Graph embedding methods are used to create representations of knowledge graph entities in a high-dimensional vector space. These embeddings can be used in downstream tasks such as classification or link prediction. However, typically graph embedding methods require training on the entire knowledge graph, making them less eficient when a knowledge graph is expected to be dynamic, such as with IoT measurements graphs, which are updated throughout the day with new numerical measurements. This paper introduces a method for eficiently creating embeddings for new knowledge graph entities, without retraining the embedding model. The proposed method estimates an embedding for new entities, by averaging the embeddingkonfetahreest neighbors, where nearness is based on numerical attributes associated with the entities. We investigate the performance of this method, both on a synthetic knowledge graph, and five real-world knowledge graphs. In these experiments, we employ RDF2vec as the embedding method, and classification as the downstream task. We compare three distance measures for determining nearest entities. We observe a trade-of between the accuracy and eficiency of estimating the embeddings and retraining the embedding model. Resulting in a significant decrease of training time, compared to retraining the full model, with only a relatively small reduction in precision. Results show that in cases where the attributes are representative enough our method is an efective and eficient method to incrementally adjust graph embeddings.
CEUR
ceur-ws.org
We detail the method and its parameters in Sec3t.ion
We evaluate this method both on a synthetic knowledge graph and on real-world knowledge graphs (Sections4 and5). The synthetic knowledge graph allows us to adjust the amount of noise in the numerical values of the graph. By adjusting this noise level we can explore the efect of noise between the numerical values and the classification targets, on the efectiveness of the embedding estimation method. We further test the embedding estimation method with five diferent knowledge graphs from diferent domains. In both experiments, we examine the trade-of between loss of accuracy due to the estimated nature of the new embeddings and time improvements.
Knowledge graphs are data structures consisting of entities and relations connected in a graph, with the entities as nodes, and the relations as ed8g].eTsh[e data can be expressed as RDF triples, which use the following shape: e<ntity1, relation, entity2>. In this section we present work related to changing graphs (Section2.1 and2.2), the related topic of inductive learning (Sec2.t3i)oannd diferent methods that can be used for entity representation learning (S2.e4catniodnSection2.5)).
Learning representations for entities in dynamic knowledge graphs has been researched in the past. Dynamic graph convolutional networ9k]sle[arn from the dynamic aspect of a graph. By considering each timestamp as a snapshot of the graph and learning over all these versions of the graphs the temporal aspect can be captured. These networks are able to learn from dynamic data, but still require all data to be available when they are being trained. Instead our method allows for new information to be processed directly. Note that in contra9s]t, otuor[ method is limited to dealing with incremental addition of entities only, and does not deal with other types of alterations, such as restructuring or entity removal.
By adding timestamps to every property of the graph, a temporal knowledge graph is created, which can also be utilized to represent dynamic knowledge graphs. In the T-GAP m1o0]d,eflo[r example, the authors use the timestamp of the query to determine which parts of the graph are most relevant in answering the query. Even though adding such timestamps introduces a temporal element, this is not what we want to capture in this research. Such models for temporal knowledge with timestamps graphs do not learn from new knowledge.
There are frameworks created to handle data streams for situations where data is expected to be
added regularly, such as Kafka-ML 1[
The field of inductive learning focuses on creating methods to use with previously unseen entities or relations. For example, by creating an embedding generator for entities in a graph, and then using it to create embeddings for new entities in that gr1a2]p.h [
Shi et al. 1[
Another inductive learning approach is proposed by Gesese et al.: R A14IL],Dw[hich in addition to learning representations to entities, also learns representations for relations, for the specific task of link prediction. The textual representations of entities and relations are encoded using a language model.
The work of Galkin et al.15[] takes inductive learning a step further by introducing ULTRA, which not only works on unseen entities, but on completely unseen graphs. It uses a pre-trained foundation model that creates representations for relations in a graph based on the interactions between those relations. Since it is pre-trained on another graph it does not have be trained on new entities.
What sets our approach apart from previous inductive learning approaches is that we leverage the numerical properties of the graph and the entities in order to make an estimation for the entity embedding. Additionally, we do not use a learning approach for the estimation part, using only information already available, while inductive learning trains requires more preparation, such as an additional model for the creation of embeddings for unseen en1t6i]t.ies [ 2.4. GCNs Graph convolutional neural networks (GCNs) are used in approaches such as Graph1S6A]GanEd[ the more recent Dynamic Knowledge Graph Embedding (DKG1E7)][and Lifelong Knowledge Graph Embedding (LKGE) [18], to learn representations for entities. By only taking into account the direct context for each entity they learn embeddings for entities without considering the entire graph. Therefore, when a new entity is added to the graph, an embedding can be created for it by only considering its new context, without altering the model or the other embeddings. However, GCNs need to be trained end-to-end, while our method considers graph embedding methods that are trained independently of various possible downstream tasks. Additionally the embedding estimation method is able to capture longer range dependencies between entities, by using the numerical values of the entities, which is a challenge in GCN-based approaches.
