Spatio-Temporal outliers detection within the space-time framework

Transcription

1 (2011) Journal of Remote Sensing 遥感学报 Spatio-Temporal outliers detection within the space-time framework LIU Qiliang, DENG Min, WANG Jiaqiu, PENG Siling, MEI Xiaoming, ZHAO Ling Department of Surveying and Geo-informatics, Central South University, Hunan Changsha , China Abstract: A novel spatio-temporal outlier detection method within the space-time framework is proposed in this paper. Firstly, a unified framework is developed for constructing spatio-temporal neighborhood, which is based on the space-time statistics and clustering analysis. Then, a spatio-temporal outlier measure involving space-time autocorrelation and heterogeneity is presented. Finally, a tree-step strategy is utilized to detect spatio-temporal outliers. Our method is employed to detect spatio-temporal outliers in Chinese annual temperature database ( ). A meaningful analysis of the spatio-temporal outliers is also provided. Key words: spatio-temporal outlier detection, spatio-temporal neighborhood, space-time statistics, clustering analysis CLC number: TP701 Document code: A Citation format: Liu Q L, Deng M, Wang J Q, Peng S L, Mei X M and Zhao L Spatio-Temporal outliers detection within the space-time framework. Journal of Remote Sensing, 15(3): INTRODUCTION Spatio-temporal data mining has been a forefront research field in geographic data mining and knowledge discovery (Miller and Han, 2009). Spatio-temporal outlier detection plays an important role on spatio-temporal data mining; it aims to identify the spatiotemporal entities whose thematic attributes are significantly different from those of other entities in its spatio-temporal neighborhood. Spatio-temporal outlier detection can be employed to reveal potential information about the phenomena, such as earthquakes, volcanic activity, and traffic accidents. Outlier is defined as which deviate so much from other observations so as to arouse suspicions that they were generated by a different mechanism (Hawkins, 1980). Traditional outlier detection methods can be roughly classified into the following five categories: (1) distribution-based (Hawkins, 1980); (2) depth-based (Johson, et al., 1998); (3) distance-based (Aggarwal, et al., 2006); (4) density-based (Breunig et al., 2000); (5) Clustering-based (Ester, et al., 1996; Li, et al., 2009a). A spatial outlier is a spatial entity whose thematic attributes are significantly different from those of other spatial entities in its spatial neighborhood (Shekhar, et al., 2003). Current spatial outlier detection methods can be generally grouped into four categories: (1) graph-based (Haslett, et al., 1991); (2) distance-based (Chen, et al., 2008; Li, et al., 2009b); (3) density-based (Chawla and Sun, et al., 2006); (4) spatial clusteringbased (Li, et al., 2008). According to the concept of spatial outlier, spatio-temporal outliers can be extended and defined as a spatiotemporal entity whose thematic attribute is significantly different from the entities in its spatio-temporal neighborhood (Cheng & Li, 2006). Cheng and Li (2006) proposed a multi-scale approach to detect spatio-temporal outliers, but their method cannot give quantitative descriptions of the outliers. Adam, et al. (2004) proposed a spatial neighborhood based method to detect spatio-temporal outliers. Esentially, it is still a spatial outlier detection method, because the time dimension is only considered during the construction of macro neighborhood. Lu and Liang (2004) detected the spatial outlier trend in meteorological streaming data utilized wavelet fuzzy classification; however, the time dimension is not combined to detect spatio-temporal outliers. Birant and Kut (2006) developed a spatio-temporal clustering method to identify spatio-temporal outliers. The methods of constructing the spatio-temporal neighborhood and of identifying spatio-temporal outlier are not clearly performed in their own paper. Some other methods (Sun, et al., 2005; Barua & Alhajj, 2007; Wu, et al., 2008; Das & Parthasarathy, 2009; Li, 2009c) detect spatio-temporal outliers from the spatial and time domain respectively, the coupling of time and space is neglected. From the current spatio-temporal outlier detection methods, it can be found that there are mainly two limitations: (1) the inherent relationships between space and time which are not considered during the process of constructing spatio-temporal neighborhood; (2) the heterogeneous entities in the spatiotemporal neighborhood which more attention should be paid to. Received: ; Accepted: Foundation: National High Technology Research and Development Program of China (863 Program) (No. 2009AA12Z206); Key Laboratory of Geo- Informatics of State Bureau of Surveying and Mapping (No ); the Scientific Research Foundation of Jiangsu Key Laboratory of Resource and Environmental Information Engineering(China University of Ming and Technology) (No , No.JS200901); Digital Land Key Laboratory of Jiangxi Province (No. DLLJ201005). First author biography: LIU Qiliang (1986 ), male, master candidate in Central South University. He is in the Department of Surveying and Geoinformatics and foucuses on spatio-temporal clustering, spatio-temporal outlier detection and their applications in global climate change. He has published 10 papers. liuqiliang192@126.com

