dataesr/scientific-paragraphs-categorization huggingface dataset:
WKB, based on a binary format, permits geography data to be exchanged between a client application and an SQL database in a very efficient way. In particular, for our purposes we consider two kind of geometries: the ST LineString is a path between locations which takes the form of an ordered sequence of two or more points; on the contrary, the ST Polygon is a representation of an area. The outer boundary of the polygon is represented by a ring, which is a ST LineString closed and simple. Since our polygon is a box, it can be univocally identified through its bottom-right and top-left points. These information are stored in the tables Segment and Projections: in particular, the former contains the sequence of points 3d-points, stored as a threedimensional ST LineString. The latter contains the three projections During the max selection step, the PostGis '&&' operator is used in order to efficiently verify if a box intersects another one.
Conclusion In this section the approach proposed in this thesis for storing and retrieving moving objects trajectories has been detailed. Starting from geometrical intuitions, it has been shown how to decompose the n-dimensional problem into a set of (n-1)-dimensional ones, and in particular how to decompose the three-dimensional problem into a set of bi-dimensional ones for managing threedimensional trajectories data. This consideration has allowed to profitably use existing spatial databases, whit their well established bi-dimensional indexes, in order to significantly improve the retrieving performance. As I will show in Section 5. 3, the proposed method has been tested both over real and synthetic datasets and its performance, compared with a state-of-the art approach, confirm its effectiveness.
The main idea exploited in this thesis is that the tree built during the previous step can be considered as a k-d tree: as a matter of fact, the generic cluster C is partitioned into two clusters C 1 and C 2 , once properly chosen a cutting axis and a cutting position; it means that, once generated the tree, a k-NN search can be easily performed without the need to analyze all the trajectories belonging to the dataset, as shown in Figure  3. 41. In order to further speedup the search, two main improvements have been conducted on the tree's building, with respect to the technique detailed in Subection 3. 2. 6: the computation of the cutting axis and the stop condition. Cutting Axis: Although being the best known heuristic, the computation of the major axis, and in particular the projection of trajectories on the major axis, is a really expensive operation if a large amount of queries has to be considered: in fact, given the cluster C, the projection on an input data (a query) on the major axis can be evaluated in O(C).
However, it is worth pointing out that, whereas the size of the dataset increases, each trajectory can be considered as an axis and the one holding the greatest variance can well approximate the major axis: var(s) = 1 |C| |C| j=1 (< ψ j , ψ s > -< µ, ψ s >) 2 (3. 64) = 1 |C| |C| j=1 k 2 (s, s j ) -   1 |C| |C| j=1 k(s, s j )   2. The main advantage in this choice lies in the fact that the projection on the cutting axis of the generic trajectory t i can be very quickly computed as the similarity between t i and t * s , in O(1). Furthermore, as we will show in Section 5. 2. 4, the results of the two strategies, major axis and axis with the greatest variance, are still comparable. Stop Condition: Our aim is to minimize the number of trajectories to be analyzed. In particular, the best case arises when only a single leaf of the tree needs to be analyzed.
Spatio Temporal Queries In Section 3. 3 we have deeply analyzed the method proposed for indexing and storing trajectories, optimized for solving a DRSQ query. It should be clear that the aim of a DRSQ is to answer queries involving spatio-temporal information: find the objects crossing a given spatial area in a given time interval. From a more formal point of view, a DRSQ can be defined as a function: DRSQ : (Q, D) → (T ⊆ D) (3. 65) in which Q is the query box, D is the entire set of trajectories stored into the database and T is the resulting subset of trajectories satisfying the DRSQ query. In order to better clarify the importance of the proposed DRSQ in real applications, a few examples are needed; for instance, in the context of traffic management systems, this kind of queries can be used for different retrieval purposes.
Conclusions In this section I detailed the module proposed in this thesis for analyzing audio streams in order to detect events of interest, namely screams, gunshots and broken glasses. The effectiveness and the robustness of the proposed approach with respect to different environmental conditions will be confirmed in Section 5. 4, devoted to the experimentation. Since no publicly available datasets have been proposed up to now by the scientific community for audio surveillance applications, in this thesis we also introduce a novel dataset for benchmarking purposes, detailed in Section 5. 4. 1. The results obtained on this dataset have been compared with a state of the art approach, confirming the very promising performance of the proposed method. Chapter 5.
