dataesr/scientific-paragraphs-categorization huggingface dataset:
The decay factor λ for RWK {10 -6 , 10 -5. , 10 -2 }, for the GK kernel we set the graphlet size κ = 3 and cross validate the precision level and the confidence δ as in the original paper  [56]. The t max parameter for PROPAK is chosen within {1, 3, 5, 8, 10, 15, 20}. For PSCN, we choose the normalized betweenness centrality as labeling procedure and cross validate the batch size in {10, 15,. , 35} and number of epochs in {10, 20,. , 100}. Finally, for FGW, γ is cross validated within {2 -10 , 2 -9 ,. , 2 10 } and α is cross validated via a logspace search in [0, 0. 5] and symmetrically [0. 5, 1] (15 values are drawn). Vector attributed graphs. The average accuracies reported in Table  1  show that FGW is a clear state-of-the-art method and performs best on four out of six datasets with performances in the error bars of the best methods on the other two datasets.
The results for CUNEIFORM are significantly below those from the original paper  [46] , which can be explained by the fact that the method in this paper uses a graph convolutional approach specially designed for this dataset and that experiment settings are different. In comparison, the other competitive methods are less consistent, as they exhibit some good performances on some datasets only. Discrete labeled graphs. We first note in Table  2  that FGW using WL attributes outperforms all competitive methods, including FGW with raw features. Indeed, the WL attributes allow for more finely encoding the neighborood of the vertices by stacking their attributes, whereas FGW with raw features only consider the shortest path distance between vertices, not their sequence of labels. This result calls for using meaningful feature and/or structure matrices in the FGW definition, which can be dataset-dependant, in order to enhance the performances.
We also note that FGW with WL attributes outperforms the WL kernel method, highlighting the benefit of an optimal transport-based distance over a kernel-based similarity. Surprisingly, the results of PSCN are significantly lower than those from the original paper. We believe that it comes from the difference between the fold assignment for training and testing, which suggests that PSCN is difficult to tune. Non-attributed graphs. The particular case of the GW distance for graph classification is also illustrated on social datasets, which contain no labels on the vertices. Note that no artificial features were added to these datasets. Accuracies reported in Table  3  show that it greatly outperforms the SPK and GK graph kernel methods. This is, to the best of our knowledge, the first application of the Gromov-Wasserstein distance for social graph classification and it highlights the fact that GW is a good metric for comparing the graph structures.
Unsupervised Learning: Graphs Clustering In the last experiment, we evaluate the ability of FGW to perform a clustering of multiple graphs and to retrieve meaningful barycenters of such clusters. To do so, we generate a dataset of four groups of community graphs. Each graph follows a simple Stochastic Block Model  [60, 61]  and the groups are defined w. r. t. the number of communities inside each graph and the distribution of their labels. More precisely, labels are drawn from a 1D gaussian distribution specific to each community: each feature of a node is drawn from a law N (n c 1 + n c 2 , σ), where n c 1 is the index of the community and n c 2 ∈ {0, 1} to create two modes per community. The dataset is composed of 40 graphs (10 graphs per group) and the number of nodes of each graph is drawn randomly from {20, 30,.
One microlitre of the labelled culture was then placed on a microscope slide covered with a thin layer of agarose (1. 2% (w/v) in 1:1 phosphate buffered saline (PBS)/TSB solution). Time-lapse images were acquired every 20 min by structured illumination microscopy (SIM) in an Elyra PS. 1 microscope (Zeiss) using a Plan-Apochromat 63x/1. 4 oil DIC M27 objective. SIM images were acquired using three grid rotations, with 34 μm grating period for the 561 nm laser (100 mW) and 28 μm period for 488 nm laser (100 mW). Images were captured using a Pco. edge 5. 5 camera and reconstructed using ZEN software (black edition, 2012, version 8. 1. 0. 484) on the basis of a structured illumination algorithm  27. For visualization of divisome proteins, overnight cultures of S. aureus strains were back-diluted 1:500 in TSB (supplemented with CdCl 2 in the case of ColFtsZ 55- 56 sGFP) and allowed to grow to an OD 600nm of ~0.
2% (w/v) in PBS:TSB in a proportion of 3:2), incubated at 37 °C in a DeltaVision OMX SR microscope (GE). Z-stacks of 19 images, with a Z step of 125 nm were acquired every 3 min by SIM using an Olympus 60X PlanApo N/1. 42 oil objective. A 488-nm laser (100 mW) was used at 11-18 W cm -2 with an exposure time of 10 ms. The software AcquireSRsoftWoRx (GE) was used for image acquisition and reconstruction of the SIM images. To image strain BCBAJ096, which expresses fluorescent derivatives of EzrA and Spo0J (fused to mCherry and YFP, respectively), cells were grown in TSB containing erythromycin and IPTG to an OD of 0. 8. To label the DNA, 1 ml of the culture was incubated with the DNA dye Hoechst 33342 (1 µg ml -1 ) for 5 min, pelleted and resuspended in 30 µl of PBS. Cells (1 µl) were placed on a thin layer of agarose (1.
