Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets @math where @math and @math are two nodes having a link between them at time @math . A very large number of studies on these objects start by aggregating the data in disjoint time windows of length @math in order to obtain a series of graphs on which are made all subsequent analyses. Here we are concerned with the impact of the chosen @math on the obtained graph series. We address the fundamental question of knowing whether a series of graphs formed using a given @math faithfully describes the original link stream. We answer the question by showing that such dynamic networks exhibit a threshold for @math , which we call the , beyond which the properties of propagation of the link stream are altered, while they are mostly preserved before. We design an automatic method to determine the saturation scale of any link stream, which we apply and validate on several real-world datasets.
Contrastingly, the goal of @cite_2 is precisely to determine an ideal aggregation period. In their method, this period is obtained as a trade-off between two metrics that vary monotonically and oppositely with regard to aggregation: one describing the loss of information (increasing with aggregation) and one describing the noise contained in the series of snapshots (decreasing with aggregation). Compared to them, here, we are concerned only with the loss of information. This allows us to avoid some drawbacks and limitations inherent to the approaches based on a trade-off: i) the value selected for the aggregation period strongly depends on the importance given to each metrics and ii) the selected value does not reveal any particular behavior of the properties of the network used in the trade-off, as each of them varies smoothly and monotonically from one extremal value to another one. On the contrary, our method does not depend on any arbitrary choice of ponderation and reveals a natural change in the way the network responds to aggregation at a certain aggregation scale that we determine.
@cite_2
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Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. The majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops. In this paper, a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure. A linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data. A link is assumed to be present between two time series if the weight of a time series, which is a linear time-invariant filter, is nonzero in the formation of the other. Reconstruction of the link connectivity structure under various scenarios is considered. It is shown that when the linear dynamic graph is allowed to admit non-causal weights, then the links structure can be recovered with the possibility of identifying spurious connections. However, it is shown that the spurious links remain local, where, a spurious link is restricted to be within one hop of a true link. Furthermore, strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed. The main tools for determining the network topology are based on variations of Wiener filtering. A significant insight provided by the article is that, in the class of network models considered in the paper, the Wiener filter estimating a stochastic process based on other processes remains local in the sense that the Wiener filter utilizes only measurements local to the node being estimated. In sparse approximation theory, the fundamental problem is to reconstruct a signal A∈ℝn from linear measurements 〈Aψi〉 with respect to a dictionary of ψi's. Recently, there is focus on the novel direction of Compressed Sensing [9] where the reconstruction can be done with very few—O(k logn)—linear measurements over a modified dictionary if the signal is compressible, that is, its information is concentrated in k coefficients with the original dictionary. In particular, these results [9, 4, 23] prove that there exists a single O(k logn) ×n measurement matrix such that any such signal can be reconstructed from these measurements, with error at most O(1) times the worst case error for the class of such signals. Compressed sensing has generated tremendous excitement both because of the sophisticated underlying Mathematics and because of its potential applications In this paper, we address outstanding open problems in Compressed Sensing. Our main result is an explicit construction of a non-adaptive measurement matrix and the corresponding reconstruction algorithm so that with a number of measurements polynomial in k, logn, 1 e, we can reconstruct compressible signals. This is the first known polynomial time explicit construction of any such measurement matrix. In addition, our result improves the error guarantee from O(1) to 1 + e and improves the reconstruction time from poly(n) to poly(k logn) Our second result is a randomized construction of O(kpolylog (n)) measurements that work for each signal with high probability and gives per-instance approximation guarantees rather than over the class of all signals. Previous work on Compressed Sensing does not provide such per-instance approximation guarantees; our result improves the best known number of measurements known from prior work in other areas including Learning Theory [20, 21], Streaming algorithms [11, 12, 6] and Complexity Theory [1] for this case Our approach is combinatorial. In particular, we use two parallel sets of group tests, one to filter and the other to certify and estimate; the resulting algorithms are quite simple to implement This paper considers the inverse problem with observed variables Y = BGX ⊕Z, where BG is the incidence matrix of a graph G, X is the vector of unknown vertex variables with a uniform prior, and Z is a noise vector with Bernoulli(e) i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery of X is possible if and only the graph G is connected, with a sharp threshold at the edge probability log(n) n for Erdős-Renyi random graphs. The first goal of this paper is to determine how the edge probability p needs to scale to allow exact recovery in the presence of noise. Defining the degree (oversampling) rate of the graph by α = np log(n), it is shown that exact recovery is possible if and only if α > 2 (1−2e)+o(1 (1−2e)). In other words, 2 (1−2e) is the information theoretic threshold for exact recovery at lowSNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. Full version available in [1]. We introduce a new, generic framework for private data analysis.The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains.Our framework allows one to release functions f of the data withinstance-based additive noise. That is, the noise magnitude is determined not only by the function we want to release, but also bythe database itself. One of the challenges is to ensure that the noise magnitude does not leak information about the database. To address that, we calibrate the noise magnitude to the smoothsensitivity of f on the database x --- a measure of variabilityof f in the neighborhood of the instance x. The new frameworkgreatly expands the applicability of output perturbation, a technique for protecting individuals' privacy by adding a smallamount of random noise to the released statistics. To our knowledge, this is the first formal analysis of the effect of instance-basednoise in the context of data privacy. Our framework raises many interesting algorithmic questions. Namely,to apply the framework one must compute or approximate the smoothsensitivity of f on x. We show how to do this efficiently for several different functions, including the median and the cost ofthe minimum spanning tree. We also give a generic procedure based on sampling that allows one to release f(x) accurately on manydatabases x. This procedure is applicable even when no efficient algorithm for approximating smooth sensitivity of f is known orwhen f is given as a black box. We illustrate the procedure by applying it to k-SED (k-means) clustering and learning mixtures of Gaussians. The goal of this paper is to determine the data routes, subchannel schedules, and power allocations that maximize a weighted-sum rate of the data communicated over a generic OFDMA wireless network in which the nodes are capable of simultaneously transmitting, receiving and relaying data. Two instances are considered. In the first instance, subchannels are allowed to be time-shared by multiple links, whereas in the second instance, each subchannel is exclusively used by one of the links. Using a change of variables, the first problem is transformed into a convex form. In contrast, the second problem is not amenable to such a transformation and results in a complex mixed integer optimization problem. To develop insight into this problem, we utilize the first instance to obtain efficiently computable lower and upper bounds on the weighted-sum rate that can be achieved in the absence of time-sharing. Another lower bound is obtained by enforcing the scheduling constraints through additional power constraints and a monomial approximation technique to formulate the design problem as a geometric program. Numerical investigations show that the obtained rates are higher when time-sharing is allowed, and that the lower bounds on rates in the absence of time-sharing are relatively tight. Complex networks are often constructed by aggregating empirical data over time, such that a link represents the existence of interactions between the endpoint nodes and the link weight represents the intensity of such interactions within the aggregation time window. The resulting networks are then often considered static. More often than not, the aggregation time window is dictated by the availability of data, and the effects of its length on the resulting networks are rarely considered. Here, we address this question by studying the structural features of networks emerging from aggregating empirical data over different time intervals, focussing on networks derived from time-stamped, anonymized mobile telephone call records. Our results show that short aggregation intervals yield networks where strong links associated with dense clusters dominate; the seeds of such clusters or communities become already visible for intervals of around one week. The degree and weight distributions are seen to become stationary around a few days and a few weeks, respectively. An aggregation interval of around 30 days results in the stablest similar networks when consecutive windows are compared. For longer intervals, the effects of weak or random links become increasingly stronger, and the average degree of the network keeps growing even