“Brown textile photo - Tan’am, Oman” by NASA

# Introduction

We are in an era where nearly everyone carries a variety of sensors, either as a mobile phone, medical device or another smart appliance (e.g. sportwatch, connected car) (IDC, n.d.). The proliferation of these devices and rapid progress in sensor technology have enabled companies to collect vast amounts of spatial data that provide information on the geographical location and course other objects of interest. In addition to the basic infrastructure requirement for the realization of the Internet of Things paradigm, the timely analysis and management of geodata is also often decisive for the growth of a company. The massive amounts of data, coupled with the need for complex spatial analysis, require high throughput and low-latency query processing (Vo, Aji, and Wang 2014).

The topic of remote sensing (e.g. remote sensing imagery, Atmospheric Radiation Measurement (ARM)) or large-scale simulations (e.g. climate data) have always been "big". Recent advances in computation make the spatiotemporal data even larger and place various limits on data analysis. Spatial computation must be transformed to meet the challenges of large spatiotemporal data (R. Vatsavai et al. 2012a).

According to Terence van Zyl et al. 2014 it is important to discuss the geospatial temporal big data conversation within the context of the three V’s: velocity, variety, and volume. In general, spatial data can be divided into three broad categories. These are raster, vector and areal data. Particularly important are the challenges in the calculation of large amounts of either raster data, point clouds or even vector data.

# Related Work

Research on geospatial data is of particular interest to academia and industry. With the constantly increasing amount of data, researchers have begun to realize that there is a great need to understand and analyze what is happening precisely in order to get the greatest possible benefit from the data collected. Ranga Raju Vatsavai et al. 2012 (R. Vatsavai et al. 2012a) reviews the majority of spatial data mining algorithms by closely looking at the computational and I/O requirements. Ahmed Eldawy and Mohamed F. Mokbel 2017 (Eldawy and Mokbel 1) provide a case study of the work in the database community for handling big spatial data. SATO is a spatial data partitioning framework for scalable query processing which was proposed by Hoang Vo et al. 2014 (Vo, Aji, and Wang 2014). He introduces a way on how to analyze data samples quickly, tear the data supported with a MapReduce based scalable partitioning scheme and finally optimize potential queries. There is also a good book entitled "Applications and Challenges of Geospatial Technology - Potential and Future Trends" (Kumar et al. 2019) which contains 16 different articles divided into 5 topics. These writings contain a variety of interesting approaches to various problems in the 5 subject areas of geospatial technologies covered by the book.

# Challenges

There are many ongoing challenges and there is no easy way to describe a general solution that applies to the majority of cases. Generally speaking, it is important to minimize the complexity of space, whereby the aim is to achieve the greatest possible linear complexity of space and a logarithmically linear, if not less time complexity. This is often not feasible and other techniques are needed as proposed by Vatsavai et al. 2012 (R. Vatsavai et al. 2012b). The more sophisticated or complex the algorithms become, the more variable and unpredictable the paths, patterns and access frequencies to the underlying data structures may get.

In order to identify possible challenges or opportunities for improvement, it should be analyzed when, where and in which context the algorithm needs certain data. To address volume and velocity challenges, multiple iterations and alterations should be eliminated or kept as low as possible. According to Cary et al. 2009 (Cary et al. 2009), all infrastructure platforms and toolsets for big data in geoinformatics now support almost any of the different algorithm styles. Nevertheless, it is important to consider the specific infrastructure in order to avoid possible limitations.

As mentioned above, algorithmic time complexity is a general problem that needs to be tackled. A typical solution is the "divide and conquer" algorithm, where the designers create an individual model per subspace or evaluate per subspace (e.g. large satellite time series data cubes that are processed using per pixel algroithms). Another typical approach to minimize space complexity is the rule: the larger the amount of data, the easier the model is to use.

A classical difficulty with many algorithms is the need to take into account the relationship between each pair of observations to create a quadratic space complexity matrix. It is inevitable that the size of this matrix will exceed the storage capacity of the system when used on large amounts of data. To compensate the large matrix we can basically use three major approaches:

1. Iteratively calculate the relationship needs

2. For algorithms that converge on correct answers, consider to use batches or subsets to continuously refine model parameters

3. Map weight matrix into lower-dimensional space (e.g. by using multidimensional scaling)

As many of the geospatial statistical algorithms use such a weight matrix to deal with autocorrelation, many of these geospatial statistical techniques become intractable solutions with regards to geospatial big data space (R. Vatsavai et al. 2012b). Another problem is that traditional algorithms rarely address the large data demands and instead try to maximize the information that can be obtained from the relatively small sample of data by making appropriate assumptions (Shekhar et al. 2015).