2% (w/v) in PBS) mounted on a microscope slide. Z-stacks of 21 epifluorescence images with a Z step of 125 nm were acquired using a DeltaVision OMX SR microscope (GE) with an Olympus 60X PlanApo N/1. 42 oil objective. The fluorophores were excited with a 488-nm laser (100 mW), a 568-nm laser (100 mW) and a 405-nm laser (100 mW). The software AcquireSRsoftWoRx (GE) was used for image acquisition and deconvolution. To image strain BCBHV005, which expresses fluorescent derivatives of FtsZ and Spo0J (fused to CFP and YFP, respectively), cells were grown in TSB supplemented with IPTG, kanamycin, neomycin and erythromycin to midexponential phase. One millilitre of cell culture was labelled with the membrane dye FM5-95 (250 ng ml -1 , Invitrogen) for 5 min, pelleted and resuspended in 20 µl PBS. Cells were placed on a thin layer of agarose (1.
Acknowledgements We thank  Sérgio R. Filipe  ( FCT-NOVA ) and  Helena Veiga  ( ITQB-NOVA ) for helpful discussions and  Ana Jorge  for the construction of strain  BCBAJ096. This study was funded by the  European Research Council  through grant  ERC-2017-CoG-771709  (to M. G. P. ), by national funds through  FCT -Fundação para a Ciência e a Tecnologia, I. P. , Project  MOSTMICRO-ITQB  with references  UIDB/04612/2020  and  UIDP/04612/2020  (to ITQB-NOVA) and fellowships from  FCT SFRH/BPD/95031/2013  (to N. T. R. ),  SFRH/ BD/147052/2019  (to B. M. S) and  PD/BD/128408/2017  (to M. S. ).
Data availability The datasets generated during the current study are available as a source data file and from the corresponding author on request. Original images for Figs. 1  and 2  are available at figshare (https://figshare. com/s/4808495d92a138aae36c and https://figshare. com/s/ 907e54dd2d24e7c5dd05, respectively). Source data are provided with this paper.
Cities are in constant change and city managers aim to keep an updated digital model of the city for city governance. There are a lot of images uploaded daily on image sharing platforms (as "Flickr", "Twitter", etc. ). These images feature a rough localization and no orientation information. Nevertheless, they can help to populate an active collaborative database of street images usable to maintain a city 3D model, but their localization and orientation need to be known. Based on these images, we propose the Data Gathering system for image Pose Estimation (DGPE) that helps to find the pose (position and orientation) of the camera used to shoot them with better accuracy than the sole GPS localization that may be embedded in the image header. DGPE uses both visual and semantic information, existing in a single image processed by a fully automatic chain composed of three main layers: Data retrieval and preprocessing layer, Features extraction layer, Decision Making layer.
Finally, websites like Openstreetmap. org provided a platform to add or modify geographical information like roads, buildings, store names, and even benches and trees. This is part of collaborative mapping approaches, which are becoming increasingly available since the Volunteered geographic information (VGI) movement led by  [8]. Lately, Google provided a platform for sharing images and geographical information and giving rewards in return to encourage people to participate in its database enrichment  [9]. In this article, we propose to use data from these active sources to update the city's information. Publicly shared images may be an interesting source of information. Unfortunately, their localization is not sufficiently accurate: according to  [10] , the average error of a public GNSS sensor is 5.
3 meters under the open sky and this margin of error increases in urban environments due to the signal reflections on the concrete and metallic structures. Also, those images do not include any orientation information in their metadata. DGPE aims to gather these images and try to refine their geolocalization and find the image orientation. We use the image extracted features and its metadata to cross them with other geographical information to provide a refined camera pose. The city's GIS managers, provided with a metric image localization and an orientation, will be able to use this information to start an investigation and update the city's 3D model or a street view database in case of detected changes. This paper is divided as follows. We first present the related works in the geolocalization field based on single images.
They start their work assuming that images with a valid orientation and GPS location are already registered in the database. The paper considers extracting for every building facade in the registered images a corresponding texture descriptor. Then, to register a new image, it uses SIFT descriptors by  [14] , matching with the registered texture descriptors. The limitation of this work lies in affine rotation (30 degrees or more) and building facades should be very different from one another to avoid SIFT descriptors confusion. The algorithm used in  [19]  achieves fast and accurate feature landmark-based camera parameter estimation by reducing the number of matching candidates and assigning priorities to them. They aim to find camera pose by matching the image with known landmarks that have been previously accurately scanned using a laser range sensor.