2 458 Journal of Remote Sensing 遥感学报 2011,15(3) In order to overcome these two limitations, a new strategy is proposed in this paper, it mainly solves two key issues: (1) the method of constructing spatio-temporal neighborhood takes both spatio-temporal autocorrelation and heterogeneity into count; (2) the correlation between thematic attribute and spatial attribute of a spatio-temporal entity is considered when the spatio-temporal outlier measure is calculated. A three steps strategy is utilized to detect spatio-temporal outliers in our method. The first step aims to construct the spatio-temporal neighborhood for each spatiotemporal entity. Spatial outliers are detected in the second step and the potential spatio-temporal outliers are obtained. In the last step, the possible outliers are validated. Our method will be fully performed as below. 2 CONSTRUCTION OF SPATIO-TEMPORAL NEIGHBORHOOD Spatio-temporal entity is defined as a spatial entity with a certain time stamp (Cheng & Li, 2006; Birant & Kut, 2006). Most methods of this kind do not construct the spatiotemporal neighborhood. They usually detect spatial outliers (or temporal outliers); and then verify the spatio-temporal outliers in their temporal neighborhood (or spatial neighborhood). Obviously, the influences of the spatio-temporal entities which are near in both space and time are not taken into count. Actually, the spatio-temporal neighborhood of a spatio-temporal entity should contain all the spatio-temporal entities which are near to the entity in both space and time. Fig. 1 shows an example of spatio-temporal neighborhood. There are nine spatial entities in three continuous time stamps t 1, t, t+1. The two-tuples (<entity name, temporal stamp>) is employed to label a spatio-temporal entity. For instance, entity A at time stamp t is expressed as <A, t>. The spatio-temporal neighborhood of the spatio-temporal entity <O, t> can be defined as: STN={<A, t-1>, <B, t-1>, <C, t-1>, <D, t-1>, <O, t-1>, <E, t-1>, <F, t-1>, <G, t-1>, <H, t-1>, <A, t>, <B, t>, <C, t>, <D, t>, <E, t>, <F, t>, <G, t>, <H, t>, <A, t+1>, <B, t+1>, <C, t+1>, <D, t+1>, <O, t+1>, <E, t+1>, <F, t+1>, <G, t+1>, <H, t+1>}. According to the definition of spatio-temporal neighborhood, it can be found that two important parameters must be required: (1) the length of time window; (2) the range of spatial neighborhood. Next, the method to determine the spatio-temporal neighborhood will be fully performed. A B C D O E F G H A B C D O E F G H A B C D O E F G H t-1 t t+1 Time evolution direction Fig. 1 Sketch map of spatio-temporal neighborhood (STN) 2.1 Determination of the time window In this paper, space-time lag operator in STARIMA (Space-Time Autoregressive Integrated Moving Average) model is employed to determine the time window of the spatio-temporal neighborhood. STARIMA model is a space-time dynamic model, it has been widely applied in the fields of space-time modeling and space-time prediction. STARIMA model can be expressed as follows. where p is the time autoregressive order; q is the time average order; m k is the spatial order of the k th time autoregressive term; n l is the spatial order of the l th time average order; k (l) is the time lag; h is the spatial lag; is the autoregressive parameter at time lag k and spatial lag h; θ lh is the average parameter at time lag l and spatial lag h; ε (t) is the random error. Space-time lag operator in Eq. (1) is used to represent the spacetime correlation in STARIMA model. The thematic attribute Z (t) at certain time stamp and location is influenced by previous time series at that location and previous time series of its spatial neighbors. The parameters, such as time autoregressive order p, time average order q, time lag k and patial lag h all can be obtained by calculating space-time autocorrelation function and partial spacetime autocorrelation function. Space-time autocorrelation function is expressed as follows (Martin & Oeppen, 1975). where ρ h0 (k) is the space-time autocorrelation coefficient; γ h0 (k) is the space-time covariance; k is time lag order; h is spatial lag order; W (h) is the spatial weight matrix that the spatial lag order is h; W (0) is the spatial weight matrix when the spatial lag order is 0, it is a unit matrix; T is the length of the time series; N is the number of the spatial entities. Space-time Yule-Walker equations are usually employed to calculate the partial space-time autocorrelation coefficient, which is represented as follows (Kamarianakis & Prastacos, 2005). where φ kh is the partial space-time autocorrelation coefficient; m k is the spatial order of the k th time autoregressive term; k is the time lag order; h is the spatial lag order; ρ is the number of the equations. In traditional space-time correlation analysis, spatial data is usually represented in a discrete form. The spatial hierarchical adjacent relationship is employed to get the spatial weight matrix, but this strategy is not suitable for the continuous spatial data. In this paper, the semivariogram is used to represent the variation characteristics among continuous spatial data (Wang, 2008). Spatial weight is a function with regard to the distance; two entities are relevant if the distance between them is smaller than the range. Actually, the spatial statistics model based on discrete space and continuous space is unified (Griffith & Csillag, 1993). So the spatial lag order of the STARIMA model is set to 1 in this paper. That is to say, only the entities in the range can be viewed as spatial neighbors. Time lag order can be (1) (2) (3)