Experimental Results In this chapter the results obtained by testing the different modules proposed in this thesis will be summarized. In particular: • Section 5. 1 analyzes the results obtained by the proposed tracking method, detailed in Section 3. 1, over two different standard datasets, namely PETS 2010 Dataset and ISSIA Soccer Dataset, both acquired in real environments. • Section 5. 2 details the results obtained by the visual behavior analysis module, introduced in Sections 3. 2 and 3. 4. Three datasets, acquired in very different environments and involving both people and vehicles, have been considered, namely MIT Trajectory dataset, Edinburgh Informatics Forum Pedestrian Database and MIT Train Station dataset. • In Section 5. 3 the module devoted to store and allow spatio temporal queries, introduced in Sections 3.
3 and 3. 4, is tested and the results are presented. The test has been conducted both over the standard MIT Trajectory dataset and on a synthetic dataset, generated in order to stress the system. • Finally, in Section 5. 4 the results of the tests conducted over the algorithm for recognizing audio events of interest (introduced in Chapter 4) are presented. Since at our knowledge there are not standard datasets, in this thesis a novel standard dataset for benchmarking purposes have been proposed and made publicly available.
Tracking Algorithm In this section we will show the results of the tracking method, detailed in Section 3. 1. 2. In particular, in Subsection 5. 1. 1 we introduce the standard datasets used for the experimentation. In Subsection 5. 1. 2 the parameters selected for the experimentation are justified, while in Subsections 5. 1. 3 and 5. 1. 4 a quantitative and qualitative evaluation is respectively provided. Finally, the computational cost of the algorithm is show in Subsection 5. 1. 5.
Datasets In order to assess the performance of the method with respect to the state of the art, we have used two different datasets: the publicly available PETS 2010 dataset  [125] , currently used by many research papers, and the ISSIA Soccer Dataset  [126]. ISSIA Soccer Dataset: it is composed by six synchronized videos acquired at 25 fps during a match by six Full-HD cameras, located along the major sides of the playing-field. Examples of the different views are given in Figure  5. 3; the difficulty arising during the tracking in this context is related to the rapid changes of trajectories of the players and their visual appearance: as a matter of fact, except for the referees and the goalkeepers, all the players, depending on their team, have a white or a blue uniform. Such an issue could make very difficult to recover occlusions by exploiting visual dissimilarities between involved players.
Parameters setup In the proposed tracking method the only parameter that needs to be properly set up is the d max parameter of equation 3. 13. In order to evaluate it, we have computed in each view the maximum speed of the objects, from which we have derived the following values: d max = 100 for views 1, 3 and 4 and d max = 150 for view 5, 6, 7 and 8 of the PETS dataset; on the other hand, d max = 80 for all the views of the ISSIA Soccer Dataset.
( The obtained results are shown in Figure  5. 4: in particular, Figure  5. 4a summarizes the performance obtained over the ISSIA Soccer dataset, highlighting similar values over all the different views. Note that the performance are even better at the light of the fact that this dataset contains some very complex occlusion patterns, involving a variable number of players, ranging from two to eight, that strongly influence the performance of the entire system. Although a direct comparison with the state-of-the-art methods is not possible as the results reported over this dataset are usually provided in a qualitative form, the high values obtained by our method both in terms of accuracy and precision confirm the validity of the proposed approach in the sport applicative domain. Figure  5. 4b shows the results of the proposed method over the PETS 2010 dataset, related to the individual sequences.
It is worth noting that the method, during an occlusion, does not attempt to find the exact position of an object inside a group; it continues to track the group as a whole, using the Kalman filter for obtaining a prevision of the position of each object inside the group itself; this choice obviously causes a degradation of the performance if it is measured using indices defined assuming that objects are always tracked individually. Comparison: PETS Contest (Performance Evaluation of Tracking and Surveillance) is a competition organized by the University of Reading, which allows to compare all the state of the art tracking algorithms: each participant has to submit the output of the proposed method over a standard dataset; the output is processed by the organizers and the results are finally disclosed during the contest session.
Alahi Olasso Al Anon An Yang Ya Nie Ni Xu Xu Xu multiview Xm Badie Ba Hoffman Ho Heili He Proposed Method PM Arsic Ar Berclaz Be Conte Co Breitenstein Br Ge Ge Alahi Ogreedy Ag Finally, Figure  5. 6d shows the average results over all the views: our method is the most precise over the entire dataset and it is outperformed, in terms of accuracy, only by the method proposed by Berclaz et al. [33] , which takes advantage of the use of a multi-camera approach and thus it is not directly comparable with our approach. It is worth highlighting that ATA, MOTA and MOTP do not perfectly fit, for their nature, the proposed method. It is due to the fact that our approach, during an occlusion, does not attempt to find the exact position of an object inside a group; it continues to track the group as a whole, using the Kalman filter for obtaining a prevision of the position of each object inside the group itself; this choice obviously causes a degradation of the performance if measured using indices assuming that objects are always tracked individually.
