A crime is a punishable offence that is harmful for an individual and his society. It is obvious to comprehend the patterns of criminal activity to prevent them. Research can help society to prevent and solve crime activates. Study shows that only 10 percent offenders commits 50 percent of the total offences. The enforcement team can respond faster if they have early information and pre-knowledge about crime activities of the different points of a city. In this paper, supervised learning technique is used to predict crimes with better accuracy. The proposed system predicts crimes by analyzing data-set that contains records of previously committed crimes and their patterns. The system stands on two main algorithms - i) decision tree, and ii) k-nearest neighbor. Random Forest algorithm and Adaboost are used to increase the accuracy of the prediction. Finally, oversampling is used for better accuracy. The proposed system is feed with a criminal-activity data set of twelve years of San Francisco city.
Crime prediction plays an impactful role in enhancing public security and sustainable development of urban. With recent advances in data collection and integration technologies, a large amount of urban data with rich crime-related information and fine-grained spatio-temporal logs has been recorded. Such helpful information can boost our understandings about the temporal evolution and spatial factors of urban crimes and can enhance accurate crime prediction. In this paper, we perform crime prediction exploiting the cross-type and spatio-temporal correlations of urban crimes. In particular, we v…
Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited information, including text descriptions, incident times, and locations. In practice, there are very few labels. We propose a new statistical modeling framework for {\it spatio-temporal-textual} data and demonstrate its usage on crime linkage detection. We capture linkages of crime incidents via multivariate marked spatio-temporal Hawkes processes and treat embed…
University of Pittsburgh（匹兹堡大学）；Middle East Technical University（中东技术大学）
Opioid overdose is a growing public health crisis in the United States. This crisis, recognized as "opioid epidemic," has widespread societal consequences including the degradation of health, and the increase in crime rates and family problems. To improve the overdose surveillance and to identify the areas in need of prevention effort, in this work, we focus on forecasting opioid overdose using real-time crime dynamics. Previous work identified various types of links between opioid use and criminal activities, such as financial motives and common causes. Motivated by these observations, we pro…
There is significant interest in being able to predict where crimes will happen, for example to aid in the efficient tasking of police and other protective measures. We aim to model both the temporal and spatial dependencies often exhibited by violent crimes in order to make such predictions. The temporal variation of crimes typically follows patterns familiar in time series analysis, but the spatial patterns are irregular and do not vary smoothly across the area. Instead we find that spatially disjoint regions exhibit correlated crime patterns. It is this indeterminate inter-region correlatio…
It is quite evident that majority of the population lives in urban area today than in any time of the human history. This trend seems to increase in coming years. A study [5] says that nearly 80.7% of total population in USA stays in urban area. By 2030 nearly 60% of the population in the world will live in or move to cities. With the increase in urban population, it is important to keep an eye on criminal activities. By doing so, governments can enforce intelligent policing systems and hence many government agencies and local authorities have made the crime data publicly available. In this pa…
Assessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of such associations due to confounding effects if they are not carefully handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong conclusions about the underlying associations between the response and the covariates. In spatio-temporal areal models, the temporal dimension may emerge as a new source of confou…
There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recoverin…
Crime has both varying patterns in space, related to features of the environment, economy, and policing, and patterns in time arising from criminal behavior, such as retaliation. Serious crimes may also be presaged by minor crimes of disorder. We demonstrate that these spatial and temporal patterns are generally confounded, requiring analyses to take both into account, and propose a spatio-temporal self-exciting point process model which incorporates spatial features, near-repeat and retaliation effects, and triggering. We develop inference methods and diagnostic tools, such as residual maps, …
Predictive Hotspot Mapping for Data-driven Crime Prediction
Operations and Decision Sciences Indian Institute of Management Ahmedabad（运营与决策科学印度管理学院艾哈迈德布雷德）；Indian Institute of Management Ahmedabad（印度管理学院艾哈迈德布雷德）；Indian Police Service (Retired)（印度警察服务（退休））