for intervals up to 180 days. The placement of the time window is also seen to affect the outcome: for short windows, different behavioural patterns play a role during weekends and weekdays, and for longer windows it is seen that networks aggregated during holiday periods are significantly different. This paper analyzes the impact of user mobility in multi-tier heterogeneous networks. We begin by obtaining the handoff rate for a mobile user in an irregular cellular network with the access point locations modeled as a homogeneous Poisson point process. The received signal-to-interference-ratio (SIR) distribution along with a chosen SIR threshold is then used to obtain the probability of coverage. To capture potential connection failures due to mobility, we assume that a fraction of handoffs result in such failures. Considering a multi-tier network with orthogonal spectrum allocation among tiers and the maximum biased average received power as the tier association metric, we derive the probability of coverage for two cases: 1) the user is stationary (i.e., handoffs do not occur, or the system is not sensitive to handoffs); 2) the user is mobile, and the system is sensitive to handoffs. We derive the optimal bias factors to maximize the coverage. We show that when the user is mobile, and the network is sensitive to handoffs, both the optimum tier association and the probability of coverage depend on the user's speed; a speed-dependent bias factor can then adjust the tier association to effectively improve the coverage, and hence system performance, in a fully-loaded network. In citepapa, Papadimitriou formalized the notion of routing stability in BGP as the following coalitional game theoretic problem: Given a network with a multicommodity flow satisfying node capacity and demand constraints, the payoff of a node is the total flow originated or terminated at it. A payoff allocation is in the core if and only if there is no subset of nodes that can increase their payoff by seceding from the network. We answer one of the open problems in citepapa by proving that for any network, the core is non-empty in both the transferable (where the nodes can compensate each other with side payments) and the non-transferable case. In the transferable case we show that such an allocation can be computed in polynomial time. We also generalize this result to the case where a strictly concave utility function is associated with each commodity. To speed up multidimensional data analysis, database systems frequently precompute aggregates on some subsets of dimensions and their corresponding hierarchies. This improves query response time. However, the decision of what and how much to precompute is a difficult one. It is further complicated by the fact that precomputation in the presence of hierarchies can result in an unintuitively large increase in the amount of storage required by the database. Hence, it is interesting and useful to estimate the storage blowup that will result from a proposed set of precomputations without actually computing them. We propose three strategies for this problem: one based on sampling, one based on mathematical approximation, and one based on probabilistic counting. We investigate the accuracy of these algorithms in estimating the blowup for different data distributions and database schemas. The algorithm based upon probabilistic counting is particularly attractive, since it estimates the storage blowup to within provable error bounds while performing only a single scan of the data. *Work supported by an IBM CAS Fellowship, NSF grant IRI9157357, and a grant from IBM under the University Partnership Program. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying 1:s by permission of the Very Large Data Base Endowm.ent. To copy otherwise, 01‘ to republish, requires a fee and or special permission j orn the En.do?ument. Proceedings of the 22nd VLDB Conference Mumbai(Bombay), India, 1996 We consider the problem of clustering a graph @math into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables @math , where @math is the incidence matrix of a graph @math , @math is the vector of unknown vertex variables (with a uniform prior), and @math is a noise vector with Bernoulli @math i.i.d. entries. All variables and operations are Boolean. This model is motivated by coding, synchronization, and community detection problems. In particular, it corresponds to a stochastic block model or a correlation clustering problem with two communities and censored edges. Without noise, exact recovery (up to global flip) of @math is possible if and only the graph @math is connected, with a sharp threshold at the edge probability @math for Erdős-Renyi random graphs. The first goal of this paper is to determine how the edge probability @math needs to scale to allow exact recovery in the presence of noise. Defining the degree rate of the graph by @math , it is shown that exact recovery is possible if and only if @math . In other words, @math is the information theoretic threshold for exact recovery at low-SNR. In addition, an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate. For a deterministic graph @math , defining the degree rate as @math , where @math is the minimum degree of the graph, it is shown that the proposed method achieves the rate @math , where @math is the spectral gap of the graph @math . Frame aggregation is one of the several enhancements proposed by IEEE 802.11 Task Group n to improve channel utilization. In frame aggregation, more than one data frame is encapsulated to form an aggregate, and once an aggregate is formed, a station contends to access the medium to transmit the entire aggregate. We refer to the number of data frames encapsulated within an aggregated frame as aggregate size. We claim that a static assignment of aggregate size leads to the following performance trade-off: a small value might be insufficient to mitigate the transmission overheads, thereby nullifying the whole purpose of frame aggregation; whereas, a large value might affect the quality of service experienced by higher layers due to the extra wait time to build an aggregate. In this paper, we characterize this trade-off by studying the impact of aggregate size on metrics like frame latency and channel utilization. To estimate these metrics, we model the transmission queue of an 802.11n station as a bulk service queuing system. We study the impact of aggregate size over a wide range of operating conditions covering several traffic arrival rates from higher layers, service distribution and data frame sizes. Apart from validating the existence of above-mentioned performance trade-off, our results indicate that the choice of aggregate size not only depends on the traffic arrival rate, but also (more interestingly) on data frame sizes. This calls for a dynamic assignment of aggregate size. The need to rank items based on user input arises in many practical applications such as elections, group-decision making and recommendation systems. The primary challenge in such scenarios is to decide a global ranking based on partial preferences provides by users. The standard approach to address this challenge is to ask users to provide explicit numerical ratings (cardinal information) of a subset of items. The main appeal of such an approach is the ease of aggregation. However, the rating scale as well as the individual ratings are often arbitrary and may not be consistent from one user to another. A more natural alternative to numerical ratings requires users to compare pairs of items (ordinal information). In contrast to cardinal information, such comparisons provide an “absolute” indicator of the user's preference. However, it is often hard to combine or aggregate comparisons to obtain a consistent global ranking. In this work, we provide a tractable framework for utilizing comparison data as well as first-order marginal information for the purpose of ranking. We treat the available information as partial samples from an unknown distribution over permutations. Using the Principle of Maximum Entropy, we devise a concise parameterization of distribution consistent with observations using only O(n2) parameters, where n is the number of items in question. We propose a distributed, iterative algorithm for estimating the parameters of the distribution. We establish the correctness of the algorithm as well as identify the rate of convergence explicitly. Using the learnt distribution, we provide efficient approach to (a) learn the mode of the distribution using ‘maximum weight matching’, (b) identification of top k items, and (c) an aggregate ranking of all n items. Through evaluation of our approach on real-data, we verify effectiveness of our solutions as well as the scalability of the algorithm. We present a new stochastic service model with capacity sharing and interruptions, appropriate for the evaluation of the quality of real-time streaming (RTS), like e.g. mobile TV, in wireless cellular networks. The general model takes into account multi-class Markovian process of call arrivals, (to capture different radio channel conditions, requested streaming bit-rates and durations) and allows for a general resource allocation policy saying which users are temporarily denied the requested fixed streaming bit-rates (put in outage) due to resource constraints. We give expressions for several important performance characteristics of the model, including mean time spent in outage and mean number of outage incidents for a typical user of a given class. These expressions involve only stationary probabilities of the (free) traffic demand process, which is a vector of independent Poisson random variables describing the number of users of different classes. In order to analyze RTS in 3GPP Long Term Evolution (LTE) cellular networks, we specify our general model assuming orthogonal user channels with the peak bit-rates close to the theoretical Shannon's bound in the additive white Gaussian noise (AWGN) channel, which leads to the resource constraints in a multi-rate linear form. In this setting we consider a natural class of least-effort-served-first resource allocation policies, for which the characteristics of the model can be further evaluated using Fourier analysis of Poisson variables. Within this class we identify and evaluate an optimal and a fair policy, the latter being suggested by LTE implementations. We also propose some intermediate policies, which allow to solve the optimality fairness tradeoff caused by unequal user radio-channel conditions. Our results can be used for the evaluation of the quality of RTS in