Frequent Itemset based Event Detection in Uncertain Sensor Networks

Transcription

1 2013 IEEE International Conference on Green Computing and Communications and IEEE Internet of Things and IEEE Cyber, Physical and Social Computing Frequent Itemset based Event Detection in Uncertain Sensor Networks Yongxuan Lai Department of Software Engineering Xiamen University, 422 Siming South Road Siming District, Xiamen , China Jinshan Xie School of Mathematics and Computer Science Longyan University, 1 Dongxiao North Road Xinluo District, Longyan , China jsxie@lyun.edu.cn Abstract More and more sensor networks are deployed for the detection of events. Yet due to the resource-constraint nature of nodes, the readings are inherently inaccurate, imprecise and are distributed among the nodes, so it is a challenging task to detect events in such a kind of networks. In this paper, we study the problem of uncertain event detection in sensor networks, and propose an efficient detection algorithm Fibed. We use a possible world semantics to interpret the uncertain data, and events are defined based on computing the frequent itemsets. A polynomial is constructed to calculate the probability of each frequent item, and the coefficient vector of the polynomial is merged and updated when it is routed towards the base station. Early decisions could be made for the events, and lots of items could be pruned to save unnecessary transmissions as their probability do not meet the probability threshold. Experimental studies show that Fibed is efficient in detecting the uncertain events and cutting down the incurred transmissions. Keywords-uncertain frequent itemset; event detection; sensor network I. INTRODUCTION Wireless sensor networks (WSNs) are often used to sense and monitor remote physical environments. A typical sensor network is composed of battery-powered sensing nodes and a base station that collects events (or readings) from a collection of sensor nodes deployed over a spatial area[1]. Event detection or event monitoring is a key application for the environmental surveillance in sensor networks [2], [3]. For example, the sensor network should report a on fire event to the base station to alarm the fire and trigger quick response; or an unknown animal appear event should be reported if the nodes see a new kind of animal entering the zone in an animal habitat studying application. These applications all belong to the event detection application in sensor networks. However, detecting the events is not an easy and trivial task in sensor networks. Firstly, the events are actually high-level knowledge extracted from the sensing data, which are raw and distributed over the reshouces-cosntaint nodes. The event detection algorithm should gather and aggregate data to deduce *supported by the Natural Science Foundation of China (No ), Natural Science Foundation of Fujian Province (No.2011J05156, No ), Fundamental Research Funds for the Central Universities (No ); Open Project Foundation of the Key Laboratory of Data Engineering and Knowledge Engineering, MOE(No. KF ); the Research Project Serving the West Coast launched by Longyan University. the event through messages transmissions and cooperations among the nodes[2], [3]. Secondly, due to the dynamics of physical environments and the possible faults of the seining nodes, the readings collected and reported by sensor nodes are inherently inaccurate and imprecise, they could only reflect approximate measurements of the environments. In other words, these readings are considered to be uncertain, and so are the events. Many state-of-the-art systems assume that the data are available in a centralized database and the data is precise and certain[4], and the event processing is centralized and deterministic. Yet it is very energy consuming to have all the nodes send their reading to the base station, and more effective methods are needed to distributively process the uncertain data and events. To the best of our knowledge, the problem of innetwork detection for uncertain events is new and has not yet been fully explored. In this paper, we study the problem of uncertain event detection in sensor networks and propose an efficient event detection algorithm Fibed(Frequent Itemset Based efficient Event Detection). We use a possible world semantics to interpret the uncertain data, where events are defined based on computing the probability of frequent itemsets. In Fibed, nodes are firstly clustered based on their readings, then a polynomial is constructed to calculate the probability for each item value. Given the polynomial, the coefficient vector of each item is merged and updated when it is routed to the base station. If the probability of frequent item does not meet the threshold, early decision of the event could be made and the items could be pruned to save unnecessary transmissions. Experimental studies show that Fibed is effective to detect the uncertain events, and more than 30 percent of transmissions are saved for the detection of uncertain events. The rest of the paper is structured as follows: section 2 describes the related works; section 3 introduces some preliminaries and defines the problem of uncertain event detection; section 4 presents the detailed mechanism of the Fibed algorithm, including the node clustering, calculation of frequent items and distributive identification of events; section 5 describes the environmental setup and analyzes the simulation results; finally, section 6 concludes the paper /13 $ IEEE DOI /GreenCom-iThings-CPSCom

