Classification and Prediction of Motion Trajectories using Spatiotemporal Approximations

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1 Classification and Prediction of Motion Trajectories using Spatioteporal Approxiations Andrew Naftel & Shehzad Khalid School of Inforatics University of Manchester Manchester, M6 1QD Abstract A new technique is proposed for classification and siilarity retrieval of video otion clips based on spatio-teporal object trajectories. The trajectories are treated as otion tie series and odelled using orthogonal basis polynoial approxiations. Trajectory clustering is then carried out to discover patterns of siilar object otion behaviour. The coefficients of the basis functions are used as input feature vectors to a Self-Organising Map which can learn siilarities between object trajectories in an unsupervised anner. Clustering in the basis coefficient space leads to efficiency gains over existing approaches that encode trajectories as discrete point-based flow vectors. Experients on pedestrian otion data deonstrate the effectiveness of our approach leading to accuracy iproveents in trajectory prediction. Applications to otion data ining in video surveillance databases are envisaged. 1 Introduction An increasing nuber of systes are now able to capture and store data about object otion such as those of huans and vehicles. This has acted as a spur to the developent of sophisticated contentbased visual data anageent techniques. General purpose tools are now urgently required for otion data search and retrieval, discovery and grouping of siilar otion patterns, detection of anoalous behaviour, otion understanding and prediction. Much of the recent research focus has been on representation schees for otion indexing and retrieval [1]-[11]. This work presupposes the existence of soe low-level tracking schee for reliably extracting object-based otion trajectories. A description of relevant tracking algoriths is not within the scope of this paper but recent surveys can be found in [12, 13]. The literature on trajectory-based otion understanding and pattern discovery is less ature but advances using learning Vector Quantization (LVQ) [14], Self-Organising Feature Maps (SOMs) [15, 16], hidden Markov Models (HMMs) [17], and fuzzy neural networks [18] have been reported. Most of these techniques attept to learn high-level otion behaviour patterns fro saple trajectories using discrete point-based flow vectors as input to the learning phase. For realistic otion sequences, convergence of these techniques is slow and the learning phase is usually carried out offline. This is due to the high diensionality of the input feature space. In this paper, we introduce a diensionality reduction technique for learning trajectory patterns based on a spatio-teporal odelling schee previously used for tie series indexing. The resulting efficiency gains ake this approach feasible to ipleent online. Related work within the teporal database counity on approxiation schees for indexing tie series data is highly relevant to the paraeterisation of object trajectories. However, coputer vision researchers have been slow to appreciate the relevance of this work. For exaple, spatioteporal trajectories have been successfully odelled using discrete Fourier transfors (DFT) [19],

2 discrete wavelet transfors (DWT) [2], adaptive piecewise constant approxiations (APCA) [21], and Chebyshev polynoials [22], to nae but a few. In this paper, we ai to apply tie series indexing of spatioteporal trajectories to the proble of trajectory classification and show how to learn otion patterns by using the indexing schee as an input feature vector to a neural network learning algorith. The reainder of the paper is organized as follow. We review soe relevant background aterial in section 2. In section 3, we present our trajectory odelling approach. The algorith for learning trajectories is then presented in section 4 within the fraework of a self-organising ap. This is applied in the context of clustering otion trajectories and experiental results for a pedestrian object tracking database are reported in section 5. The paper concludes with a discussion of the advantages of our proposed technique over copeting approaches and outlines further work. 2 Review of Previous Work Motion trajectory descriptors are known to be useful candidates for video indexing and retrieval schees. Previous work has sought to represent oving object trajectories through piecewise linear or quadratic interpolation functions [1, 2], otion histogras [4] or discretised direction-based schees [3, 8, 9]. Spatioteporal representations using piecewise-defined polynoials were proposed by Hsu [6], although consistency in applying a trajectory-splitting schee across query and searched trajectories can be probleatic. Affine and ore general spatioteporally invariant schees for trajectory retrieval have also been presented [5, 7, 1]. The iportance of selecting the ost appropriate trajectory odel and siilarity search etric has received relatively scant attention [11]. In addition to polynoial odels, a wide variety of basis functions have been used to approxiate object trajectories [19, 2, 22]. Efficient indexing schees can then be constructed in the coefficient space of the basis functions. These schees have been copared with respect to search pruning power, CPU and I/O efficiency costs [21, 22]. It is surprising to find that any of these candidate tie series indexing schees have not yet been applied to the proble of otion data ining and trajectory clustering. Recent work has either used probabilistic odels such as HMMs [17] or discrete point-based trajectory flow vectors [14, 16, 18] as a eans of learning patterns of otion activity. Point-based flow vectors generally consist of spatial coordinates augented by instantaneous object velocities and accelerations. These can be noralised to account for variations in trajectory length. The contribution of this paper is to show that a trajectory-encoding schee based on input feature vectors consisting of basis function approxiation coefficients can be used to learn otion patterns ore effectively. Hence, clustering and classification processes can be carried out ore efficiently in the basis coefficient space. 3 Trajectory Representation 3.1 Least Squares Polynoials The output of a otion tracking algorith is usually a set of noisy 2-D tracker points (x i, y i ) representing the object s otion path over a sequence of n fraes, where i = 1,,n. Often the representative point is taken to be the centroid or edge idpoint of the object s iniu bounding rectangle. The otion trajectory can be considered as two separate 1-diensional tie series, <t i, x i > and <t i, y i >, the horizontal and vertical displaceent against tie where t 1 < < t n. We consider three alternative trajectory odels: Least Squares (LS), Chebyshev polynoial approxiations (CS) and discrete Fourier transfor (FS). LS polynoials are suitable for odelling siple otion trails in the spatial doain, e.g. vehicles oving uniforly along highways, or for soothing x-y projections of ore coplex spatio-teporal trajectories. Chebyshev approxiations are ore appropriate for odelling highly coplex spatioteporal trajectories such as pedestrian otion exhibiting stop-start

