Integrating semantically related, multi-modal, heterogeneous data sources is challenging, especially if one of the modalities includes spatial data, such as field measurements organized in geographical grids. Since geographical grids can have diferent rotations, be translated along one or more axes, or have diferent resolutions, a particular challenge when integrating such data is to reduce the information loss from projecting diferent grids into a common format. In this paper, we study this problem and sketch a method for integrating such spatial data using knowledge graphs. We discuss this solution in the context of a real-world use case, where we integrate geographically annotated microbial data (Microflora Danica) as well as environmental data to enable joint analysis. The first results of our experiments show that our method reduces the information loss compared to baseline methods.
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Integrating and linking semantically related heterogeneous and multi-modal data is an important
task that is often very challenging [
The need for data integration appears in a multitude of domains. One such domain is the
study of microbiomes, i.e., the interaction between microbes and the environment they inhabit.
Understanding these interactions is essential for solving current and future environmental
challenges [
One method to facilitate the integration of multi-modal data is through a knowledge graph
(KG) [
In this paper, we present a case study for integrating spatial heterogeneous multi-modal data
sources using a KG. The case study is based on the Microflora Danica 1 (MfD) dataset, an archive
of microorganisms in Denmark. We present the challenges and possible solutions of enriching
this dataset with data from EcoDes-DK15 [
Data integration using KGs has recently gained attention, mainly due to their flexibility, but also
because of the advantages when dealing with heterogeneous multi-modal data [
GeoTriples [
Tran et al. [
Zhu et al. [
Several hierarchical discrete global grids (HDGG) have been proposed to represent spatial data, including H34, Bing Maps Tile System5, and S2 Geometry6. Common among them is the hierarchical division of the Earth into subsets. H3 utilizes hexagons, but, since hexagons cannot be perfectly subdivided into smaller hexagons, child cells are only approximately contained within their parent cells. Bing Maps Tile System projects the Earth onto a map; however, this projection distorts the scales in proportion to the distance to the poles. The S2 Geometry decomposes Earth into a hierarchy of cells. Instead of mapping points to a plane, S2 maps them to a perfect sphere. Since Earth is closer to being a sphere than a plane, this creates less distortion. At the top-most level of the S2 hierarchy, Earth is represented by six cells, perfectly covering the Earth, with each lower level subdividing each cell into four children.
The KnowWhereGraph (KWG) [
In this paper, we consider a use case where we want to integrate several real-world heterogeneous data sources of microbes and ecological descriptors of their habitats, exploiting the capabilities of KGs for flexible multi-modal integration of spatially related data. In this section, we describe the available data sources and how they shape our case study.
The Microflora Danica Dataset. The Microflora Danica 7 (MfD) dataset comprises more than 10, 000 measured samples collected from diferent sample sites in Denmark. The MfD dataset was created to provide a database of all microbes in Denmark, and contains several diferent modalities. Information on where each sample was taken is geographical vector data, and DNA reads can be considered as very long strings. Each sample in the MfD dataset is sequenced at least once, which is a process that constructs probable DNA reads from a sample. Through this process, each sample is associated with approximately 10 million DNA reads, , each being a fragment of a full genome consisting of the four bases, Adenine (A), Thymine (T), Cytosine (C), and Guanine (G), found in DNA, ∈ {, , , } +. In total, the MfD contains 28 TB of reads.
The structure of the MfD dataset is shown in Figure 1. Each sample site is described in the Fieldsample Metadata, which contains information such as GPS location and habitat type, 4https://www.uber.com/en-SE/blog/h3/ 5https://learn.microsoft.com/en-us/bingmaps/articles/bing-maps-tile-system 6https://s2geometry.io 7https://www.bio.aau.dk/forskning/projekter/microflora-danica with the habitat types linked to three external taxonomies. Each sample is sequenced multiple times, each sequencing being described in the Sequencing Metadata, linked to their related sample site through a fieldsample_barcode . The Sequencing Metadata describes how each sample was sequenced and handled in the laboratory. Each sequencing leads to a number of reads, collected in a single file we denote as Read Data, connected to their related sequencing through a sequence_id. In a Read Data file, there is, besides the reads themselves, a certainty measure for each base of the reads. Finally, each site was sampled as part of diferent projects, each project potentially collecting multiple samples. The projects are described in the Project Metadata, containing information on the parties responsible for the projects. Each sample site is linked to its related project through a project_id.
