mean squared error(RMSE)quantifies the typical size of the error in the predictions,in absolute units.The equation for The visualized prediction of occupancy schedule based on the RMSE is provided in Eq.(10).where Ei is the observed data of oc- third method is shown in Fig.14.Since there are 16 terminal nodes cupants,Ei is the prediction results,and n is the total number of in decision tree(Fig.13).there are 16 conditions of prediction. predictions.by the attributes. Any samples can be classified to different patterns top down along the path of the tree. The first decision level is season. If season is winter, the branch is to the terminal node. If not, the process will reach to the second decision level, namely week￾day. After split by the weekday nodes, the final decisions can be generated. It needs to be noted that the DST is not included in the decision tree, which means DST cannot contribute enough infor￾mation to reach the threshold of gain radio. Namely, DST is not a key attribute in the classification of patterns. Not only the classification, but also the probability of the clas￾sification can be provided by the decision tree. In Fig. 13, the lengths of different colors represent the probability of different patterns. For example, if the season is winter, the decision is Pattern 3. Behind this decision, there is more information of probability: the Pattern 3 is of the highest probability, Patterns 1 and 2 are of lower probabilities, and the probability of Pattern 4 is zero. Table 4 shows the rules of patterns in detail. 80% of all the training samples are correctly classified based on these rules. The result of the decision tree model shows relatively good performance to be further applied to prediction in the next step. 3.4. Prediction of occupancy schedule Based on the rules deduced by decision tree, the occupancy schedule can be predicted. Three prediction methods are compared in this study. The first is the mean-day method. The predictions depend only on the time of day. The method is presented by Eq. (7), where t denotes the time of the day (e.g. 3 pm) and Mday denotes the mean value of all days. For example, the prediction for 3 pm is the average of all of the data for 3 pm in history. Therefore, there is no different profile for each day of the week, for different seasons or for other factors. This prediction method is simple and can be compared as a baseline. PrdictionðtÞ ¼ MdayðtÞ (7) The second method is mean-week method. The method is presented by Eq. (8), where day denotes the day of samples and Mweekday denotes the mean value of the assigned weekday. For example, the prediction of 3 pm on a Monday in spring is the average of all historical data for 3 pm on Monday. Prdictionðweekday;tÞ ¼ MweekdayðtÞ (8) The third method is the proposed method in this study, which is based on the probability of decision tree. The method is presented by Eq. (9), where Mpi (i¼1,2,3,4) denotes the mean value of the Pattern i and Ppi denotes the probability of Pattern i. For example, the prediction of 3 pm on a Monday in spring is the expectation of all historical data for 3 pm based on probability of patterns. Prdictionðday;tÞ ¼ Mp1ðtÞ$Pp1 þ Mp2ðtÞ$Pp2 þ Mp3ðtÞ$Pp3 þ Mp4ðtÞ$Pp4 (9) The visualized prediction of occupancy schedule based on the third method is shown in Fig. 14. Since there are 16 terminal nodes in decision tree (Fig. 13), there are 16 conditions of prediction. 3.5. Validation Several statistical performance metrics are used to evaluate prediction. The definitions are described below. The root mean squared error (RMSE) quantifies the typical size of the error in the predictions, in absolute units. The equation for RMSE is provided in Eq. (10), where Ei is the observed data of oc￾cupants, bEi is the prediction results, and n is the total number of predictions. Table 3 Characteristics of occupant presence patterns. Pattern Occupancy rate Working time Going to work time Going home time Noon break time Pattern 1 Lowest Shortest Latest Earliest NA Pattern 2 Highest Longest Earliest Later 12 pm Pattern 3 Medium Medium Later Latest 2 pm Pattern 4 Medium Medium Earlier Earlier 1 pm Fig. 12. Relationship between occupancy patterns and weekdays, seasons and DST. 188 X. Liang et al. / Building and Environment 102 (2016) 179e192