3 and looping otions, whilst Fourier series approxiation are suitable for ixed types of trajectory. We copare the perforance of the 3 different odelling approaches in section 5. The trajectory can be approxiated by a polynoial P (t) of degree < n as x y] P ( t) = a + a1t + K + at [ (1) The projections in (x, t) and (y, t) planes are odelled as independent polynoials P x, P y in t. Note that separate 1-D trajectories are created for each spatial coordinate [x y]. The unknown 2(+1) coefficients {a xi, a yi }, i =,..., can be deterined using LS by iniising the function E with respect to a, a 1,... n 2, a1, K, a ) = {[ xi yi ] ( a + a1t + K ati )} i= 1 E ( a + The otion trajectories are thus indexed by vector of coefficients {(a x,,a x ),( a y,,a y )}. 3.2 Chebyshev Polynoials Alternatively, a spatioteporal trajectory can be approxiated by a function f(t) expressed as a weighted su of Chebyshev polynoials C k (t) up to degree, defined as 1 t where ( t) = cos( k cos ( )) and C k [ x y] = f ( t) b k C k k= (2) (3) 1 b = f ( t k ) k= 1 2, bi = f ( tk ) Ci ( tk ) k= 1 (4) for t [-1,1] and i = 1,...,. The k roots of C k (t) are given by t j for 1 j k. Ipleentation details can be found in [23]. Occasionally, it ay be possible to approxiate the otion trail (spatial trajectory shape only) in the x-y plane. In this case, we would replace t by x or y in one of the above equations depending on the choice of principal axis [6]. This would only be worthwhile if all trajectories could be aligned with the sae principal axis. An exaple would be the odelling of vehicle trajectories in highway traffic surveillance. 3.3 Discrete Fourier Transfor (DFT) The DFT coefficients of the spatioteporal trajectory can be calculated using the well known Fast Fourier Transfor (FFT). The forulas for evaluating the Fourier coefficients can be found in [19, 23]. 3.4 Siilarity Search Metric A Euclidean distance is used as the basis for coparing the siilarity of otion trajectories. Each approxiation produces a vector of coefficients which can be used to index a 2-diensional spatioteporal trajectory. Given two trajectories Q and S, we can index these by a vector of 2(+1) coefficients Q = { q,..., } and S { s,..., } T yi q = s, where i si q, are s i = [ sxi, s ] (i =,..., ). A Euclidean distance function (ED) on the coefficient space can be expressed as T q i [ qxi, q yi ] = and