Besides information on the reads, sequences, and sample site, we are also provided a mapping
from each sample to potential microbial species (taxons) present in that sample. Since reads
are only fragments of the complete genome of a taxon, the mappings are uncertain. They are
structured as shown in Table 1. Each Operational Taxonomic Unit (OTU) is a DNA sequence
that encodes a specific, potentially undiscovered taxon. Each MFD_X column represents a
ifeldsample_barcode and shows how many reads from a sample site were mapped to that OTU.
Environmental Raster Files. The EcoDes-DK15 [
A raster file is a matrix organized into a grid of rows and columns of raster cells, each cell representing a geographical area. Each raster cell of a raster file is furthermore associated with a value representing information about the geographical area, such as temperature or pH. In total, the environmental data contains approximately 200 GB across approximately 100 files, each containing a diferent type of measure.
A raster file contains the geo-location of the upper-left cell of its matrix and a transformation matrix containing information on what translations and rotations are needed to get the rest of the spatial locations of all the other cells. In our datasets, raster cells have a resolution of 10 × 10 meters, and the spatial location is given on the Universal Transverse Mercator (UTM) coordinate system. In the UTM coordinate system, each location is defined by the pair (, ) with , easting, being the distance east of the Greenwich Meridian, and , northing, being the distance north of the equator.
The S2 Geometry. In order to handle the integration of raster files with potentially diferent transformation matrices, we integrate them into a common grid, the S2 Geometry, as all raster cells in a raster file can be mapped to a set of corresponding cells in the S2 Geometry, regardless of the transformation matrix.
The S2 Geometry is a 31-level hierarchical grid that decomposes Earth into a hierarchy of cells. At the top-most level (level 0) of the hierarchy, Earth is divided into six cells perfectly covering it, while each higher level of granularity subdivides each cell into four children, such that there are 24 cells at level 1, 96 cells at level 2, and so on.
In this section, we present our KG design for spatial integration, demonstrating how the S2 Geometry can be adopted to independently integrate the spatial aspect of each data source. Further, we show how we extend the KG design to integrate the rest of the MfD dataset. The code is available on GitHub8.
Spatial Data. We build upon well-established ontologies to model the spatial dimension, as shown in Table 2. The geo ontology is used to model the spatial relations between raster cells, S2 cells, and MfD sample sites; the upper level ontology oboe is used to model the environmental observations and measurements; and the kwg-ont ontology is the ontology of the KnowWhereGraph.
We can consider a raster file as a collection of raster cells, where each raster cell is associated with at least one measurement. For raster files where their raster cells perfectly overlap one another, such as they do in our use case, each raster cell is associated with multiple measurements (pH value, soil salinity, etc.). This is modeled using the oboe concepts ObservationCollection, Observation, Measurement, and MeasurementType; and properties hasMember, hasMeasurement, hasValue, and containsMeasurementsOfType (see Figure 2).
To model the spatial relation between S2 Geometry and the MfD sample sites, we link each site to the S2 cell that covers it, using the GPS location obtained from the MfD dataset, described in Section 3. For the spatial relation between the raster cells and S2 Geometry, we associate
each raster cell with the set of S2 cells that covers it. To model these spatial relations between raster cells, S2 cells, and MfD sample sites, we utilize the geo ontology properties coveredBy and covers, see Figure 2, where the data from the raster files is colored in orange, the data from the MfD dataset is colored in blue, and the spatial integration layer, S2 Geometry, in bold.
Our current datasets do not have significant overlaps, so we do not have significant interoperability conflicts among them. However, in the future, we would like to integrate data from diferent sources; therefore, a semantic alignment pipeline will be needed.