Developing spatio-temporal crime prediction models, and to a lesser extent, developing measures of accuracy and operational efficiency for them, has been an active area of research for almost two decades. Despite calls for rigorous and independent evaluations of model performance, such studies have been few and far between. In this paper, we argue that studies should focus not on finding the one predictive model or the one measure that is the most appropriate at all times, but instead on careful consideration of several factors that affect the choice of the model and the choice of the measure,…
Santa Fe Institute（圣塔菲研究所）；University of Chicago（芝加哥大学）
Large-scale trends in urban crime and global terrorism are well-predicted by socio-economic drivers, but focused, event-level predictions have had limited success. Standard machine learning approaches are promising, but lack interpretability, are generally interpolative, and ineffective for precise future interventions with costly and wasteful false positives. Here, we are introducing Granger Network inference as a new forecasting approach for individual infractions with demonstrated performance far surpassing past results, yet transparent enough to validate and extend social theory. Consideri…
Bilkent University（比尔肯特大学）；DataBoss A. S.（DataBoss股份公司）
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transfor…
We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such as crime, earthquake, and social event prediction. Despite these thorough studies, specific problems inherent to the application domain are not yet fully explored. Here, we address the non-stationary spatio-temporal prediction problem on both densely and sparsely distributed sequences. We introduce a probabilistic approach that partitions the spatial domain…
When sensors collect spatio-temporal data in a large geographical area, the existence of missing data cannot be escaped. Missing data negatively impacts the performance of data analysis and machine learning algorithms. In this paper, we study deep autoencoders for missing data imputation in spatio-temporal problems. We propose a convolution bidirectional-LSTM for capturing spatial and temporal patterns. Moreover, we analyze an autoencoder's latent feature representation in spatio-temporal data and illustrate its performance for missing data imputation. Traffic flow data are used for evaluation…
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting the global field into many lower-dimensional "light cones". We review light cone decompositions for predictive state reconstruction, introducing three simple light cone algorithms. These methods allow for tractable inference of spatio-temporal data, such as full-frame video. The algorithms make few assumptions on the underlying process yet have good predictiv…
I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. I apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA, and a study of crime rates in neighborhoods of Columbus, OH, USA.
Peking University（北京大学）；Beijing Institute of Big Data Research（北京大数据研究院）
The spatio-temporal graph learning is becoming an increasingly important object of graph study. Many application domains involve highly dynamic graphs where temporal information is crucial, e.g. traffic networks and financial transaction graphs. Despite the constant progress made on learning structured data, there is still a lack of effective means to extract dynamic complex features from spatio-temporal structures. Particularly, conventional models such as convolutional networks or recurrent neural networks are incapable of revealing the temporal patterns in short or long terms and exploring …
We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we develop a localized spatio-temporal covariance model of the process that can capture spatially varying temporal periodicities in the data. We then apply a covariance-fitting methodology to learn the model parameters which yields a predictor that can be updated sequentially with each new data point. The proposed method is evaluated using both synthetic and real cli…
We present a novel approach to estimate the delay observed between the occurrence and reporting of rape crimes. We explore spatial, temporal and social effects in sparse aggregated (area-level) and high-dimensional disaggregated (event-level) data for New York and Los Angeles. Focusing on inference, we apply Gradient Boosting and Random Forests to assess predictor importance, as well as Gaussian Processes to model spatial disparities in reporting times. Our results highlight differences and similarities between the two cities. We identify at-risk populations and communities which may be target…
Artificial Intelligence Department Universidad Nacional de Educación a Distancia — UNED（西班牙马德里国立远程教育大学（UNED）人工智能系）
Spatio-temporal forecasting is an open research field whose interest is growing exponentially. In this work we focus on creating a complex deep neural framework for spatio-temporal traffic forecasting with comparatively very good performance and that shows to be adaptable over several spatio-temporal conditions while remaining easy to understand and interpret. Our proposal is based on an interpretable attention-based neural network in which several modules are combined in order to capture key spatio-temporal time series components. Through extensive experimentation, we show how the results of …