Therefore, a 3D model landmarks database is unavoidable with such a technique. The authors of  [20]  propose a combination of simultaneous localization and mapping, called SLAM, and a global localization method. The authors consider an AR application built on smartphone devices that will use the first two frames to initialize a structure from motion reconstruction. Then, the server will then compare the reconstructed environment with a global cloud of points. Finally, the client will update the current pose using his sensors and the initial information. On the other hand, Bioret et al. [16]  propose a localization approach in urban environments based on correspondences between 2D GIS and a single 2D street photograph. Practically, Bioret uses the vanishing points and the limits of the facades in the 2D image to find the angles between facades and their width ratio in the image building.
Building Detection and 3D Scenes Reconstruction In this section, we present some building detection methods that have been developed by other researchers as we will use building detected in the image and GIS information for pose image refining. Urban environment understanding is an active research field partly based on street images use. Several techniques like  [24]  [25] and  [26]  used stereography to reconstruct urban environments using several images or video sequences. However, we seek to reconstruct an urban environment, or at least understand it, using a single 2D image. Therefore, the preceding methods are not suitable for our image datasets. Derek Hoiem et al. [27] [28]  propose a method of 3D environments reconstruction using 2D images. They divide their images into superpixels and estimate the orientation of each one.
Therefore, this last method can only detect the building boundaries from two sides. In other words, only 3 building vertical edges can be detected, even if more are available. Available vertical edges can only be transformed into two facades, although  [16]  proved that when more facades are available, his 2D GIS matching performs much better. Our goal is to refine the geolocalization of online published photos. Therefore, we only have a single monocular image and rough GPS information with no orientation information. After exploring the state-of-the-art techniques, the ones that fit the most with our datasets should be  [16]  or  [17]. We thus propose in section 3 the Data Gathering system for image Pose Estimation (DGPE) that will help to refine image geolocalization and orientation using a single image, a 2D map, and corresponding techniques, such as  [16].
Data Gathering System for Image Pose Estimation (DGPE) In this section, we propose the DGPE system for image geolocalization using simple and widely available information. DGPE takes as input 2D images, either from a dataset we have already shot or images downloaded from social media websites (Flickr, in our case). The second input information is 2D maps that represent the city buildings. All the images that we will present were taken by us using an iPhone 5 device with a GNSS sensor. To save the reference localization, the photographer's location was pinned on a satellite view map, and the location coordinates were then retrieved. We assume using in DGPE dynamic information sources (updated regularly), therefore we used maps extracted from OpenStreetMap. org. We also used the Nominatim API  [32].
A Three-Layer System Architecture We have created a three-layer system and summarized its main functionalities in the diagram shown in Figure  1. The first layer of DGPE is the "Data retrieval and preprocessing layer". This layer takes as an input the user requirements about the zone one wants to find new images in. DGPE reads the images from a local dataset or downloads images shared on social media websites and filters them by keeping only the ones verifying the user needs. The "Features extraction layer" is the second part of DGPE. Its function is to extract from every image the existing features in the visual part of the image. We divide the extracted information into two categories: Geometric information that represents the building shape (ratios and angles between facades) and Semantic information that provides information about the image location (stores logos, street names, landmarks, metadata, etc.
Data Retrieval and Preprocessing Layer The first layer of DGPE retrieves the images from local or online databases and filters them using the user requirements. The user should specify at least the search zone he/she wants to extract images from. He may also add a minimum and maximum date limitation in order to avoid retrieving images that have been already processed. We have designed DGPE using multiple modules to allow modifications or module replacement later on. This layer comprises four modules presented in this section. The image retrieval module is responsible for querying images from the image database. Two options are available for images and their metadata retrieval: from a local dataset or an online database. When using the online image retrieval module, many advantages exist. First, retrieved images belong to a restricted geographical zone that is determined beforehand by DGPE user, image shooting or uploading date are also taken into consideration.
Therefore, we start by filtering metadata in this case. A second advantage is the metadata information that we can retrieve from such a database. Regardless of the GPS location, the image shooting or uploading date, images retrieved from the social media websites also have some semantical metadata that could be useful for our processing. The module retrieves hashtags, image descriptions and titles that are in plain text format. On the other hand, images retrieved from local datasets or databases that store and allow to retrieve EXIF 1  metadata are sent to the Meta-data Extractor module. This simple module extracts geographical information and camera shooting parameters to initialize the next steps of the system. These images are also filtered using the image filtering module according to their metadata, especially the location information, to make sure that the image belongs to the user's specified zone.
Location Detection Using Semantic Information Retrieval Figure  3  shows a module that finds possible geotags of an image using textual input information. The text can come from the metadata of the image extracted from an online database as described above. Images can also include semantic information in their visual parts, such as landmarks, logos from storefronts, urban furniture and text. We have applied the text recognition extraction because it automatically returns the textual information visible in the image. Store logos and city landmarks may also be useful in such analysis, we are looking forward to including them in future implementations. Several text recognition techniques have been developed in previous work  [34]  [35]  [36]. In our implementation, we have used Google Vision API, but it could be replaced by any other text detection method in an image.