3 LIU Qiliang, et al.: Spatio-Temporal outliers detection within the space-time framework 459 obtained by calculating the space-time autocorrelation function and the partial space-time autocorrelation function. However, it must be paid more attention that the time window of the spatiotemporal neighborhood is somewhat different from the meanings of time lag order in STARIMA model. Take the instance in Fig. 1 for example; the time lag order is half of the width of the time window. Time lag only considers the past time stamp. Actually, the time lag operator can be unutilized to determine the radius of the time window. If the time lag order is k, then it means that a spatio-temporal entity is only relevant with the entities in the past k time stamps or in the next k time stamps. However, the spatial lag operator in the STARIMA model cannot be directly employed to define the spatial neighborhood. From Eq. (2) and Eq. (3), it can be found that the space-time autocorrelation coefficient and partial space-time autocorrelation coefficient are all global statistics; the spatial neighbors of a spatial entity should contain all the entities which are relevant with it. Though a spatial entity is relevant with most of the entities in its range, there may be also some heterogeneous entities or some entities which are less relevant with that entity. This error can be neglected in the process of space-time analysis, but it should not define the spatial neighborhood for spatio-temporal outlier detection. While detecting spatio-temporal outliers, the spatial neighborhood should meet two requirements: (1) the unevenly distribution of the thematic attribute, the local character should be fully considered, for example, there is obvious difference between the temperature in southern China and northern China. (2) An entity should be highly relevant with entities in its spatial neighborhood. In order to meet those requirements, spatial clustering and Delaunay triangulation net are employed to define the spatial neighborhood. 2.2 Construction of spatial neighborhood The heterogeneity among the spatio-temporal entities is usually long-term and stable. In this paper, spatial clustering is firstly utilized to identify the local regions according to the average level of the thematic attribute of the spatio-temporal entities. the k-means algorithm (Miller & Han, 2009) is used in our research. Maybe other spatial clustering algorithms can be selected for different applications. The distance function for the k-means algorithms is expressed as follows (Jiao, et al., 2009). where d(st i, ST j ) is the great circle distance between two spatial entities; is the average value of the thematic attribute of a spatial entity; w E and w A are weight values, which can be defined by employing the prior knowledge, they are all set to 1 in this paper. The spatial and thematic attributes are all normalized. Secondly, Delaunay triangulation net is used to construct spatial neighborhood in each cluster. The average length of the edges is defined as the threshold to prune the long edges which lie at the borders (Kolingerova & Zalik, 2006). Lastly, the spatial entities which share a common edge in same cluster will be considered as spatial proximity. Thus, two parameters of the spatio-temporal neighborhood have been got. The radius of the (4) time window is the time lag order k. Two spatial entities are spatial neighbors when they are in the same cluster and share a common edge. 3 SPATIAL OUTLIERS DETECTION If a spatio-temporal entity is an outlier, it must be a spatial outlier at a certain time stamp. So we detect spatial outliers at each time stamp, and obtain the candidate spatio-temporal outliers set. The current methods only involve thematic attribute which used to label a spatial outlier. Actually, the thematic attribute is usually relevant with other the thematic attribute and spatial attribute which should be fully considered when the spatial outliers are detected. For different applications, it is necessary for us to design the pertinence spatial outlier detection methods. Our work aims to detect outliers in the temperature database of China. Temperature is viewed as the thematic attribute to identify outliers. The current researches show that the temperature of a location is highly relevant with the latitude, longitude and elevation. Thus, the gradient plus inverse distance squared interpolation method (Nalder & Wein, 1998) is employed to define the spatial outlier measure as follows. (5) where SOM i is the spatial outlier measure value of a location i; Z i is the thematic attribute of the location i; is the interpolation value of the thematic attribute via the gradient plus inverse distance squared interpolation method; X i and X k are the X axis coordinates value of location i and k; Y i and Y k are the Y axis coordinates value of location i and k; E i and E k are the elevations of the location j and k; C X, C Y and C E are regression coefficients for X, Y and elevation. d (X i, X k ) is the great circle distance between two location i and k; n is the number of the neighbors. According to Eq. (5), one can find that if the difference between the interpolation value and the actual value of a location is significantly high, it will be labeled as a spatial outlier. Usually, there are two methods to generate spatial outliers: (1) rank the top m spatial entities to construct spatial outlier set; (2) employ the statistical methods to identify spatial outliers. Without the prior knowledge or users requirement, the statistical method is usually used to obtain the spatial outlier set. In this paper, the following statistical variables are adopted to label spatial outliers. (7) (8) where is the median of the spatial outlier measure values of all the spatial entities at a certain time stamp; is the median absolute deviation of the spatial outlier measure values of all the spatial entities at a certain time stamp. (6) (9)

