An object is a primitive object, a vector or in the form of a tuple of data components:
Object ={o| o is Primitive or
o=[o_1, ... , o_n] such that o_i is Object(Vector of object) or
o=(Prop_1, ... , Prop_n) forall i in {1...n}, Prop_i(o) is Object}
Time might be a point, in case of an instantaneous event, or an interval during if it is durative. Supported durative time is range.
time | [start_time:end_time]
| (Type, Value) |
SensorId |
Time |
| Id |
Name |
Cumulative |
OnChange |
Nominal |
Range |
Location |
Object |
Sensor |
| Id |
Name |
Cumulative |
OnChange |
Nominal |
Range |
Location |
Object |
Sensor |
| int |
string |
bool |
bool |
bool |
json {min,max}/{items} |
string |
string |
string |
| in case of nominal sensors, the range contain items and for numeric sensors, the range contain min and max |
|
|
|
|
|
|
|
|
| ActivityId |
ActorId |
StartTime |
EndTime |
\begin{Example}[Different Segmentation approaches]
\end{Example}
\begin{lstlisting}[mathescape=true]
function Fixed time window(S,X,r,l) {//S=SegmentHistory, X=Events,
//r=Shift, l=windowLength
p=begin(S[last])
return X.eventsIn([p + r : p + r + l]);
}
function Fixed siding window(S,X,r,l) {
prev_w=S[last]; p=begin(S[last])
be=first({e \in X| p + r $\leq$ time(e)}
return X.eventsIn([be : be + l]);
}
function Significant events(S,X,m) {//m=significant events per segments
se=significantEvents(X) $\subseteq$ X
begin=time(se[1]);//next significant event
end=time(se[1 + m]);
return X.eventsIn([begin:end]);
}
//Probabilistic Approach
given:(By analyzing training set)
$ws(A_m)$ is average window size of activity $A_m$
$w_1 = min {ws(A_1), ws(A_2), ..., ws(A_M)}$
$w_L = median{ws(A_1), ws(A_2), ..., ws(A_M)}$
$w_l=(w_L-w_1)\times l/L+w_1$
$window_sizes= {w_1, w_2, . . . , w_L}$
$P(w_l /A_m)$//probability of windows length $w_l$ for an activity Am
$P(A_m /s_i)$//probability of Activity $A_i$ associated with the sensor $s_i$.
function Probabilistic Approach(S,X) {
x=nextEvent(X)
$w^{\star} =\underset{w_l}{max} {P(w_l /x)}=\underset{w_l}{max}[P(w_l /A_m)\times P(A_m /x)] $
end=time(x);//Next event
return X.eventsIn(end-$w^\star$,end]);
}
function Metric base Approach(S,X) {//S=SegmentHistory, X=Events
indx=len(S[last])+1 //first event not in old segment
$m_i=metric({X[indx],...,X[i]})$
find first i which $H({m_{0}....m_i})$ is true//
return X.eventsIn([time(X[indx]):time(X[i])]);
}
function SWAB Approach(S,X,bs) {//bs=Buffer size
indx=len(S[last])+1 //first event not in old segment
$m=BottomUp({X[indx],...,X[indx+bs]})$
return m[0];
}
\end{lstlisting}
pyActLearn -> documents