Experimentation 2 In this section the performance of the proposed method in terms of resolution percentage of split and occlusion patterns is analyzed. The results are summarized in Table  5. 7, where a comparison with our previous method  [131]  is performed over the PETS dataset. Note that  [131]  is more robust with respect to the occlusion occurrences, rather than to the split ones. It is mainly due to the association manager module, which uses a greedy strategy to solve split and occlusion patterns. The main novelty of the proposed approach lies in the introduction of a graph based approach, which proves to significantly improve the performance with respect to  [131] , both in terms of split and occlusion patterns.
Qualitative Evaluation A qualitative evaluation has been finally performed in order to confirm the efficiency of the proposed approach. In particular, we show how the proposed algorithm deals with splits and occlusions respectively in Figure  5. 11 and 5. 12: in particular, Figure  5. 11 reports an example of split caused by an error during the detection phase and properly adjusted. On the other hand, Figures 5. 12 shows some excerpts of the video sequences, with two complex occlusion patterns among three and two persons; as it can be seen, the system preserves the object identities across the occlusions. Finally, we show in Figure  5. 13 the trajectories obtained by applying the proposed algorithm over the PETS 2010 Dataset. Despite the complexity of each view, the trajectories are generally stable and reliable, so confirming the goodness of the proposed approach.
Visual Behavior Analysis In this section we will detail the results obtained by the method for visual behavior understanding detailed in Section 3. 2. Furthermore, the two typologies of interactions based on the above mentioned method, namely anomaly detection (Subsection 3. 4. 1) and queries by sketch (Subsection 3. 4. 2) will be tested and the results will be analyzed. In particular, a description of the considered datasets and a discussion on the setup of the parameters of our method will be provided respectively in Subsections 5. 2. 1 and 5. 2. 2; Subsection 5. 2. 3 will highlight the expressive power of the string based representation and in Subsection 5. 2. 4 we will show the performance of the clustering algorithm, while in Subsection 5. 2. 5 we will focus on the classification method.
Datasets Three different well-known datasets (Figure  5. 15), acquired in very different environments, have been used in order to test the proposed system: • MIT Trajectory dataset  [106]  (hereinafter MIT1) is a standard and freely available dataset composed by 40. 453 trajectories obtained from a parking lot scene within five days. Starting from the entire dataset, a subset of trajectories belonging to vehicles (10. 335) has been manually extracted by an expert. (i) (ii) • Edinburgh Informatics Forum Pedestrian Database  [134]  (hereinafter EDH) consists of a set of detected targets of people walking through the Informatics Forum, the main building of the School of Informatics at the University of Edinburgh. In particular, we focused on the 7146 trajectories acquired on August, 2010. As already said for the MIT1, it has been manually labeled and approximatively 90% of them have been evaluated as normal.
• MIT Train Station dataset  [135]  (hereinafter MIT2) has been acquired into the New York Grand Central Station; the video, compressed into 1. 1 GB AVI file, lasts 33:20 minutes and it is composed by 50. 010 frames (25 fps) among which 42. 821 moving objects trajectories have been automatically extracted and filtered in order to remove the noise, resulting in 12. 414 trajectories. It is worth pointing out that the trajectories used in all the above mentioned datasets have not been manually extracted by a human operator, but instead by means of different kinds of tracking algorithms. This is a very important consideration, since it allows us to confirm that the statistical nature of the proposed method allows to also deal with the typical errors of tracking algorithms as well as noisy trajectories.
Parameters Setup This subsection is devoted to justify the choice of the free parameters in the proposed method. The first parameter to be defined is the number of zones |Z| used to partition the scene. It plays a fundamental role since a very small number of zones does not give enough informative content to represent trajectories (think, as an example, if we just use a single zone). On the other hand, a very large number of zones would avoid the system to be enough general to deal with rare but normal trajectories and at the same time would make the system too much sensitive to the error of the tracking phase. However, in Section 5. 2. 5 we will show that the exact number of zones does not significantly influence the performance of the system, and the range |Z| ∈ {20,. , 40} is a good compromise for all the considered datasets.
String representation: experimental results Different trajectory representations and different similarity measures between these representations have been proposed in this paper: decomposition of the trajectory into a sequence of traversed zones, encoding of the speed and shape of each trajectory within each zone and encoding of a similarity measure between zones through a weighted graph (Section 3. 2. 4). In order to measure the insight provided by these different representations, we propose to compare the different Area Under Curve (AUC) obtained by a one nearest neighbor classifier based on different trajectory representations and different kernels. To that end, we consider the cluster represented in Figure  3. 26(c). Given one trajectory representation, and one kernel between these representations, we consider each trajectory of this cluster and sort increasingly all the remaining trajectories of the dataset according to their distance to this trajectory.