4 460 Journal of Remote Sensing 遥感学报 2011,15(3) 4 VERIFICATION OF SPATIO-TEMPORAL OUTLIER For each spatial outlier, further verifying in its spatiotemporal neighborhood is required. If the thematic attribute of the spatio-temporal entity is significantly different from the others in its spatio-temporal neighborhood, that the mentioned entity will be identified as a spatio-temporal outlier. The current methods usually use the arithmetic average to estimate the overall behavior of a set of spatio-temporal neighbors (Cheng & Anbaroglu, 2009), but the impacts of the location, elevation and outliers in spatio-temporal neighborhood should not be ignored. In this paper, a two steps strategy is utilized to verify the possible outliers in a spatio-temporal neighborhood. For a spatiotemporal entity, the spatial outliers and spatio-temporal outliers is firstly, removed from its spatio-temporal neighborhood, and the spatial neighbors in each time stamp is used to calculate the gradient plus inverse distance squared interpolation value which can be employed to integrate the influence of spatial properties. After this step, the spatio-temporal neighbors are weighted actually. Then, a statistical method is utilized to discover the possible spatio-temporal outlier by using weighted spatio-temporal neighbors. The statistical criterions are shown as follows. (10) (11) Table 1 The attribute table of the database Variables Type Description of the character Station name Float The name of the meteorological station Set up Time Datetime Establishing time of the station longitude Integer WGS_1984 coordinate system latitude Integer WGS_1984 coordinate system elevation Integer Height from seal level temperature Integer Annual average temperature( ) 5.2 Construction of spatio-temporal neighborhood When use STARIMA model to construct spatio-temporal neighborhood, the spatial weighted matrix should be firstly built. As mentioned in section 2.1, gaussian variance function is employed to define the spatial weighted matrix (Isaaks & Srivastana, 1989; Fotheringtham, et al., 2002). Variance function can be expressed as follows. (13) where N (h) is the number the spatial entity pairs, the distance between each pair is h; Z i and Z i+h are the thematic values of location i and i+h respectively; Gaussian variance function is shown as follows. 1 2 (12) where ST outliers is the spatio-temporal outliers set; ST i is a spatiotemporal entity; are the spatio-temporal neighbors which have been weighted; are the thematic values of ; μ i is the median value of ; is the median absolute deviation value of. 5 DETECT SPATIO-TEMPORAL OUTLIERS IN METEOROLOGICAL DATA IN CHINA 5.1 Description of data The data in this paper is the annual average temperature ( ) at 137 meteorological stations (with geographical coordinates) which was provided by the national meteorological center of China. The distribution of the stations is shown in Fig. 2, the attribute of the database is shown in Table 1. N 103 Fig. 2 The spatial distribution of weather stations in China (14) where C 0 is the nugget constant; C is the arch rise; C 0 +C is the sill; h is the great circle distance; r is range. Furthermore, the weight can be defined as a function with regards to the spatial lag h: or (15) where r, C and C 0 +C are all the average value for each year, r =1364 km, C=8.4, C 0 +C=11.6. Though the method introduced above, the spatial weight matrix can be firstly obtained and then normalized. Based on the analysis of spatio-temporal autocorrelation and partial autocorrelation, the time lag order can be determined as two years, that is to say the width of the time window can be set as two years. It should be noted that the stationarity assumption of the spatio-temporal data does not need to be strictly satisfied in actual applications (Nalder & Wein, 1998). In our research, if the average value and the variance of the spatio-temporal data are constants, and the covariance is a function with regards to time lag and spatial lag, then we consider that the data is approximate stationarity. For nonstationarity spatial data, first remove the spatial trend, and then calculate the variance function. The ordinary kringing interpolation results for six years are shown in Fig. 3. The deep color region represents high temperature region, and the light color region represents low temperature region. From the interpolation results, one can find that the regional character of the temperature distribution in China is obvious. Thus,