2 II. RELATED WORK 1) Uncertain Data Processing.: Research on uncertain data management mainly focuses on the query processing and mining. The queries include the aggregate queries [5], [6], nearest neighbor queries[7], ranking and top-k queries[8], [9], skyline queries[10], and etc. These queries use the similar query semantics with their deterministic versions, yet they take the probability of the data into account. For example, a concept of possible worlds [11] was introduced to facilitate the understanding and processing of uncertain data. With the possible world semantic, an uncertain database is viewed as multiple deterministic database instances; and the probability of the query results are based on computing of the sum of the probability of the world instances. For the research of mining on uncertain dataset, reference [12], [13] proposed an algorithm to compute the expected support of itemsets by summing all itemset probabilities. It used a probabilistic filter to prune candidates as soon as their most optimistic values fall below the threshold. Reference [14] proposed the UF-growth algorithm to compute frequent itemsets by means of the expected support, and the FPtree[15] was adopted to avoid expensive candidate generation. The itemsets are considered frequent if the expected support exceeds minsup in reference[12], [14]. Yet in [16] an itemset X is called frequent if the probability that X occurs in at least minsup transactions is above a given threshold τ. The authors proposed a dynamic programming method for computing the probability that an itemset is frequent, as well as the entire probability distribution function of the support of an itemset. In [17], the authors proposed a polynomial algorithm for calculating the probabilities of the items in an uncertain database. The algorithm also computes the upper bound of each round to filter the tuples that would not be included in the set of the top-k frequent items. 2) Distributive Event Detection.: Early prototype systems in WSN, such as Cougar[18] and TinyDB [19], employed a threshold-based strategy to detect the events. Data satisfying the thresholds are aggregated within the network and sent to the base station. Then more complex types of events were also defined and studied in the research area of sensor networks. References [3] specifed common types of events as patterns in contour maps, and abstracted the spatiotemporal patterns of sensory data. The event detection process was then viewed as the contour map matching between the events and the data. Reference [1] studied the issue of tracking the correlations among sensor data within a time window to detect events of interest. It views the event detection as the process of window self-join, and proposes the two-phase self-join scheme to evaluate the self-join queries in sensor networks. Reference [2] used a division-based technique to detect global events. It divides a global event into regional events for the ease of monitoring, and also takes advantage of the temporal correlations of sensing data to gain energy efficiency. Then there exists work that took the uncertainty into account for detecting the events. Reference [20] proposed a Fig. 1. House example: nodes are deployed in a house for surveillance. Bayesian network based approach to materialize new events given the arrival of an uncertain event and to compute its probability. It also developed a sampling algorithm to compute the probabilities of a set of events efficiently. Reference [21] proposed an algorithm for the complex event detection in probabilistic stream. The algorithm adopts a tree alike data structure to store conditional probabilities, it also prunes event instances with query requirements and filters the complex events whose probability is less than the threshold. These studies, however, all focus on event detection on the scenario of centralized streaming system, which is not suitable for the distributed sensor networks. The most relevant work is [22], which proposed a general event modeling and reasoning model that can represent and reason with events from multiple sources. It also introduced a notion called event cluster to represent uncertain and incomplete events induced from an observation. This paper borrows the idea of event clusters for the merging and inference process, yet we add the frequentitem semantics into the definition of events, which define the uncertain events in a more proper way. III. PRELIMINARIES AND PROBLEM DEFINITION A. Interpreting the Uncertain Readings We consider nodes are deployed for surveillance and monitoring, and each