1. An Event-Based Data Fusion Algorithm for Smart Cities
Avinash Kalyanaraman
Kamin Whitehouse

2. Sensors, sensors everywhere !!!
Source: Cisco

3. Static & personal sensing systems need to be fused to capture complete story
Static measures : what (appliance), how much (power), what (action) etc
Personal measures + activity recognition measures: who (used appliance), who (cutting) etc

4. Motivating Examples

5. Example-1: Energy Footprint
(Time: 12:30:03PM,
Appliance: LivingRoom Lamp,
Power: 150W)
(Time: 12:30:08PM,
Appliance: LivingRoom Lamp,
User: Bob,
Power: 150W)
(Time: 12:30:14PM,
Appliance : LivingRoom Lamp,
User : Bob)
Get good gesture image from J’s slide deck?

6. Example-2: Automatic dietary monitoring
(Time: 12:30:03PM,
Activity: Cutting,
Entity: Apple)
(Time: 12:30:08PM,
Activity: Cutting
User: Bob,
Entity: Apple)
(Time: 12:30:14PM,
Activity: Cutting,
User : Bob)

7. Fusion Properties Two systems observe
different attributes of same event
(e.g. power vs identity for
same Light ON event)
Non time sync
One system has notion of identity with per-identity event ordering

8. Fusion Properties 4. Other system has
global event ordering (e.g. NILM)
5. False positives and false negatives occur
6. Only similar events of the two systems can be matched (e.g. NILM microwave must match with gesture microwave event, and not Fridge event)

9. Different from traditional Bipartite Matching Algorithms
Simply maximizes matches without any notion of identity
Results in crossing matches
Crossing matches represent contradictions

10. Algorithm
i) Naive MHT
ii) Naive MHT-with optimal pruning
iii) The Divide and Conquer approach

11. Iteration 1 : Naive MHT Above timeline shows:
a can potentially match d,e or f but not x or z
b can potentially match with d, e or f but not x or z
c can potentially match with d,e or f but not x or z
w can potentially match with x or z but not d, e or f
y can potentially match with x or z but not d, e or f

12. Iteration 1 : Naive MHT A Hypothesis
Cost of an association = timestamp difference e.g. |d - a| , |e - a|.
Cost of hypothesis = total cost of all associations
A Hypothesis

13. Iteration 1 : Naive MHT (contd)
Finally, choose hypothesis having maximum associations at minimum cost

14. Iteration 1 : Naive MHT (contd)
Finally, choose hypothesis having maximum associations at minimum cost
Exponential explosion

15. Iteration 2: Naive MHT with optimal pruning
State of hypothesis
Intuition: Two hypotheses ending in same state will behave identically moving forward.
Optimal pruning condition:
“If two hypotheses end in same state, choose the better one”
Maintains: O(|P1| * |P2| * … |Pn|) hypotheses, |Pi| = # events of the i-th identity in SS2
State is the last associated SS2 Timestamp of each person

16. Iteration 3 : Divide and Conquer Approach
Hypotheses { [(a→d) , (b→e), (c→ɸ)] , [(a→d) , (b→f), (c→ɸ)] , [(a→e) , (b→d), (c→ɸ)] … } worse than [(a→d) , (b→e), (c→f)]
Any hypotheses forked from the above set will be worse than those forked from [(a→d) , (b→e), (c→f)]
No event >= (w), can match with an event <= (f)
Two independent sub-problems:
[SS1 = {a,b,c}, SS2={d,e,f}] and
[SS1 = {w,y}, SS2={x,z}]

17. Iteration 3 : Divide and Conquer Approach
“How to partition the given matching problem into sub-problems that can be solved independently?”
Maintains: O(|P1| * |P2| * … |Pn|) hypotheses, |Pi| = # events of the i-th identity in the largest sub-problem

18. Experimental setup: System evaluation
(Time: 12:30:03PM,
Doorway : Bedroom,
Height : 180cm)
Tracking Algorithm
(EO,GT mappings) :
12:30:03 → 12:30:17
...
12:30:03 :: Bob, IN
(Time: 12:30:17PM,
Doorway : Bedroom,
Person : Bob,
Direction : IN)

19. Experimental Setup Doorjamb-like setup
Timeline-1 : (Timestamp, person, doorway, direction)
Timeline-2 (Doorjamb-like): Empirically modified timeline-1, studying effect of skew, FP and FN

20. Experimental Setup (contd)
Skew : -10 to +10s
FP : 20% FP, according to Uniform distribution
FN : 10% FN, according to Uniform distribution
Metric :
Matching accuracy = % of phone transitions correctly matched with its Doorjamb event
Baselines:
Greedy closest match (used by Saha et al)
Greedy min cost (used by Hnat et al)
Greedy closest match : Go in increasing time order, and match each event with closest event in other timeline
Greedy Min cost : (1) Sort all matches by cost, (2) Go in increasing order of cost, and match events if they don’t criss-cross (criss-cross is a contradiction. Slide 9)

21. Evaluation Skew b. Skew + FP
G-opt suffers from lowest accuracy variance despite FP, FN and time skew.
Greedy algorithms suffer with larger skews because higher likelihood of local optima
2 other graphs are in the paper.
In interest of time, showing only the main result.
c. Skew + FN

22. Conclusion
Present three diverse use-cases for static-personal sensing system fusion
G-opt Algorithm : MHT + optimal pruning + Divide And Conquer
Maintains: O(|P1| * |P2| * … |Pn|) hypotheses, |Pi| = # events of the i-th identity in the largest sub-problem
G-opt has lesser accuracy variance than greedy algorithms despite FP, FN and skew
More important with time as more diverse sensors get deployed for smart-city applications