5 LIU Qiliang, et al.: Spatio-Temporal outliers detection within the space-time framework 461 (a) (b) (c) (d) (e) (f) -5.2 Fig (South China Sea and East China Sea are excluded) (a) 1970; (b) 1975; (c) 1980; (d) 1990; (e) 1995; (f) 2000 ferent clusters are labeled with different symbols, and the four clusters is named as the Northeast, the North, the Northwest and the South respectively. Then the spatial neighborhoods are constructed in each cluster (Fig. 5). If the length of an edge in Delaunay triangulation net is more than three times of the average length, it will be deleted. Range 5.3 Fig Spatial distribution of temperatures in the year 1970, 1975, 1980, 1990, 1995 and 2000 N Northeast 14.9 North Northwest South Spatial clustering result it is necessary to discover the local patterns of the temperature by spatial clustering. The spatial clustering result is shown in Fig. 4. According to existing research, the cluster number is set to 4. Spatial entities in dif- Spatial outlier detection Based on the analysis of the distribution of the temperature in China (Fig. 3), it can be found that the temperature of a location is highly relevant with the latitude, longitude and elevation. So it is necessary to take the impacts of latitude, longitude and elevation into consideration for the detection of the spatial outliers. As for each year s tempreture data, we calculate the regression coefficients for X, Y and elevation in each cluster at first, then, calculate the spatial outlier measure and detect spatial outliers; after this step, obtaine 424 spatial outliers. 5.4 Spatio-temporal outlier detection As for each spatial outlier, it needs to verify whether it is significantly deviate from others in its spatio-temporal neighborhood according to Eq. (10). Finally, eight spatio-temporal outliers are

6 462 Journal of Remote Sensing 遥感学报 2011,15(3) N N Fig. 5 The construction of spatial neighborhood Fig. 6 The spatial distribution of spatio-temporal outliers ( outliers ) Temperature/ Spatio-temporal neighborhood (a) Temperature/ Spatio-temporal neighborhood (b) Temperature/ Spatio-temporal neighborhood (c) Temperature/ Temperature/ Temperature/ Spatio-temporal neighborhood Spatio-temporal neighborhood Spatio-temporal neighborhood (d) (e) (f) Temperature/ Temperature/ Spatio-temporal neighborhood Spatio-temporal neighborhood (g) (h) Fig. 7 Schematic diagrams of spatio-temporal outliers (a) Station 22 in 1993; (b) Station 51 in 1993; (c) Station 52 in 1987; (d) Station 52 in 1989; (e) Station 52 in 1990; (f) Station 52 in 1994; (g) Station 107 in 1984; (h) Station 123 in 1987 got, the distribution of them are performed in Fig. 6. The temperatures of the entities in the spatio-temporal neighborhood of an outlier are shown in Fig. 7. The temperature is ranked from the near to the far according to spatial distance and time. The entities in the spatio-temporal neighborhood of an outlier are listed in Table 2.