Spatial Integration. The spatial aspect of each data source is mapped to the S2 Geometry. The integration can be split into two types: the vector-based GPS integration of the MfD sample sites and the area-based integration of raster files. We focus on the integration of raster files in this section, as the integration of the vector-based MfD sample sites simply requires us to integrate the given coordinates directly to the covering S2 cell.
As described in Section 3, the S2 Geometry is a hierarchy of levels determining the granularity of S2 cells. Increasing the granularity of the S2 level results in the area of each S2 cells being lowered by a factor of 4. Therefore, the S2 level afects the number of S2 cells required to cover each raster cell; a high granularity requires many S2 cells, whereas a low granularity requires fewer. Consequently, lower granularities of the S2 level increase the over-coverage, i.e, the area of S2 cells that covers an area outside their associated raster cells. The over-coverage is illustrated for two diferent granularities of the S2 level in Figure 3, where the S2 cells (red) are covering area outside the raster cell (green).
Ideally, a set of S2 cells covers each raster cell perfectly; however, this is not the case, and as such, choosing the highest granularity will yield the lowest possible over-coverage. The issue with this is that each level quadruples storage requirements, as each S2 cell has four child cells.
The EcoDes-DK15 and soil raster files have a resolution of 100 m2; hence, to minimize over-coverage, an S2 level of 24 is chosen as S2 cells have an area of approximately 0.3 m2 at that S2 level.
Irrespective of the S2 level, S2 cells over-covering a raster cell Figure 3: S2 cells covering will overlap neighboring raster cells. This is not desirable since raster cells at difeach S2 cell should only correspond to one value per feature, e.g., ferent levels we cannot associate two pH values with the same location. To address this issue, we use a majority rule; however, one could also aggregate the values, as long as they are continuous. The majority rule disassociates S2 cells from any raster cells in which their centroids are not located. However, disassociating S2 cells from a raster will introduce under-coverage, i.e., the sub-area of a raster cell that is not covered by any S2 cells.
A potential error introduced by over- and under-coverage is integrating an MfD site to an S2 cell corresponding to an incorrect raster cell. For example, in the left of Figure 3, the sample site (cross) is linked to an S2 cell that covers the shown raster cell instead of an S2 cell covering the raster cell below it. S2 cells of higher granularity diminishes this problem.
In general, the integration of raster files is challenging due to diferent raster files possibly having diferent transformations, i.e., resolutions, rotations, and translations. However, utilizing the S2 Geometry, the integration of raster files is independent across diferent transformations. Thus, our approach afords the integration of arbitrary raster files.
Microbial Data. The MfD dataset contains sample-specific information such as metadata,
DNA reads, sequencing metadata, sample-to-OTU mappings, and habitat information of the
sample site. As the focus of this paper is on spatial integration, we omit details on this part;
however, we outline the design for this integration in Figure 4. Note that each entity has
properties, but due to limitations, we do not discuss metadata associated with the microbial
data. Each sample site, marked in blue, has a habitat type, such as ’forests’ or ’grasslands’,
which we map to a corresponding concept in the Environment Ontology, ENVO [
the information loss of using the S2 Geometry as the integration layer and compare it to a baseline method. Furthermore, we highlight potential issues when using the S2 Geometry.
Information Loss. We observe two contributing factors to the Figure 5: Over- and underinformation loss from our integration to the S2 Geometry. The coverage ifrst type of information loss is over-coverage ( Equation 1), where a part of the area of the 9https://obofoundry.org/ontology/ncbitaxon.html minimal set of covering S2 cells associated with a raster cell is outside the bounds of the raster cell. The over-coverage is calculated as the proportionate area of the set of S2 cells not contained within the raster cell. The second type of information loss results from the implementation of the majority rule, and is denoted under-coverage (Equation 2), where a raster cell is only partly covered by its associated minimal set of covering S2 cells. The under-coverage is calculated as the proportionate area of the raster cell not contained within the set of S2 cells. These two types of information loss are visualized in Figure 5, with the blue area being over-coverage and the red area being under-coverage.