4 ED( Q, S) = 2 ( q i s i ) i= r r = 2 ( qxi sxi ) + ( q yi s yi ) i= 2 (5) 4 Learning Trajectory Patterns Using Self- Organizing Maps Self-organised aps (SOMs) have been previously used for otion trajectory clustering and classification [15, 16] with trajectories encoded as discrete point-based flow vectors. This step can be replaced by the proposed coefficient indexing schee. A SOM can discover the underlying structure of otion trajectory in an appropriate feature space through unsupervised learning. As we shall see the feature space can be the original high diensional trajectory space or the reduced coefficient subspace. 4.1 Network Model The architecture chosen for the SOM is very siple with a layer of input neurons connected directly to a single 1-D output layer. Each input neuron is connected to every output neuron with the connection represented by a weight vector. The network topology is shown in Fig. 1. A siilar architecture was used in [16] for learning vehicle trajectories as a eans for accident prediction.... Output layer Fig. 1. SOM network architecture used for trajectory clustering In a SOM network, physically adjacent output nodes encode the patterns in the trajectory data that are siilar and, hence, it is known as a topology-preserving ap. Consequently, siilar object trajectories are apped to the sae output neuron. The nuber of input neurons is deterined by the size of the feature vector which in this case relates to the selected nuber of coefficients for the basis functions. The degree of the polynoial can be chosen by setting a threshold on the axiu deviation of the function approxiation fro the data or ean-squared error. The nuber of output neurons represents the nuber of clusters in the trajectory data and this is selected anually. 4.2 Learning Algorith Input layer The algorith used to cluster the trajectories differs slightly fro the original SOM proposed by Kohonen [24]. The nuber of output neurons is initially set to a higher value than the desired nuber of clusters which we wish to produce. After training the network, clusters representing the ost siilar patterns are erged using an aggloerative ethod until the cluster count is reduced to the required nuber. The weights are initialised to linearly spaced values lying within the range of input values. Neighbourhood size is initially set to cover over half the diaeter of the output neurons. Let B be the input feature vector representing the set of trajectory basis function coefficients, and W the weight vector associated to each output neuron. The learning algorith coprises the following steps:

5 1. Deterine the winning output node k (indexed by c) such that the Euclidean distance between the current input vector B and the weight vector W k is a iniu aongst all output neurons, given by the condition B Wc ( t) B Wk ( t) k (6) 2. Train the network by updating the weights. A subset of the weights constituting a neighbourhood centred around node c are updated using Wk ( t + 1) = Wk ( t) + α ( t) η( k, c)( B Wk ( t)) (7) where η(k, c) = exp( r k r c 2 / 2σ 2 ) is a neighbourhood function that has value 1 when k=c and falls off with distance r k r c between nodes k and c in the output layer, σ is a width paraeter that is gradually decreased over tie and t is the training cycle index. 3. Decrease the learning rate α(t) linearly over tie. 4. After a pre-deterined nuber of training cycles, decrease the neighbourhood size. 5. At the end of the training phase, erge the ost siilar cluster pairs until the desired nuber of groupings is achieved. Clusters are erged by calculating the weighted ean of the weights associated with each neuron taking into account the nuber of input saples allocated to the cluster. Assuing W a and W b are the weight vectors associated with output neurons representing the ost siilar clusters, and, n are the nuber of saple trajectories apped to these neurons respectively, a new weight value W ab for the erged cluster can be calculated as Wa + nwb Wab = + n (8) 5 Experients We now present soe results to indicate the effectiveness of the proposed trajectory clustering technique. We have evaluated the perforance of the trajectory clustering algorith using the CAVIAR visual tracking database [26]. The database consisted of hand annotated video sequences of oving and stationary people and are intended to provide a testbed for bencharking vision understanding algoriths. Seantic descriptions of the target object behaviours and otion had been previously generated and stored in XML files. These files have been parsed to extract ground truthlabelled object trajectories. The dataset contains 222 trajectories as shown in Fig. 2. Fig. 2. Background scene containing ground truth labelled object trajectories extracted fro the CAVIAR dataset [26]. The perforance of the 3 different trajectory representation schees have been copared. The purpose of the experient is to test the retrieval accuracy for each approxiation schee and to