This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a unified framework for different types of spatio-temporal data including both, purely qualitatively (multivariate) cases and multivariate cases with additional quantitative marks. The proposed graphical model is defined through partial spectral density characteristics, it is highly computationally efficient and reflects the conditional similarity among sets of spat…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in fields where spatio-temporal clustering of events is observed, such as earthquake modeling, infectious disease, and crime. In the past several decades, advances have been made in estimation, inference, simulation, and diagnostic tools for self-exciting point process models. In this review, I describe the basic theory, survey related estimation and inference …
As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle the climate crisis. Indeed, being universal nonlinear function approximation tools, Machine Learning algorithms are efficient in analysing and modelling spatially and temporally variable environmental data. While Deep Learning models have proved to be able to capture spatial, temporal, and spatio-temporal dependencies through their automatic feature representa…
Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal variability. The data sets associated with many of these processes are increasing in size due to advances in automated data measurement, management, and numerical simulator output. Non- linear spatio-temporal models have only recently seen interest in statistics, but there are many classes of such models in the engineering and geophysical sciences. Tradi- tion…
Warsaw University of Technology（华沙理工大学）；Carnegie Mellon University（卡内基梅隆大学）
In this article, we introduce a novel type of spatio-temporal sequential patterns called Constricted Spatio-Temporal Sequential (CSTS) patterns and thoroughly analyze their properties. We demonstrate that the set of CSTS patterns is a concise representation of all spatio-temporal sequential patterns that can be discovered in a given dataset. To measure significance of the discovered CSTS patterns we adapt the participation index measure. We also provide CSTS-Miner: an algorithm that discovers all participation index strong CSTS patterns in event data. We experimentally evaluate the proposed al…
Models for fitting spatio-temporal point processes should incorporate spatio-temporal inhomogeneity and allow for different types of interaction between points (clustering or regularity). This paper proposes an extension of the spatial multi-scale area-interaction model to a spatio-temporal framework. This model allows for interaction between points at different spatio-temporal scales and the inclusion of covariates. We fit the proposed model to varicella cases registered during 2013 in Valencia, Spain. The fitted model indicates small scale clustering and regularity for higher spatio-temporal…
This paper defines the class of càdlàg functional marked point processes (CFMPPs). These are (spatio-temporal) point processes marked by random elements which take values in a càdlàg function space, i.e. the marks are given by càdlàg stochastic processes. We generalise notions of marked (spatio-temporal) point processes and indicate how this class, in a sensible way, connects the point process framework with the random fields framework. We also show how they can be used to construct a class of spatio-temporal Boolean models, how to construct different classes of these models by choosing specif…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance functions which are separable and non-separable in space and time.
Fine particulate matter (PM$_{2.5}$) has become a great concern worldwide due to its adverse health effects. PM$_{2.5}$ concentrations typically exhibit complex spatio-temporal variations. Both the mean and the spatio-temporal dependence evolve with time due to seasonality, which makes the statistical analysis of PM$_{2.5}$ challenging. In geostatistics, Gaussian process is a powerful tool for characterizing and predicting such spatio-temporal dynamics, for which the specification of a spatio-temporal covariance function is the key. While the extant literature offers a wide range of choices fo…
We propose a new centered autologistic spatio-temporal model for binary data on a lattice. The centering allows the interpretation of the autoregression coefficients in separating the large scale structure of the model corresponding to an expected mean and the small-scale structure corresponding to the auto-correlation. We discuss the existence of the joint law of the process and show by simulation the interest of this kind of centering. We propose and show the efficiency of the maximum pseudo-likelihood estimator and also a method to choose the best structure of neighborhood. Method is applie…
There are many data sources available that report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate-spatio-temporal dependencies. As such, we introduce the multivariate-spatio-temporal mixed effects model (MSTM) to analyze areal data with multivariate-spatio-temporal dependencies. The proposed MSTM extends the notion of Moran's I basis functions to the multivariate-spatio-temporal setting. This extension leads to several methodologica…
Spatial and spatio-temporal single-structure point process models are widely used in epidemiology, biology, ecology, seismology... . However, most natural phenomena present multiple interaction structure or exhibit dependence at multiple scales in space and/or time, leading to define new spatial and spatio-temporal multi-structure point process models. In this paper, we investigate and review such multi-structure point process models mainly based on Gibbs and Cox processes.