node senses the environment and generates primitive readings. As illustrated in example 1, a sensor reading is typically defined as {sid, loc, time, (v 1,p 1 ),.., (v k, p k )}, where sid is the id of the node that detects the event, loc is the location of the node, time is the exact time when the event occurs, and (v i,p i ) is an item pair denotes the node has detected v i with confidence p i. Example 1: A sensor network is deployed for the surveillance of a house (Fig. 1). Nodes with cameras are placed in several locations such as yards, doors, parlors, and rooms, and they periodically take pictures to monitoring the surrounding environments. The pictures are processed through an image recognition process, and {Dog, Cat, Lady, Man, Child, Ball, Car,... }could be recognized in the image processing algorithm. Yet the node could only make rough judgement on what has been detected in the pictures. For every recognized 1038

3 item, there is a confidence attached to it. Example readings from sensors are as follows: t 1 : {s1, door 1, 12 : 18, (Dog, 1.0), (Ball,0.6)} t 2 : {s2, door 1, 12 : 18, (Dog, 0.3), (Lady, 0.6)} Here we consider the Possible World Semantics[11] to interpret the uncertain data and event. Conceptually, the readings in sensor network are viewed as a set of deterministic instances world, and each world contains a set of tuples. For {t 1,t 2 } in example 1, there are 4 items (in table I) and 8 possible worlds (table II). TABLE I READINGS AND THE ITEMS Reading Time Node Item Probability t 1 12:18 s1 Dog 1.0 t 1 12:18 s1 Ball 0.6 t 2 12:18 s2 Lady 0.3 t 2 12:18 s2 Ball 0.6 TABLE II POSSIBLE WORLD INSTANCES Id World instance Calculation Pr w 1 {Dog}, {} 1*(1-0.6)*(1-0.3)*(1-0.6) w 2 {Dog}, {Lady} 1*(1-0.6)*0.3*(1-0.6) w 3 {Dog}, {Ball} 1*(1-0.6)*(1-0.3)* w 4 {Dog}, {Lady, Ball} 1*(1-0.6)*0.3* w 5 {Dog, Ball}, {} 1*0.6*(1-0.3)*(1-0.6) w 6 {Dog, Ball}, {Lady} 1*0.6*0.3*(1-0.6) w 7 {Dog, Ball}, {Ball} 1*0.6*(1-0.3)* w 8 {Dog, Ball}, {Lady, Ball} 1*0.6*0.3* Each world instance has a probability Pr(w). The set of all possible world instances is denoted W, and w W Pr(w) = 1.0 holds. B. Reading Cluster and Event In the surveillance applications, usually more than one nodes are deployed at the same location for the monitoring to improve the confidence of the detection result. We call the set of readings within the same time span and targeted at the same area form a reading cluster: Ω(span, area) ={t i t i.time span, t i.loc area} In example 1, if span=[12:15, 12:30], area = door 1, then {t 1,t 2 } form a reading cluster Ω([12 : 15, 12 : 30], door 1 ), and Ω corresponds to a set of world instance W Ω. Events are defined based on the frequency of items within the reading cluster. We call event e(v i,τ,α,ω) happens in Ω if the probability of item v i meets the following formulas: Pr(v i,τ,ω) = Pr(w) >α (1) w W Ω,count(v i,w)>τ where count(v i,w) is the number of times that item v i appears in world instance w, τ is the frequent threshold, and α is the user-defined confidence threshold. If τ and α are predefined, we usually use Pr(v i, Ω) and e(v i, Ω) to denote Pr(v i,τ,ω) and event e(v i,τ,α,ω) for short. In example 1, if τ =2,α=0.35, then only item Ball meets the condition: count(ball,w 7 )=2,count(Ball,w 8 )=2 Pr(Ball, {t 1,t 2 })=Pr(w 7 )+Pr(w 8 )=0.36 As Pr(Ball, {t 1,t 2 }) >α=0.35, then event e(ball, 2) is said to happen in reading cluster {t 1,t 2 }. Events are actually defined based on the frequency and the probability of the items. The idea behind is that an event is more likely to occur if items related to the event is reported by the nodes for multiple times and with greater confidence. IV. FREQUENT ITEMSET BASED EVENT DETECTION A. Node Clustering As discussed in section III, events are defined based on reading clusters. Yet readings generated at roughly the same time and area do not necessarily belong to the same reading cluster. For example, in the house surveillance application (illustrated in Fig. 1), the camera s angle plays an important role for the readings. Node s 2, s 3, and s 4 locate near the door and are close to each other. s 2 and s 3 are deployed to monitor the door area, yet s 4 is to monitor the parlor. Soitis important for the algorithm to cluster the nodes based on their readings, rather than their locations, for detecting the events. Nodes could be labeled and assigned to a group manually, yet it is too labor-consuming for large scale networks. Here we present an automatic scheme for node clustering, which is to execute at the network initialization phase. There are three steps in the clustering procedure: 1) When nodes are deployed, a tree-based routing infrastructure is built for the message communications. Within the predefined time interval, every node would sense the environment, and the generated data (e.g. photos) are routed up the tree to the base station. 2) The base station receives the reading tuples, and stores the tuples into a table (id, loc, time, (v 1,p 1 ), (v 2,p 2 ).., (v k,p k )), where id is the ID of the node, (v i,p i ) is the pair of value items of the reading. Then the tuples are grouped into different groups at the base station. There are some clustering algorithms available for the processing, yet we adopt the k-means partitioning algorithm [23]. The distance of any two tuples are further defined as: dis(t i,t j )= (2) max( t i, t j ) v t i,v t j min(p v t i,p v t j ) f time f loc (3) where t i is the number of value items in tuple t i, p v t i is the confidence of item v in tuple t i. f time and f loc are the normalization factors for the time and loc attributes 1039