6 investigate the effect of varying the nuber of coefficients used for odel fitting. We also wish to exaine the effect on retrieval perforance by introducing additive noise. A corrupted dataset S C is produced by adding the ter η*u[,1]*rangevalues to each coordinate in the original set S, where η is a scaling factor such that η 1, U[,1] is unifor rando noise on the interval [,1], and rangevalues is the range on X or Y coordinates. Each corrupted trajectory in S C then serves as an exaple query Q C and we search for its closest atch in the original dataset S by searching for iniu ED(Q C,S). A set of rankings over all Q is produced. In the absence of noise and when no data is excluded, the ean ranked value should be 1. For ease of coparison we record the proportion of ties (as a percentage) the query trajectory is ranked correctly as 1. This is repeated for different nuber of coefficients in LS, Chebyshev and Fourier approxiations and for various values of η. The results are suarised in Fig % retrieval accuracy w =.5 w = 1. w = 2. LS=2 LS=3 LS=4 CS=4 CS=8 CS=16 FS=2 FS=4 FS=8 # coefficients Fig. 3. Effect of scaled unifor noise on trajectory retrieval accuracy. w is the scaling factor, LS= least squares, CS = Chebyshev polynoials, and FS = Fourier series approxiation. For sall aounts of noise, the choice of approxiation schee or nuber of coefficients does not appear to be too critical, although there is a slight fall off in perforance of LS as the coefficient nuber increases. For higher noise levels, it is apparent that Fourier series approxiations outperfor LS and Chebyshev polynoials. This ay be explained by the fact that Euclidean distance defined over Fourier coefficients is ore noise resistant in the frequency doain. In previous work, it has been shown that a LS-RANSAC approach would be beneficial if it is known that the tracking algorith produces very noisy estiates with a significant nuber of outliers [11]. The retrieval experient was then repeated but this tie under siulated object occlusion by reoving at rando a subsequence of points. The proportion of points reoved (p) varied between 1, 2 and 3% of the trajectories length. Each of the results obtained were averaged over 1 rando occluding subsequences. In this instance there was no added noise. The percentage retrieval accuracy over all query trajectories was deterined as before for each choice of approxiation schee and nuber of coefficients. The results are shown in Fig. 4. In this case LS approxiations perfor best under conditions of siulated occlusion. The ED-etric defined over the coefficient subspace is now used to perfor the trajectory clustering step. We ran the SOM clustering algorith using the 3 different spatioteporal approxiations. Fro epirical observations it was noticed that if the nuber of coefficients is too low (typically < 3), poor clustering results are obtained. As a sanity check, we repeated the clustering using a standard K-Means algorith [25] and the sae result was observed. Although satisfactory results are obtained in retrieval experients with a sall nuber of coefficients, there is insufficient discriinatory power in a very low diensional coefficient subspace to achieve a eaningful clustering outcoe. In practice we have found no discernible differences in SOM clustering results between spatioteporal trajectory odels generated by CS=4..8 and FS=4..6 for about K=1 clusters. The

7 SOM algorith always produces visually better cluster separations than K-eans. This is to be expected given that SOM better preserves the topology of the original trajectory space. We do not attept to noralise to achieve scale or translational invariance since we wish to preserve these differences in the clustering step % retrieval accuracy p = 1% p = 2% p = 3% LS=2 LS=3 LS=4 CS=4 CS=8 CS=16 FS=2 FS=4 FS=8 # coefficients Fig. 4. Effect of occluding subsequences on trajectory retrieval accuracy. p is the percentage of subsequence length reoved fro the original trajectory. Results are averaged over 1 rando reovals. LS= least squares, CS = Chebyshev polynoials, and FS = Fourier series approxiation. Fig. 5. Clustering of spatioteporal object trajectories fro CAVIAR database using SOM algorith and Chebyshev polynoial of degree 8. The trajectory closest to the codebook vector is displayed in red.