Clustering: experimental results The three above mentioned datasets have been used in order to evaluate the performance of the proposed clustering algorithm. The experiments have been conducted on a MacBook Pro equipped with Intel Core 2 Duo running at 2. 4 GHz. Two different evaluations have been carried out: the former is a quantitative evaluation, performed in terms of C-index and computational cost. The latter is a qualitative evaluation, aiming at visually confirming the effectiveness of the proposed method by showing some of the most representative clusters obtained by using the proposed method. Finally, a comparison both in terms of C-index and computational cost will be carried out by considering other state of the art approaches. Quantitative Evaluation: the C-index  [136]  is often used in order to evaluate the performance of the clustering algorithms.
It is defined as: C = S -S min S max -S min , (5. 5) where S is the sum of distances over all pairs of objects from the same cluster, n is the number of those pairs and S min is the sum of the n smallest distances if all pairs of objects are considered. Likewise S max is the sum of the n largest distances out of all pairs. The C-index ranges from 0 to 1 and the optimum value is 0. Figure  5. 17 shows the performance of the proposed algorithm, both in terms of computational cost and C-index for the three different considered datasets. In particular, the graphics in the first row confirm that the time needed to perform the clustering is linear with the number of clusters, which is in turn strongly dependent in our method on the chosen threshold. Furthermore, we can also note that the greatest variance based approach is a good approximation of the major axis based approach: in fact, it is, as expected, less expensive than the major axis based clustering but the C-index score is in practice still comparable.
This consideration is confirmed by the second row of Figure  5. 17, where it is shown how the C-index varies with different stop condition criteria (and then with different thresholds). As a matter of fact, we can note that the two methods are comparable in all the considered datasets. We can also observe in Figure  5. 17 that the evolution of the C-index according to the threshold strongly depends on the particular dataset and on the homogeneity of trajectories belonging to it. In fact, the number of clusters is a decreasing function of the threshold. By varying the number of clusters, we induce a variation of the number n of pairs of trajectories in a same cluster. This value of n has a direct influence on both the numerator and the denominator of the C-index, hence leading to results difficult to predict.
The C-index is thus not specifically designed to select an optimal number of clusters but rather to compare different clustering methods using a same number of clusters. This type of protocol is applied in Table  5. 18 explained bellow. Qualitative Evaluation: a qualitative evaluation of the algorithm is pro- vided in Figure  5. 19. In particular, some representative clusters for each dataset are depicted. The color of each trajectory highlights its direction: it starts in black and progressively turns its color into red. As confirmed by the previous quantitative evaluation, the quality of the clustering algorithm is strongly related to the particular environment: as a matter of fact, the first dataset mainly contains vehicles trajectories: the trajectories are much more compact, being the scenario a constraint one, so implying that all the clusters are very homogeneous (see Figure  5.
19(a)). On the other hand, in the other datasets the trajectories belong to people freely moving inside a square, without a street which forces them to follow a given path. Although in this case the problem is much more difficult, the results obtained by the proposed clustering algorithm are really promising, as shown in Comparison: in order to confirm the effectiveness of the proposed approach, a comparison with the following algorithms has been carried out, in terms of C-index and computational cost: in particular, the traditional Kernel k-means and two improved versions, the Global Kernel k-means and the Fast Global Kernel k-means  [70] , are considered. A standard implementation of the Kernel K-means has been used and can be found in  [137] , while as for the other two considered methods, the code has been made available by the authors.
The results for the different datasets are shown in Table  5. 18. In particular, we fixed the threshold to 0. 5 for the proposed method and the so obtained numbers of clusters have been considered as input for the other state-of-the-art approaches. Even if the proposed method is slower than the traditional Kernel k-Means and the Fast Global Kernel k-Means, it clearly outperforms both of these in terms of C-Index over all the three considered datasets. It is worth pointing out that in general the low performance of the above mentioned approaches is mainly due to the so-called problem of the curse of dimensionality  [138] : when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. It implies that the amount of data needed to obtain a statistically sound and reliable result grows exponentially with the dimensionality.
Furthermore, also the distance functions loose their usefulness: as a matter of fact, the distance between any two points in a given dataset converges and then the discrimination of the nearest and furthest point in particular becomes meaningless. This issue can be overcome by reducing the dimensionality of the space  [139] : the kernel PCA is applied and only the first N components, being N the number of clusters, are considered. Finally, the traditional k-means is used in order to find out the clusters. Although this approach reveals to be better than the Kernel k-Means, the proposed method still outperforms it, both in terms of C-index and time needed to perform the clustering. This is mainly due to the fact that our method, based on successive projections, does not use a global initial projection which may induce an important loss of information, but instead analyzes at each iteration all the information pertaining a given cluster in order to find its major axis.