4 of the tuples, which are further defined as: f time = max(1, t i.time t j.time ) unit time (xi x j ) 2 +(y i y j ) 2 f loc = max(1, ) unit loc where (x i,y i )=t i.loc and (x j,y j )=t j.loc, unit time and unit loc are the unit measurement of time and location for the calculation. In example 1, the tuples are t 1 = {s1, 12 : 18, door 1 (9, 15). (Dog, 1.0), (Ball,0.6)}, t 2 ={s2,12 : 18, door 1 (10, 13), (Dog, 0.3), (Lady, 0.6)}, the time factor f time = max(1, 12 : : 18 )=1, (9 10)2 +(15 13) location factor is max(1, 2 2 )=1.12, so the distance of t 1 and t 2 is: dis(t 1,t 2 ) = max(2,2),p Dog = 2 min(p Dog t 1 t ) min(0.3,1) 1.12 = ) When tuples are clustered into groups, node s i is assigned to cluster Ω m if count(s i, Ω m ) count(s i, Ω i ), m i, and i = 1, 2,..,m 1,m +1,..,k, where count(s i, Ω m ) is the number of readings generated in s i and are grouped to cluster Ω m. The cluster assignments such as (s i, Ω m ) are then routed back to the nodes in the network, and the number of nodes a cluster contains, denoted as Ω m is also forwarded to the nodes as global knowledge. B. Probability Calculation of Frequent Items After the nodes are clustered, the readings in a cluster are then used as input for the detection of uncertain events. Given a reading cluster Ω, if the probability of frequent item v is higher than threshold α, then an event labelled with v is reported. A straightforward approach for the calculation is as follows: 1)list all possible worlds of uncertain database, 2) identify all frequent items in all possible worlds, 3) calculate the probability of all the frequent items based on equation 1, and 4) output the frequent items whose probability is greater than the threshold. However, the number of generated possible worlds is exponentially related to the number of tuples. So this approach is exponential in both space and time, which makes it impractical for the resource-constraint sensor nodes. In this paper, we adopt a polynomial approach [17] to calculate the frequent items on the reading cluster. First, the polynomial F v (x) is defined as: F v (x) Ω = n a i (x), a i (x) = i=1 (4) { (1 p i )+p i x, if v t i 1, if v / t i (5) where n is the total number of tuples in the reading cluster Ω. Fibed constructs the polynomial F v (x) Ω for each distinct item v, and F v (x) Ω can be rewritten in the normalization form, as shown in equation 6: c F v (x) Ω = b i x i (6) i=0 where c n is the total number of item v in cluster Ω. Then the coefficient of x i in F v (x) Ω, denoted as b i,isthe total probability of possible worlds for which item v appears i times. Based on this definition, the probability that item v is frequent is calculated as: c Pr(v i,τ,ω) = b i (7) The space complexity of the probability calculation is S(n, c) = n c, where n is the total number of tuples, c is the number of value items in the reading cluster. C. Distributive Identification of Events As mentioned in section IV-A, nodes are assigned to clusters; and a cluster Ω is actually composed of sub-clusters, denoted as: Ω= Ω 1 Ω2..Ωk, and Ω x Ωy =,x y. Then for every item v, according to equation 5, the polynomial F v (x) Ω could be rewritten as: k F v (x) Ω = F v (x) Ωi (8) i=1 For each node, e.g. s i, the generated readings form a subcluster, and it maintains a coefficient vector for every value item it has. The vector for that value (e.g. v) is denoted as vec(s i,v) = {b 1,b 2,.., b c }, and would be aggregated and routed up the routing tree. The aggregated algorithm is similar with that in TAG [19], yet in Fibed the aggregation operations are replaced by the mergence of the coefficient vectors of items at the intermedia nodes. Due to the limited space of the paper, here we use an example to illustrate the detailed routing, probability updating, and filtering procedure of the value items in Fibed. Example 2: In Fig. 2, the network adopts a tree-structured routing strategy, and tuples are routed and aggregated based on epochs. Node s 1,s 3,s 5 belong to cluster Ω 1 (black), s 2,s 4,s 6, and s 8 belong to cluster Ω 2 (red), s 7 belongs to cluster Ω 3 (blue). At each epoch, the processing is as follows: Epoch 1: The leaf nodes s 1, s 4 and s 5 send tuples containing the items to their parents. For s 2, both s 3 and s 6 could be its parent, yet it choose s 6 because they are in the same cluster. When s 3 and s 6 receive the messages, they merge the coefficient vector for all the value items that belong to the same cluster. Epoch 2: The aggregated coefficient vectors are wrapped into tuples and routed up the tree. As s 7 is the only parent of s 3, tuples from s 3 are sent to s 7 immediately. Node s 6 has two parent node s 7 and s 8. Node s 8 belongs to Ω 2, so tuples of Ω 2 are sent to s 8 ; and tuples from s 5 belong to Ω 1, which is different from the clusters that s 6 s parents belong to. Node s 6 would wait for a predefined time, and then forward the coefficient vector from s 5 to s 7. When s 7 receives the tuples from s 3, it would have the coefficient vector of two tuples belonging to Ω 1, and Ω 1 is the cluster that s 5 belongs to. Epoch i: Nodes merge the coefficient vectors of items belonging to the same reading cluster as far as they i=τ 1040