7 LIU Qiliang, et al.: Spatio-Temporal outliers detection within the space-time framework 463 Table 2 Spatio-temporal outliers and the elevations of their neighbors Spatio-temporal outlier Spatio-temporal neighbors Spatio-temporal outlier Spatio-temporal neighbors Elevation Elevation Elevation Elevation No. Name No. Name No. Name No. Name /m /m /m /m 76 Xilinhaote Hechi Abaga Zhurihe Baise Erlianhaote Guiping Dongwuzhumuqin Guilin Wuzhou Zhurihe Shaoguan Huade Nanchang Erlianhaote Yining Huade Kelamayi Abaga Jinghe Hebukesaier Longzhou Kuche Hechi Wulumuqi Nanning 73.1 In Fig. 7, parts on the left side of the dashed line represent the deviation of a spatio-temporal outlier in continuous time series, and the red circle marks the spatio-temporal outlier. It can be found that the deviation of the spatio-temporal outlier is significant in continuous time series. Indeed, there are inherent heterogeneities in the neighborhood because of the differences of distance and elevation. For example, in the neighborhood of 107 th Guilin station, the latitude of 113 th Nanchang station is obviously higher than the others, so it is normal that the temperature of it is relatively lower; in the neighborhood of 22 th Jinghe station, the elevation of the 20 th Hebusaier station is significantly higher than the others, correspondingly its temperature is relatively lower according to the meteorological rules. Therefore, it is essential to take the distance and elevation differences into acount when detecting the spatio-temporal outlier. However, the informed methods only considered the differences of the temperature in a neighborhood, thus it is usually difficult to discover the local outliers. 5.5 Analysis of spatio-temporal outliers Considering serious natural disasters and agricultural development in our country, we will give an analysis of the spatio-temporal abnormal phenomenon detected above. Continuous spatio-temporal outliers existed in Abaga station and Zhurihe station which are located in the east of Inner Mongolia from the year 1987 to In particular, there were almost continuous spatio-temporal outliers in Zhurihe station. During this period, a forest fire occurred in the northeastern Daxing an Mountain range, which is the most serious forest fire in the history of China. It had lasted nearly one month and more than 135 million hectares area were destroyed. Considering terrain character in this region, It can see that the spatiotemporal outliers are located between Inner Mongolia plateau and the Northeast plain. It can be inferred that the spatio-temporal outliers in this area may be caused by the great destruction of ecological environment on the Northeast region. Additionally, we can also speculate that the forest in Daxing an Mountain range plays an important role on the ecological environment of that area. These conclusions may be applied in the fields of ecological, forestry and agricultural in the future. When spatio-temporal outliers had occurred in Guilin station and Baise station in Guangxi province from 1984 to1987, the area of farmland influenced by drought is up to 8%. Compared with 1.7% from 1980 to 1984 and 3.5% from 1990 to 1993, it is terribly higher (Shi, et al., 1997). La Nina phenomenon may be an important influence factor. As a result, it can provide a valuable reference for the research of La Nina phenomenon by means of spatio-temporal outliers. According to the analysis above, it can be concluded that spatiotemporal outliers are closely associated with the extreme natural disasters. Spatio-temporal outlier detection and interpretation will play an important part in spatio-temporal modeling and decisionmaking. 6 CONCLUSIONS AND FUTURE WORK Spatio-temporal outlier detection has been one of the hot issues in spatio-temporal data mining. Though it has attracted the attentions of many scholars home and abroad, there are also some limitations in existing spatio-temporal outlier detection methods. In this paper, a new method of constructing the spatio-temporal neighborhood has been firstly developed. Then, a three steps strategy to detect spatio-temporal outliers is performed. The method proposed in this paper is finally utilized to detect spatio-temporal outliers in Chinese annual temperature database ( ). Compared with current methods, there are mainly two aspects of advantages. The first one is that in the construction of spatio-temporal neighborhood, spatio-temporal autocorrelation and heterogeneity among entities are fully considered. The second one is that a framework of spatio-temporal outlier detection has been presented, which can be easily utilized in the other types of data. Future work will focus on the two aspects. One is to develop a spatio-temporal outlier detection method which can fully consider the non-stationary characteristics of the spatio-temporal data; the other is to increase the accuracy of the results of the spatio-temporal outlier detection method. REFERENCES Adam N R, Janeja V P and Atiuri Neighborhood based detection of anomalies in high dimensional spatio-temporal sensor datasets. Proceedings of ACM Symposium on Applied Computing, Aggarwal C, Basta S and Pizzuti C Distance-based detection and prediction of outliers. IEEE Transactions on Knowledge Discovery