LTE networks and dimensioning of these networks. We investigate a wireless system of multiple cells, each having a downlink shared channel in support of high-speed packet data services. In practice, such a system consists of hierarchically organized entities including a central server, Base Stations (BSs), and Mobile Stations (MSs). Our goal is to improve global resource utilization and reduce regional congestion given asymmetric arrivals and departures of mobile users, a goal requiring load balancing among multiple cells. For this purpose, we propose a scalable cross-layer framework to coordinate packet-level scheduling, call-level cell-site selection and handoff, and system-level cell coverage based on load, throughput, and channel measurements. In this framework, an opportunistic scheduling algorithm--the weighted Alpha-Rule--exploits the gain of multiuser diversity in each cell independently, trading aggregate (mean) down-link throughput for fairness and minimum rate guarantees among MSs. Each MS adapts to its channel dynamics and the load fluctuations in neighboring cells, in accordance with MSs' mobility or their arrival and departure, by initiating load-aware handoff and cell-site selection. The central server adjusts schedulers of all cells to coordinate their coverage by prompting cell breathing or distributed MS handoffs. Across the whole system, BSs and MSs constantly monitor their load, throughput, or channel quality in order to facilitate the overall system coordination. Our specific contributions in such a framework are highlighted by the minimum-rate guaranteed weighted Alpha-Rule scheduling, the load-aware MS handoff cell-site selection, and the Media Access Control (MAC)-layer cell breathing. Our evaluations show that the proposed framework can improve global resource utilization and load balancing, resulting in a smaller blocking rate of MS arrivals without extra resources while the aggregate throughput remains roughly the same or improved at the hot-spots. Our simulation tests also show that the coordinated system is robust to dynamic load fluctuations and is scalable to both the system dimension and the size of MS population. We consider the continual count tracking problem in a distributed environment where the input is an aggregate stream that originates from k distinct sites and the updates are allowed to be non-monotonic, i.e. both increments and decrements are allowed. The goal is to continually track the count within a prescribed relative accuracy e at the lowest possible communication cost. Specifically, we consider an adversarial setting where the input values are selected and assigned to sites by an adversary but the order is according to a random permutation or is a random i.i.d process. The input stream of values is allowed to be non-monotonic with an unknown drift -1≤μ=1 where the case μ = 1 corresponds to the special case of a monotonic stream of only non-negative updates. We show that a randomized algorithm guarantees to track the count accurately with high probability and has the expected communication cost O(min√k (|#956;|e), √k n e, n ), for an input stream of length n, and establish matching lower bounds. This improves upon previously best known algorithm whose expected communication cost is Θ(min√k e,n]) that applies only to an important but more restrictive class of monotonic input streams, and our results are substantially more positive than the communication complexity of Ω(n) under fully adversarial input. We also show how our framework can also accommodate other types of random input streams, including fractional Brownian motion that has been widely used to model temporal long-range dependencies observed in many natural phenomena. Last but not least, we show how our non-monotonic counter can be applied to track the second frequency moment and to a Bayesian linear regression problem. textabstractForecasting financial time series using past observations has been a significant topic of interest. While temporal relationships in the data exist, they are difficult to analyze and predict accurately due to the non-linear trends and noise present in the series. We propose to learn these dependencies by a convolutional neural network. In particular the focus is on multivariate time series forecasting. Effectively, we use multiple financial time series as input in the neural network, thus conditioning the forecast of a time series x(t) on both its own history as well as that of a second (or third) time series y(t). Training a model on multiple stock series allows the network to exploit the correlation structure between these series so that the network can learn the market dynamics in shorter sequences of data. We show that long-term temporal dependencies in and between financial time series can be learned by means of a deep convolutional neural network based on the WaveNet model [2]. The network makes use of dilated convolutions applied to multiple time series so that the receptive field of the network is wide enough to learn both short and long-term dependencies. The architecture includes batch normalization and uses a 1 × k convolution with parametrized skip connections from the input time series as well as the time series we condition on, in this way learning long-term interdependencies in an efficient