This paper proposes a log-linear model for the latent intensity functions of a replicated spatio-temporal point process. By simultaneously fitting correlated spatial and temporal Karhunen-Loève expansions, the model produces spatial and temporal components that are usually easy to interpret and capture the most important modes of variation and spatio-temporal correlation of the process. The asymptotic distribution of the estimators is derived. The finite sample properties are studied by simulations. As an example of application, we analyze bike usage patterns on the Divvy bike sharing system o…
Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscri…
We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as observed sample, we obtain expressions for the spatio-temporal covariance functions and the spectral density functions of the spatio-temporal random processes. These spectra correspond to non separable class of random processes. The spatio-temporal covariance functions, obtained here are functions of the spatial distance and the temporal frequency and are simil…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance stationarity, which is unrealistic in many geophysical applications. In this article, we introduce a deep-learning-inspired approach to construct descriptive nonstationary spatio-temporal models by modeling stationary processes on warped spatio-temporal domains. The warping functions we use are constructed using several simple injective warping units which, when co…
In the absence of Gaussianity assumptions without disturbing spatial continuity interpolating along the whole spatial surface for different time lags is challenging. The past researchers pay enough attention to Spatio-temporal interpolation ignoring the dynamic behavior of a spatial mean function, threshold distance, and direction of maintaining spatial continuity. Therefore, we employ hierarchical spatial clustering (HSC) to preserve local spatial stationarity. This research work introduces a hybrid extreme valued copula-based Spatio-temporal interpolation algorithm. Spatial dependence is cap…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that assume a simpler spatio-temporal dependence structure with separability and full symmetry. However, it is challenging to visualize and assess separability and full symmetry from spatio-temporal observations. In this work, we propose a functional data analysis approach that constructs test functions using the cross-covariances from time series observed at each pai…
To study the impact of climate variables on morbidity of some diseases in Mexico, we propose a spatio-temporal varying coefficients regression model. For that we introduce a new spatio-temporal dependent process prior, in a Bayesian context, with identically distributed normal marginal distributions and joint multivariate normal distribution. We study its properties and characterise the dependence induced. Our results show that the effect of climate variables, on the incidence of specific diseases, is not constant across space and time and our proposed model is able to capture and quantify tho…
The importance of modelling temperature fields goes beyond the need to understand a region's climate and serves too as a starting point for understanding their socioeconomic, and health consequences. The topography of the study region contributes much to the complexity of modelling these fields and demands flexible spatio-temporal models that are able to handle nonstationarity and changes in trend. In this paper, we develop a flexible stochastic spatio-temporal model for daily temperatures in the Pacific Northwest, and describe a methodology for performing Bayesian spatial prediction. A novel …
Models that capture the spatial and temporal dynamics are applicable in many science fields. Non-separable spatio-temporal models were introduced in the literature to capture these features. However, these models are generally complicated in construction and interpretation. We introduce a class of non-separable Transformed Gaussian Markov Random Fields (TGMRF) in which the dependence structure is flexible and facilitates simple interpretations concerning spatial, temporal and spatio-temporal parameters. Moreover, TGMRF models have the advantage of allowing specialists to define any desired mar…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out non-parametrically through kernel functions, where one of the most frequent handicaps is the selection of kernel bandwidths prior to estimation. This work presents an intensity estimation mechanism in which the spatial and temporal bandwidths change at each data point in a spatio-temporal point pattern. This class of estimators is called adaptive estimators, an…
Spatio-temporal models are widely used in many research areas including ecology. The recent proliferation of the use of in-situ sensors in streams and rivers supports space-time water quality modelling and monitoring in near real-time. A new family of spatio-temporal models is introduced. These models incorporate spatial dependence using stream distance while temporal autocorrelation is captured using vector autoregression approaches. Several variations of these novel models are proposed using a Bayesian framework. The results show that our proposed models perform well using spatio-temporal da…
Many physical processes involve spatio-temporal observations, which can be studied at different spatial and temporal scales. For example, rainfall data measured daily by rain gauges can be considered at daily, monthly or annual temporal scales, and local, grid-wise, region-wise or country-wise spatial scales. In this work, we focus on detection of anomalies in such multi-scale spatio-temporal data. We consider an anomaly as an event where the measured values over a spatio-temporally extended region are significantly different from their long-term means. However we aim to avoid setting any thre…