Another semantic aspect of our images is the content that they are showing. Images within an urban zone can be taken on the streets and represent buildings, but others may represent people, food, or indoor locations. We thus use the Google Vision API to make sure the image we are using in DGPE does contain buildings. The API returns a list of words describing the scene for every image. We only keep images that have in their description list words related to the buildings (e. g. Building, architecture, property, facade, town, house, etc. ), and other images are skipped by the system. The list of words was chosen based on statistics performed using responses returned from the same API. The selected words are the ones that had a confidence score above 90%, given by the API. Lastly, a list of textual information is created using the words detected from the visual part of the image, as well as the text retrieved from the image's metadata found on the image-sharing platform.
Location Detection Using Geometric Information Retrieval We assume in this part of DGPE that a building can be represented using segments and simple rectangular polygons. We will now explain the global geometric process for image geolocalization. We will, later on, explain in detail the building detection module developed in this part of DGPE. We can find in Figure  3  a module named visual features extractor. It aims to extract basic features from an urban image. We thus search in the features' extraction module to find all the segments that could be extracted from the image. For this, we use the LSD  [37]  segments extractor. It returns several segments of different sizes. Small segments are filtered out using a parameter relative to the image size. These segments are usually found in far buildings, trees, and other urban furniture that is not related to the main building in the picture.
SBBD Results We have tested SBBD using different conditions and datasets. In Figure  9 , we have tested the method on urban images under two different weather conditions. In the top row of Figure  9 , the images were taken in January 2017 on a sunny day. Trees were smaller and some with no leaves, some buildings were exposed to the sun and its shade. In the bottom row of Figure  9 , images were taken in April 2017 on a rainy day. Tree leaves started appearing, announcing the spring, some other trees had grown and in some images, scaffolding was added to the building for renovation. Yet, we have obtained the same detection of the building. Even if in some cases it was not a perfect detection of the complete building, it gave us the same information about the facades and the angle in between.
Regarding the Chu dataset, we have found that his method gives 56% (see Figure  10  Chu Summary column) as a whole. We have also tested Chu's dataset using SBBD that gave slightly lower detection performance with a 54% detection rate (see Figure  10  Chu Summary column). We have found that when our method works on a specific location, no matter how the camera moves, the method can still detect the building. Yet, the detection fails when the roof edge includes a lot of small details (Location 3 in Figure  11 ), or when many buildings exist in the image (Locations 6, 7, and 8 in Figure  11 ). We have then tested our dataset with both building detection methods. We have found that on our dataset, SBBD performs better than the Chu et al. one. In fact, Chu's method found only 15% (see Figure  10  Our places column) of the buildings in our dataset.
Numbers and Discussions We present in this section some charts showing the results of DGPE applied to two image databases we have created. The first one contains 19 images that have been used with no associated semantic data, the results are presented in Figure  19. The second database contains 28 images that we have uploaded to the "Flickr" platform and thus contains additional semantic data available as comments, image titles and hashtags. We compare this database's results when using semantic data (Figure  20 ) and when semantic data are ignored (Figure  21 ) in order to understand the importance of this information in the pose detection process. We can find in Figure  19  that we detected in 32% of the images part of the text that may reveal geographical information. In 21% of the cases, we find only the text that reveals geographical information and in 21% of the images text that reveals geographical information is detected with useless text in addition.
We then use the database of the image uploaded to "Flickr". We found that the text detection module returns in 32% of the cases text revealing geographical information. In 18% of the cases, the text is partially detected and in another 18% of the cases, the text is detected with additional text that does not reveal any localization information. When using the semantic information, we can notice that in 39% of the cases the building present in the image is found, and in 25% of the cases the correct building is found with additional locations. This information, based on text detection and other information downloaded from social media is not used in the results of Figure  21. The results also show that all the images contain buildings according to the "Google Vision API". We can also see that in both Figure  20  and Figure  21 , the building is detected in 32% of the cases and is partially detected in 29% of the cases.
We then notice that the results generated using the image and GIS matching are successful in 11% to 14% of the cases. We can also find wrong detections in 18% to 21% of the cases. The rest of the matching cases return no results. The building was identified in only 11% of the cases when no semantic information was available. The same images' results were improved using the semantic data and 59% of the buildings were identified. We are looking forward to adding more functionality to DGPE by integrating logos and known landmarks detector. Using methods such as the ones described in  [40]  and  [41]  can improve our semantic understanding of the scene. Such algorithms help us choose the right area of the image in order to build a specific information query among the other modules. We are also thinking about improving our building detection method to recognize tilted roofs arcs and add the ability to detect multiple buildings.