5 Fig. 2. Coefficient vectors are merged and routed up the routing tree. Fig. 3. Snapshot of the simulation field. could. As discussed in 4.1, nodes also know the number of tuples each cluster should contain. If a node gathers exactly Ω i tuples of cluster Ω i, it would calculate the probability for each of the frequent items. If there is any frequent item whose probability is greater than α, then the item is output as an event labeled with that item and probability. If only k < Ω i tuples are collected, and the polynomial Fv(x) for item v is: Fv(x) ={b k x k + b k 1 x k b 1 x}, then the upper bound of probability for item v could be calculated in the case that the unseen Ω i k tuples all contain item v with probability 1.0. The supposed polynomial F v(x) is defined as: {b k x Ωi + b k 1 x Ωi b 1 x Ωi k }, and the upper bound of the probability Pr(v, τ, Ω i ) is: k up bound(pr(v, τ, Ω i )) = b j (9) j= Ω i τ If the upper bound is smaller than α, then there should not have an event for item v, and the coefficient vector of item v would no longer be routed up the tree. Epoch n: some coefficient vectors are aggregated and received by the base station (root of the tree), and the detected events are output to the users. The mergence of coefficient vector is epoch-based. Some cost efficient synchronism mechanisms [24] could be used for the network, so nodes could synchronize their time for the processing. V. EXPERIMENTAL STUDY A. Environment Setup We implement Fibed in C# to verify its efficiency and effectiveness. A rectangle field is divided into 64 small cells, and nodes are randomly distributed among the borders of the cells. As illustrated in Fig. 3, every four conjunct cells form a grid, and nodes are attached to the grids. There are totally 16 grids in the network, and they are the basis for dividing the nodes into clusters at the setup phase. Nodes located inside a grid has full view of the grid, and could sense all the events within the grid; yet nodes located on the borders of two adjacent grids would monitor the grids according to their viewing angles. If a node locates on the border of a grid, the viewing angle could be LEFT, RIGHT, UP, or DOWN, which is predefined at the setup phase. To simulate the events, we also conduct a data generator to inject sensing data into the network. At every epoch, the data generator randomly selects n g grids, and injects data Θ to the nodes within the grids, where Θ is a set of items. For every node within grid g, it then randomly selects x< Θ items from Θ and assigns a confidence (> 0.5) for each of the item, where Θ is the number of items in Θ. Then these uncertain item values are wrapped into tuples and routed to other nodes to impel the event detection process. The network adopts a tree-based routing strategy, where the base station is the root and tuples are routed up a routing tree to the base station. Here we assume ideal links for the communications. There are no data errors or retransmissions. As the cost of communication dominates the depletion of the limited battery energy in sensor nodes, many distributed algorithms in sensor networks focus on reducing communication cost. Here we present the event detection rate and the total communication cost (number of messages) incurred by the algorithms. Table III lists the default parameters in the simulations. B. Experimental Analysis Events are based on the reading clusters, and nodes are clustered to groups based on their readings for event detection. So we first conduct experiments to study the mechanism of node clustering. The number of transmissions for the clustering is about , which is less than 5 percent of the whole transmissions for Fibed. This is because only 4 epochs of the readings are needed in the clustering phase. Yet when there are more than 10 items, more than 94 percent (136 of 144) of the nodes are correctly clustered, which is illustrated in Fig. 4. The percentage of nodes that are correctly clustered grows with the size of item set Θ. If the event generator generates more different items for the nodes, the distance of readings belong to different clusters will become larger, which makes it easier for the node assignment and clustering for the event detection. We also vary the number of events generated by the data generator at each epoch. As illustrated in Fig. 5, the number of transmissions grows with the events for both the algorithms. Yet more than 30 percent of transmissions are saved for Fibed than that of Naive, and it grows at a much lower rate. This is because Naive send all tuples to the base station, yet Fibed adopts an in-network calculation for the frequent items. An intermediate node of the routing tree would calculate whether 1041