8 We initially train a SOM network with 5 output neurons and then reduce these to 9 using the aggloerative clustering ethod described in section 4.2. The resulting trajectory groups are shown in Fig. 5 for Chebyshev polynoial of degree 8, although siilar results are obtained using Fourier approxiations of degrees 4 to 6. Visual inspection shows that qualitatively siilar otion trajectories have been grouped together quite successfully. Motions across the corridor fro left-to-right and right-to-left are grouped into separate clusters as expected. In order to visualise the effects of trajectory clustering in the coefficient subspace, we have perfored Principal Coponent Analysis (PCA) on the vector of Fourier coefficients ( = 4) and calculated the first 3 PCs which explain 94% of the total variation. The results are shown in Fig. 6. Each point represents an instance trajectory and these are colour/arker coded to highlight the separate cluster groups each trajectory is allocated to. These plots show a good degree of cluster separation in the PCA reduced coefficient subspace. Fig. 6. Trajectory clustering in the Fourier coefficient subspace ( = 4). For visualisation purposes we have perfored PCA on the coefficient vector and plotted PC 1 vs PC 2 (left), PC 1 vs PC 3 (centre), and PC 2 vs PC 3 (right). Error ellipses for the covariance atrix are shown for each cluster group. To investigate the effectiveness of clustering in the diensionally reduced coefficient subspace copared to clustering in the original space using trajectories encoded as discrete point-based flow (PBF) vectors, we perfored soe classification tests. The class labels of the otion trajectory patterns were learned using the SOM and K-eans unsupervised techniques on the CAVIAR training data. The dataset Ξ was then randoly partitioned into training and test sets of equal sizes for crossvalidation purposes. We used a k-nn classifier (with k = 1) to classify instance trajectories fro the test set and generated the overall classification accuracy. To avoid bias, we repeated the rando partitoning 5 ties and averaged the classification errors over the test set. The results suarised in Table 1 deonstrate the superiority of learning trajectory patterns in the coefficient subspace. The classification accuracy obtained using coefficient subspace learning is higher than that of discrete PBF vector encoding for both SOM and K-eans algoriths. Method type Accuracy % SOM: coefficient subspace 91.9 SOM: PBF vectors 79.9 K-Means: coefficient subspace 88.8 K-Means: PBF vectors 85.6 Table 1. Coparison of ean overall classification accuracy for 2 different clustering techniques (SOM and K-eans) and 2 different trajectory encodings (coefficient subspace and discrete PBF vectors). #classes : #trajectories = 9 : 111. Significant speed-ups are thus possible using this approach and it now becoes feasible to learn otion activity patterns and perfor trajectory classification online. This is not currently possible when trajectories are encoded as discrete PBF vectors. In the next experient we copare the perforance of all 4 ethods in trajectory prediction and classification. Fro the original set S, we define a set of partial trajectories S P by sapling a subset of points fro the original trajectories fro 1% of the original length up to 1% in steps of 1. A partial trajectory is said to be isclassified if it is not assigned to the original cluster group based on the full trajectory set S. The classification is perfored based on the input vectors consisting of

9 coefficients or PBF vectors. This is repeated for the SOM and K-Means defined set of codebook vectors. Assuing the size of the input vector to be, the Euclidean distance is then calculated between the input vector B i representing the partial trajectory and weight vector W ik associated with kth output neuron as D k = ( Bi Wik ) i=1 2 k (9) The partial trajectory is then allocated to the class associated with the iniu value of D k. If the class is different fro the one to which the full trajectory was allocated then it is recorded as a isclassification. In the case of flow vector encoded trajectories, the point-based Euclidean distance easure is used. The percentage of isclassified trajectories taken over S P is calculated for each ethod and for various sapling rates. The use of eq. (9) rather than k-nn classifier saves tie as only the weight vectors need be exained rather than the full test set. As evidenced fro Fig. 7, the classifier derived fro SOM in the coefficient subspace again outperfors K-Means. Furtherore, paraeterized odels prove ore effective than point-based flow vectors in the trajectory prediction and classification task. These results give further ipetus to the developent of alternative diensionality reduction techniques for learning and prediction of otion activity patterns. Misclassification % Coeffs based SOM Coeffs based KMean Points based SOM Points based KMean % of Sapled Trajectory Fig. 7. Coparison of ean overall classification accuracy in trajectory prediction using 2 different clustering techniques (SOM and K-eans) and 2 different trajectory encodings (coefficient subspace and discrete PBF vectors). #classes : #trajectories = 9 : 111. Finally, we repeated the above experient on trajectory prediction but copared the classification accuracy perforance of the 3 approxiations schees for coefficient subspace learning using SOM and K-eans. The use of SOM outperfors K-eans in all cases of unsupervised learning and Fourier approxiations records the highest classification accuracy over the partial sapling range 4-9%. The potential for predicting the correct spatioteporal trajectory pattern fro a partial trajectory has therefore been deonstrated. 7 % Mis-classification SOM-LS SOM-CS SOM-FS KM-LS KM-CS KM-FS % sapled trajectory