# State of the art algorithms

As already mentioned in the upper lines spatial and/or temporal algorithms are still demanded to handle a variety of data types e.g. raster data cubes such as time series of satellite images. In the following we consider the current state of the art of algorithms for geospatial and/or temporal big data.

The predominant difficulties are volume problems, as it is unlikely that this will diminish in the near future. On the contrary, data volume will multiply rapidly. Current solutions which tackle this problem will be briefly discussed below. Markov random field (Li 2001) with $$O(N^2)$$ space requirements and $$O(N^3)$$ computational complexity, can be reduced to $$O(N)$$ and $$O(N^2)$$ through the use of clever algorithms. Another method is stochastic relaxation and iterative approaches to spatial auto-regression, also called spatial autoregressive model (SAR). In spatial regression, the spatial dependencies of the error term, or, the dependet variable, are directly modeled in the regression equation (Anselin 1988). SAR models require an $$O(N^2)$$ memory to store the neighborhood matrix and without any optimizations $$O(N^3)$$ operations (R. Vatsavai et al. 2012a). Many efficient techniques for solving SAR developed in the past are investigated and compared in (Kazar et al. 2004).

Before we look at possible solution methodologies for velocity problems, we must first classify emerging issues. In general, these can be divided into two main classes: the so-called online and streaming algorithms. The former have to make decisions as soon as data is received and processed. Streaming algorithms, on the other hand, allow data to be aggregated and examined as a batch (they are mostly used because of limited resources). The following is a brief explanation of some selected streaming algorithms for handling large amounts of data. A framework for clustering real-time stream data is called D-Stream. The algorithm is split into an online component that maps each input data record into a grid and an offline component which calculates the density of each grid and groups the grids with a density-based algorithm (Chen and Tu 2007). This technique proposed by Yixin Chen and Li Tu allows clustering of high-speed data streams without affecting the quality of the clustering. Another approach is the Naïve Bayes classifier which is based on Bayes’ Theorem where predictors are treated as independent. The Naïve Bayes Classifier is a datamining classification technique that uses probabilities of attributes belonging to a class for prediction (Netti and Radhika 2016). This approach is particularly interesting due to its low time and space complexity.

The last category of algorithms in the field of geospatial big data to be mentioned are variety algorithms. These in turn split into two groups. Gandomi et al. 2015 (Gandomi and Haider 2015) explains that traditionally the variety refers to data heterogeneity. The first group contains all types of unstructured or semi-structured data. The complexity here is that it’s necessary to process large amounts of unstructured data to filter out the useful information. In the second section a large variety of features are considered from a large number of sources. Additional temporal complexity arises with a large number of characteristics, because they add up. This causes dimensionality challenges and can often be correlated, which can lead to instability. Generally variety is still an open challenge in the big data community today. In (Robinson et al. 2017) several problems within this spectrum are outlined, such as the development of techniques for understanding the temporal variation of large-scale geospatial data.

# Brief introduction into classical algorithms

There are plenty of geospatial and temporal algorithms within the geospatial statistics and geospatial analytics community. To give a brief overview, we now cover some classical and common algorithms in the short. The majority of these methods have been developed in the past for situations with sparse data, such as Kriging. It was developed for the spatial interpolation of geological properties using a limited number of core samples and has an $$O(N^3)$$ space complexity (Ryu et al. 2002). Geographically Weighted Regression and Logistic Regression are conventional algorithms for classification and regression. Both have an $$O(N^3)$$ space complexity, but with the use of several improved optimization techniques it is possible to reduce their temporal complexity significantly. A typical method in spatial and temporal modelling considering parameterizations is the maximum likelihood estimation with $$O(N^3)$$ time complexity. For a large number of solutions, the Gaussian elimination algorithm is used. It has an $$O(N^3)$$ time complexity and an $$O(N^2)$$ space complexity. These metrics can be improved considerably by some clever tweaks more about this below in Section 6.

Within the next section some approaches and hints how to scale algorithms for big data are presented. These procedures can be applied to the algorithms described in the previous Section.

## Divide and Conquer

An important fact to consider when working with large amounts of data is that one $$[N \times N]$$ matrix is considerably larger than two $$[\frac{N}{2} \times \frac{N}{2}]$$ matrices. By means of this effect, problems can be intelligently divided into sub-problems that can be solved. The overall result can then be cumulated from the individual solutions. The biggest advantage of the decomposition is that now the whole problem can be parallelized. This fact allows us the use of frameworks like MapReduce or Hardoop to distribute the computations over several computing units to increase the performance. In (Deng et al. 2016) the authors provide a method for space–time prediction with the aid of the divide and conquer approach. In terms of data velocity, the information can be divided into sub-streams, each of which can be processed separately to archive the same results but much faster thanks to the divide and conquer approach. In general the devide and conquer methodology can be particularly useful for conceptually difficult problems. Furthermore, it can be implemented very efficiently and is also suitable for parallel processing as mentioned above.