OC = | 2 ⧵ Raster| | 2| (1)
UC = |Raster ⧵ 2| |Raster| (2)
Since the two contributing factors are equally unwanted, we define the information loss as the harmonic mean of the over- and under-coverage (Equation 3). Due to the nature of the harmonic mean, higher values are desirable; however, this is not the case for the over- and under-coverage calculations. Therefore, we use the complement of each coverage. This yields an information accuracy, which we subtract from 1 to get the loss.
Information Loss = 1 − 2 (1 − OC) ⋅ (1 − UC) (1 − OC) + (1 − UC) .
(3)
The mean information loss for integrating with and without the majority rule is reported in Figure 6 for diferent S2 levels, based on random sample of 100 raster cells. Low granularity S2 levels have a mean information loss approaching 1, whereas higher granularities of the S2 level reduce the information loss. The advantage of using the majority rule is visible for higher granularities, starting from S2 level 20. However, for low granularity S2 cells, the majority rule introduces high under-coverage, as many raster cells become associated with no S2 cells, due to the centroid of large S2 cells that covers many raster cells being located only within a single raster cell.
The S2 levels 1 through 15 and 27 through 30 are not shown, as these approach an information loss of 1 and 0, respectively. At S2 level 24, where the information loss is 0.022, the information loss begins to stagnate with higher granularity of the S2 levels, which is an indication that this is a suitable level to integrate the use case raster files into.
Using the S2 Geometry as the spatial layer is not without issues, especially when using a granularity for the S2 cells. The grid of the raster files used for this case study is approximately 35,000 × 45,000, resulting in 1.575 billion raster cells. For an S2 level of 24, each raster cell is linked to 625 S2 cells on average. Combining these two numbers yields a total of approximately 1 trillion triples. However, as the raster files for this case study lack measurements for raster cells located in the ocean, the actual amount of integrated raster cells diminishes by around 75%, yielding approximately 250 billion triples solely for the integration of raster cells. Up- and Downsampling. To evaluate the gain of using the S2 Geometry as an integration layer, we compare it to using up- and downsampling for combining raster files of diferent resolutions. Upsampling refers to taking a set of cells at a lower granularity and then aggregating them into higher granularity and vice versa for downsampling. We exemplify the information loss from up- and downsampling via two hypothetical resolutions 10 × 10 and 7.5 × 7.5 meters, in red and blue, respectively, as illustrated in Figure 7.
In order to upsample and downsample, we define how the majority rule works in this setting. For the highlighted red cell, we see that it is covered by four diferent blue cells. Since only two of the blue cells have their centroids within the red cell, we downsample only into those two cells. Conversely, we upsample the highlighted two blue cells into the single red cell in which their centroids are located. We note that upsampling is more dificult than simply aggregating if we deal with categorical attributes.
An information loss of 0.5 is obtained for upsampling into the 10 × 10 grid and 0.298 for downsampling into the 7.5 × 7.5 grid. In comparison, integrating the two grids into the S2 Geometry at level 24 results in an information loss of 0.028 and 0.019, respectively.
In this paper, we have presented an approach for integrating multi-modal heterogeneous data sources through a spatial KG layer in the context of integrating geographically annotated microbial data and environmental features to enable joint analysis. While the emphasis has been on integrating the spatial data sources, we have also discussed the design of the complete multi-modal data integration of raster data, DNA reads, and ontologies. We propose an approach based on the S2 Geometry that can integrate raster files of diferent resolutions, translations, and rotations without performing significant aggregations of the raster cell measurements. In the future, we plan to work on improving scalability given the large number of RDF triples related to the use of the S2 Geometry as well as to capture provenance through the use of the PROV-O ontology10.
This work is partially funded by the Villum Foundation (DarkScience project, 50093). We further thank the SustainScapes group from Aarhus University for sharing the environmental dataset.