10 6 Discussion and Conclusion This paper presents a neural network learning algorith for classifying spatioteporal trajectories. Global features of otion trajectories are found to be represented well by polynoial and Fourier series approxiations and this is apparent in the cluster visualizations. Using coefficients of basis functions as input feature vectors to a neural network learning algorith offers an efficient alternative to the use of flow vectors for trajectory classification and prediction. A current disadvantage is the representation of highly coplex trajectories (e.g. hand trajectories in sign language) which are inherently unsuited to a global polynoial-based or Fourier representation. One possibility is to use a trajectory segentation or ultiscale approach and augent the feature vector with additional entries relating to object shape or colour. In future work we would like to extend this work to the autonoous detection of anoalous trajectories and prediction of unusual otion behaviour. A ore coprehensive perforance evaluation of other diensionality reduction techniques in trajectory classification is also needed, e.g. ICA, HMMs and distance etric learning. References [1] S-F. Chang, W. Chen, H.J. Meng, H. Sundara, and D. Zhong, A fully autoated content-based video search engine supporting spatioteporal queries, IEEE Trans. Circuits Syst. Video Technol., vol. 8, no. 5, pp , Sept [2] S. Jeannin and A. Divakaran, MPEG-7 visual otion descriptors, IEEE Trans. Circuits Syst. Video Technol., vol. 11, no. 6, pp , June 21. [3] S. Dagtas, W. Ali-Khatib, A. Ghafor, and R.L. Kashyap, Models for otion-based video indexing and retrieval, IEEE Trans. Iage Proc., vol. 9, no. 1, pp , Jan 2. [4] Z. Aghbari, K. Kaneko, and A. Makinouchi, Content-trajectory approach for searching video databases, IEEE Trans. Multiedia, vol. 5, no. 4, pp , Dec. 23. [5] F. Bashir, A. Khokhar, and D. Schonfeld, Segented trajectory-based indexing and retrieval of video data, in Proc. IEEE Int. Conf. Iage Processing, Spain, 23, pp [6] C-T. Hsu and S-J. Teng, Motion trajectory based video indexing and retrieval, in Proc. IEEE Int. Conf. Iage Processing, pt 1, 22, pp [7] F. Bashir, A. Khokhar, and D. Schonfeld, A hybrid syste for affine-invariant trajectory retrieval, in Proc. MIR 4, 24, pp [8] C. Shi and J. Chang, Content-based retrieval using trajectories of oving objects in video databases, in Proc. IEEE. 7th Int. Conf. Database Systes for Advanced Applications, 21, pp [9] C. Shi and J. Chang, Trajectory-based video retrieval for ultiedia inforation systes, in Proc. ADVIS, LNCS 3261, 24, pp [1] Y. Jin and F. Mokhtarian, Efficient video retrieval by otion trajectory, in Proc. BMVC 4, 24. [11] S. Khalid and A. Naftel, Evaluation of atching etrics for trajectory-based indexing and retrieval of video clips, in Proc.7th IEEE Workshop Applics. Cop. Vision (WACV/MOTION 5), Colorado, USA, Jan. 25, [12] L. Wang, W. Hu, and T. Tan, Recent developents in huan otion analysis, Pattern Recognition, vol. 36, no. 3, pp , 23. [13] W. Hu, T. Tan, L. Wang, and S. Maybank, A survey on visual surveillance of object otion and behaviors, IEEE Trans. Systes, Man & Cybernetic, Part C, vol.34, no.3, pp , August 24. [14] N. Johnson and D. Hogg, Learning the distribution of object trajectories for event recognition, Iage Vis. Coput., vol. 14, no. 8, pp , [15] J. Owens and A. Hunter, Application of the self-organising ap to trajectory classification, in Proc. IEEE Int. Workshop Visual Surveillance, pp , 2. [16] W. Hu, X. Xiao, D. Xie, T. Tan, and S. Maybank, Traffic accident prediction using 3-D odel-based vehicle tracking, IEEE Trans. Vehicular Tech., vol. 53, no. 3, pp , May 24. [17] J. Alon, S. Sclaroff, G. Kollios, and V. Pavlovic, Discovering clusters in otion tie-series data, in Proc. IEEE CVPR, June 24. [18] W. Hu, D. Xie, T. Tan, and S. Maybank, Learning activity patterns using fuzzy self-organizing neural networks, IEEE Trans. Systes, Man & Cybernetic, Pt. B, vol. 34, no. 3, pp , June 24. [19] R. Agrawal, C. Faloutsas, and A. Swai, Efficient siilarity search in sequence databases, in Proc. 4 th Int. Conf. on Foundations of Data Organization and Algoriths., 1993.

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