8 464 Journal of Remote Sensing 遥感学报 2011,15(3) and data engineering, 18(2): Barua S and Alhajj R Parallel wavelet transform for spatiotemporal outlier detection in large meteorological data. Intelligent Data Engineering and Automated learning, Birant D and Kut A Spatio-temporal outlier detection in large databases. Journal of computering and information technology, 14(4): Box G E P, Jenkins G M and Reinsel G C Time series analysis: forecasting and control. Prentice-Hall Press Breunig M, Kriegel H, Ng R T and Sander J LOF: identifying density-based local outliers. Proceeding of the ACM SIGMOD Conference. On Management of Data 2000, Dallas, TX: Chawla S and Sun P SLOM: A new measure for local spatial outliers. Knowledge and Information Systems, 9(4): Chen D C, Lu C T, Kou Y F and Chen F On detecting spatial outliers. Geoinformatica, 12(4): Cheng T and Li Z A multiscale approach for spatio-temporal outlier detection. Transaction in GIS, 10(2): Cheng T and Anbaroglu B Spatio-temporal outlier detection in environment data. COSIT-09 Workshop on Spatial and Temporal Reasoning for Ambient Intelligence Systems, 1 8 Das M and Parthasarathy S Anomaly detection and spatio-temporal analysis of global climate system. Proceedings of SensorK- DD 09, Ester M, Kriegel H P, Sander J and Xu X A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, Portland, OR: Fotheringtham A S, Brunsdon C and Charlton M E Geographically Weighted Regression: The Analysis of Spatially Varying Relationships Chichester. Wiley Press Griffith D and Csillag F Exploring relationships between semivariogram and spatial autoregressive models. Regional science Association International, 72(3): Haslett J, Brandley R, Craig P, Unwin A and Wills G Dynamic graphics for exploring spatial data with application to locating global and local anomalies. The American Statistician, 45(3): Hawkins D Identification of Outliers. London: Chapman and Hall Isaaks E H and Srivastana R M An Introduction to Applied Geostatistics. London Oxford University Press Jiao L M, Liu Y L and Liu Y F Spatial autocorrelation patterns of datum land price of cities in a region. Geomatics and Information Science of Wuhan University, 34(7): Johson T, Kwok I and Ng R T Fast computation of 2-dimensional depth contours. Proceeding of KDD 98: Kamarianakis Y and Prastacos P Space-time modeling of traffic flow. Computers & Geoscience, 31(2): Kolingerova I and Zalik B Reconstructing domain boundaries within a given set of points using delaunay triangulation. Computers & Geosciences, 2006, 32(9): Li G Q, Deng M, Cheng T and Zhu J J A dual distance based spatial clustering method. Acta Geodaetica et Cartographica Sinica, 37(4): Li G Q, Deng M, Liu Q L and Cheng T. 2009a. A spatial clustering method adaptive to local density change. Acta Geodaetica et Cartographica Sinica, 38(3): Li G Q, Deng M, Zhu J J, Cheng T and Liu Q L. 2009b. Spatial outlier detection considering distances among their neighbors. Journal of Remote Sensing, 13(2): Li G Q. 2009c. Theories and Methods of Spatio-temporal Outlier Detection. Changsha: Central South University Lu C T and Liang L R Wavelet fuzzy classification for detecting and tracking region outliers in meteorological data. Proceedings of the 12th Annual ACM International Workshop on GIS, Martin R L and Oeppen J E The identification of regional forecasting models using space-time correlation functions. Transaction of the Institute of British Geographers, 66: Miller H and Han J Geographic Data Mining and Knowledge Discovery (second edition). London: CRC Press: 2009 Nalder I A and Wein R W Spatial interpolation of climate normals: test of a new method in the canadian boreal forest. Agric. For. Meteorol, 92: Shekhar S, Lu C T and Zhang P S A unified approach to detecting spatial outliers. Geoinformatica, 7(2): Shi P J, Wang J G, Xie Y, Wang P and Zhou W G A preliminary study of the climatic change, natural disasters of agriculture and grain yield in China during the past 15 years. Journal of Natural Resource, 12(3): Sun Y X, Xie K, Ma X, Jin X, Pu W and Gao X Detecting spatio-temporal outliers in climate dataset. International Geoscience and Remote Sensing Symposium, Wang J Q Space-time Series Data Analysis and Modeling. Guangzhou: Sun yat-sen University Wu E, Liu W and Chawla S Spatio-temporal outlier detection in precipitation data. Proceedings of Sensor-KDD 08, 6 13

9

10

11

12

13

14

15

16

17

18