6 TABLE III DEFAULT PARAMETERS Parameter Value Meaning Parameter Value Meaning sim t 200 number of epochs epoch t 25s time interval of an epoch width 100m width of the field height 100m height of the field N 144 number of nodes W c 12.5m width & height of cell W g 25m width and height size of storage space S 1024K of the grid for ordinary node R 20m radio range msg size 512B message size unit time 10s normalization factors normalization factors unit for time loc 15m for loc α 0.2 confidence threshold τ 3 frequent threshold n g 6 number of events at number of items selected x 5 each epoch by the data generator Θ 10 number of items in Θ k 16 # of reading clusters 1.0 Accuracy Rate Number of Items Fig. 4. Rate of correct clustered nodes Fig. 6. Number of events vs. event detection rate Fig. 5. Number of events vs. transmissions Fig. 7. Frequency threshold vs. transmissions an item is frequent or not, and it filters the unfrequent items, saving lots of transmissions that otherwise would be sent to the base station. Fig. 6 shows the detection rate of events. For Naive, the readings are available at the base station, and are processed in a centralized way. So the event detection rate is 100%. Yet the detection rate of Fibed is also high, it is as high as 94%. The undetected events are mainly because some of the nodes are not correctly clustered, and their readings are counted for other reading clusters for the event detection. when the number of events grows at the network, more reading clusters are supposed to have, and the nodes and readings for each reading cluster are fewer. The readings, which are generated by the nodes that are incorrectly clustered, would make a greater impact for the outcome of event detection. So the detection rate has a little decrease when the number of events grows larger. We then construct experiments to study the impact of frequent threshold of events. For Naive, as all readings are sent to the base station, the number of transmissions and detection rate are unrelated with the frequent threshold. Yet for Fibed, when the frequent threshold increases from 2 to 6, the number of transmissions decreases from to , and the the detection rate slightly grows up from 94% to 97%. This is because when the threshold is large, there are fewer events in the network (as showed in Fig. 8); and it is easier to filter the unfrequent items given the upper bound of the probability of items when there are still some unseen tuples. This could be verified by the average number of hops that the coefficient vector of an item value is transmitted. As showed in Fig. 9, when the threshold becomes larger, the average number of hops of the coefficient vector become smaller. The coefficient vector of an item is only transmitted by about 2.3 hops on 1042

7 Fig. 8. Frequency threshold vs. rate and # of events Fig. 9. Average Hops of transmissions average when the threshold is 6. This means lots of items are not routed up the routing tree because Fibed has been able to compute whether an item is frequent or not after 2 hops of transmissions. So more transmission are saved by Fibed for larger frequent threshold. VI. CONCLUSIONS In this paper, we have proposed an in-network uncertain even detection algorithm Fibed for sensor networks. In Fibed, events are defined based on computing the probability of frequent itemsets. Nodes are firstly clustered based on their readings, then a polynomial is constructed to calculate the probability of an item value. The coefficient vector for the polynomial of each item is merged and updated when they are routed to the base station, and some items could be filtered to save unnecessary transmissions as their probability do not meet the threshold, saving lots of transmissions. Experimental studies show that Fibed is efficient to detect the events, and more than 30 percent of transmissions are saved for the detection of uncertain events. For the future work, firstly we are to investigate the early pruning strategies of the unfrequent items that would not meet the thresholds; secondly, we would study other types of uncertain events, and propose algorithms to efficiently detect the events of high-level semantics. REFERENCES [3] W. Xue, Q. Luo, L. Chen, and Y. Liu, Contour map matching for event detection in sensor networks, the ACM international conference on Management of data, pp , [4] A. Artikis, O. Etzion, Z. Feldman, and F. Fournier, Event processing under uncertainty, ACM International Conference on Distributed Event-Based Systems, pp , [5] R. Ross, V. Subrahmanian, and J. Grant, Aggregate operators in probabilistic databases, Journal of the ACM (JACM), vol. 52, no. 1, pp , [6] M. Ye, K. C. Lee, W.-C. Lee, X. Liu, and M.-C. 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