manner [1]. This improves the forecast, while at the same time limiting the requirement for a long historical price series and reducing the noise. Knowing the strong performance of CNNs on classification problems we show that they can be applied successfully to forecasting financial time series, without the need of large samples of data. We compare the performance of the WaveNet model to a state-of-the-art fully convolutional network (FCN), and an autoregressive model popular in econometrics and show that our model is much better able to learn important dependencies in between financial time series resulting in a more robust and accurate forecast. Visual search and image retrieval underpin numerous applications, however the task is still challenging predominantly due to the variability of object appearance and ever increasing size of the databases, often exceeding billions of images. Prior art methods rely on aggregation of local scale-invariant descriptors, such as SIFT, via mechanisms including Bag of Visual Words (BoW), Vector of Locally Aggregated Descriptors (VLAD) and Fisher Vectors (FV). However, their performance is still short of what is required. This paper presents a novel method for deriving a compact and distinctive representation of image content called Robust Visual Descriptor with Whitening (RVD-W). It significantly advances the state of the art and delivers world-class performance. In our approach local descriptors are rank-assigned to multiple clusters. Residual vectors are then computed in each cluster, normalized using a direction-preserving normalization function and aggregated based on the neighborhood rank. Importantly, the residual vectors are de-correlated and whitened in each cluster before aggregation, leading to a balanced energy distribution in each dimension and significantly improved performance. We also propose a new post-PCA normalization approach which improves separability between the matching and non-matching global descriptors. This new normalization benefits not only our RVD-W descriptor but also improves existing approaches based on FV and VLAD aggregation. Furthermore, we show that the aggregation framework developed using hand-crafted SIFT features also performs exceptionally well with Convolutional Neural Network (CNN) based features. The RVD-W pipeline outperforms state-of-the-art global descriptors on both the Holidays and Oxford datasets. On the large scale datasets, Holidays1M and Oxford1M, SIFT-based RVD-W representation obtains a mAP of 45.1 and 35.1 percent, while CNN-based RVD-W achieve a mAP of 63.5 and 44.8 percent, all yielding superior performance to the state-of-the-art. This paper investigates a new learning formulation called dynamic group sparsity. It is a natural extension of the standard sparsity concept in compressive sensing, and is motivated by the observation that in some practical sparse data the nonzero coefficients are often not random but tend to be clustered. Intuitively, better results can be achieved in these cases by reasonably utilizing both clustering and sparsity priors. Motivated by this idea, we have developed a new greedy sparse recovery algorithm, which prunes data residues in the iterative process according to both sparsity and group clustering priors rather than only sparsity as in previous methods. The proposed algorithm can recover stably sparse data with clustering trends using far fewer measurements and computations than current state-of-the-art algorithms with provable guarantees. Moreover, our algorithm can adaptively learn the dynamic group structure and the sparsity number if they are not available in the practical applications. We have applied the algorithm to sparse recovery and background subtraction in videos. Numerous experiments with improved performance over previous methods further validate our theoretical proofs and the effectiveness of the proposed algorithm. We present a new sketch for summarizing network data. The sketch has the following properties which make it useful in communication-efficient aggregation in distributed streaming scenarios, such as sensor networks: the sketch is duplicate insensitive, i.e., reinsertions of the same data will not affect the sketch and hence the estimates of aggregates. Unlike previous duplicate-insensitive sketches for sensor data aggregation [S. , Synposis diffusion for robust aggregation in sensor networks, in Proceedings of the 2nd International Conference on Embedded Network Sensor Systems, (2004), pp. 250-262], [J. , Approximate aggregation techniques for sensor databases, in Proceedings of the 20th International Conference on Data Engineering (ICDE), 2004, pp. 449-460], it is also time decaying, so that the weight of a data item in the sketch can decrease with time according to a user-specified decay function. The sketch can give provably approximate guarantees for various aggregates of data, including the sum, median, quantiles, and frequent elements. The size of the sketch and the time taken to update it are both polylogarithmic in the size of the relevant data. Further, multiple sketches computed over distributed data can be combined without loss of accuracy. To our knowledge, this is the first sketch that combines all the above properties. The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.