## Subsampling

Subsampling is a method that is often used to reduce the complexity of large datasets. These approaches must however guarantee that the data examined are representative of the original data set. If the subset of input data is selected appropriately and in such a way that it is not biased, it may be considered adequate to allow good parameterization of the models. In case the obtained results do not meet the expectations, additional data can be added to increase the accuracy. In the Paper "Semiparametric Subsampling and Data Condensation for Large-scale Data Analytics" (Alhussein et al. 2019) they introduce a new clustering-based data condensation framework for large datasets. With the use of stratified sampling, Vonoroi diagrams and the variation inference machinery for clustering they show that they can achieve better performance on the used dataset then stratified sampling. The objective of stratified sampling is to obtain the most efficient stratified method. The goals are that the interval gap is greatest and the internal difference is smallest (Wang and Tong 2008). On the whole, though, the sub-sampling has its own concerns. Most critical is to find out exactly the right sample size to ensure that all underlying properties that are modified are represented.

## Filtering

Another approach in regard to challenges in big data is to filter the data intelligently. The statistical method is slightly different from the subsample approach (as described in Section 6.2), where we select a subset of the data using some stochastic criteria. In filtering, we choose a subset of the data using a few key criteria. It is assumed that this subset is representative of the data we need for our modeling purposes in the area of interest. The goal is to achieve enhanced and robust results in spatial data analysis by decomposing a spatial variable into trend, a spatially structured random component (i.e. a spatial stochastic signal) and random noise. The aim is to separate spatially structured random components from both trend and coincidental noise. Thus, the statistical modeling leads to more substantiated statistical conclusions and useful visualization (Griffith and Chun 2014). An example of filtering is the use of spatial indices such as R trees. This allows us to get a feel for the points that are close together and then use this subset of points to build the model. This is extensively used for large amounts of data to minimize time and space complexity and is therefore characteristic of K-nearest neighbor algorithms.

## Online Algorithms

Online algorithms demand an immediate action for each input date when it arrives, and preferably in real time. The necessity for such algorithms often results from the needs and not particularly from the large data itself. However, large amounts of data aggravate this situation and make it even more complex to solve. There is a wide range of solutions for various applications such as DeepWalk(Perozzi, Al-Rfou, and Skiena 2014), LIBOL(Hoi, Wang, and Zhao 2014) or DeepTrack(Li, Li, and Porikli 2016). Most use machine learning to handle the enormous amount of data and still deliver the answer in a desirable time.

## Streaming Algorithms

Streaming algorithms are similar to online algorithms. However, the main problem is the limited space and not the need for immediate action per element. The response can usually be postponed to a later time, but given finite resources, some restrictions on the amount of data to be considered are often needed. Especially in the age of the Internet of Things (IoT) many continuous sensor data streams, video recordings or user interactions have to be processed. Most IoT appliance are a kind of resource-limited device, which means it lacks performance, connectivity (e.g. sensors in remote places) and battery capacity. The memory limitation must therefore obviously be taken into account, and applied algorithms can only consider some relevant subsets of the data. Galić et al. 2014 (Galić et al. 2014) present a formal framework consisting of data types and operations needed to support geospatial data in data streams. This framework can be used as a foundation for the development of a completely new geospatial data stream management system (DSMS). In summary, streaming algorithms are classical methods to cope with the requirements for large quantities of data, since they meet the challenges of all three Vs.

# Conclusion

There are still some major open challenges that need exploration when considering some of the strategies considered in this paper to overcome the big data challenges in the geospatial sector. Even though we might solve all problems in terms of feasibility and performance one day, there are many other problems, particularly in the area of variety space, which have not been taken fully into account yet (e.g. privacy concerns). Zhen Lie et al. 2016 (LIU, GUO, and WANG 2016) presents in their work four main future research areas of geospatial data, covering spatial correlation, analytics, visualization and scientific knowledge discovery and some general considerations for upcoming research in this sector. If the methods that we presented in this paper are used in combination or in conjunction with large data, the capabilities resulting from the spatial characteristics of the data can be massively increased to reduce temporal and spatial complexity. In summary, it is clear that progress is being made along the road to solving the challenges of large-scale geospatial and temporal data. Although there are many unresolved problems, and there will never be a silver bullet.

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