Leveraging modalities was investigated in multimodal lear1n9i]n, gw[here the authors create a
pipeline with a dedicated neural network for specific modalities, and then combining their embeddings
with a GCN to learn more specific representations. However these methods were trained end-to-end,
with the learned representation only being relevant for a specific task. Our estimation method is able
to use embeddings created to represent entities from the knowledge graph independently of a task.
Additionally our method would not require any changes to the pipeline in place, only the addition of
the method.
2.5. RDF2Vec
RDF2Vec [
Recent work by2[
Our estimation method intends to supplement RDF2Vec, or any other task agnostic graph embedding model. We base the estimated embeddings for new entities on the existing embeddings, by leveraging the related numerical attributes of the entities.
In this section, we present the main contribution of this paper, which is the embedding estimation method. The setup of the experiment and its results follow in Se4ctainodn5, respectively. The method estimates an embedding for new entities based on the embeddings of most similar previously embedded entities (we refer to the latter as “original entities”). Similarity between original entities and new entities is determined with a distance measure (Sect3i.2o)nbetween the numerical attribute values of the entities.
Algorithm1 provides pseudocode of our method for one individual new entity. Besides the new entity it requires: all original entities (including their previously calculated embeddings) and pka,rameter which determines the number of original entities used to calculate the embedding for the new entity.
The first step is calculating the distance between the attribute values of the new entities and each individual original entity. By sorting these distances in ascending order we create a ranking of original entities most similar to every new entity. The embeddings okfmtohset similar entities are averaged to create the embedding for the new entity. In other words, the distance measure between the attributes is used as aproxy for the (ideal) distance in the embedding space.
In this implementation of the estimation method we do not apply normalization. The estimation method assumes that the attribute values will be a reasonable representation for the entities, using them to estimate a new embedding for each new entity.
Algorithm 1 Calculates the estimated embedding for a new entity, based on the similarity between its attributes and those of the original entities.
= 1 new entity for which we want an embedding = All original entities with embeddings = number of nearest entities to consider function embedding_estimator( for all ∈
← distance_measure( end for ℎ = sort_ascending() _ℎ = get_top_k(ℎ, ) = get_embeddings( _ℎ, = average() return end function 3.2. Distance Measures do ,
, ) ., ) .) We implement three diferent distance measures: Euclidean, Chebyshev and Manhattan distance. Below we give a short description of each distance measure. WeAtraenadtB as vectors. The length of the vectors depends on the number of numerical values the knowledge graph contains.
Euclidean distance = √∑ ( − )
2, The shortest line between two points.
DaGtarappohints Classification
Task
Chebyshev distance = max | − | , The longest distance between two points, in any one of the dimensions of the points.
Manhattan distance = ∑ | − | , the summed distance between two points over all dimensions of the points.
In order to test the efectiveness of the estimation method, we measure the accuracy and runtime of the classification task on 10 variants of a synthetic knowledge graph and five real-world knowledge graphs, comparing the estimation method against the retraining method. The setup of this experiment is described in Sectio4n.1.
The creation of the ten variations of the synthetic knowledge graph are detailed 4in.2.S1e.cBtyion adjusting the noise level in the synthetic knowledge graph we will determine the efect of noise on the efectiveness of the estimation method, and the efect of changing vak.lue
The five domain knowledge graphs presented in Sectio4n.2s.2, 4.2.3 and4.2.4 demonstrate how the embedding estimation method performs on real-world knowledge graph. 4.1. Setup The setup of the experiment assumes there already existosriagninal pipeline, from which multiple elements will be reused by the estimation method. An example of how we expect such a pipeline to look like is given in Figur1e.
For the embedding estimation method we reuse the original embeddings and entities from the graph to create the embedding estimator, which uses the new entities to create the new embeddings. By reusing the classification method, new accuracies are calculated. We use 21 values for parameter ranging between 1 and 250, a n,dwith being the total amount of original entities. This results in the average embedding of all original entities to be used for all new entities. This is added as a baseline. The experiments are repeated, with all three distance measures, to determine the efect of choosing the distance metric.
The retraining method combines the new and original knowledge graph and original entities to completely retrain all models created in the original pipeline, reusing nothing.
RDF2Vec [
The experiment is performed with: a synthetic knowledge graph using the SAREF ontology, two smart building knowledge graphs and a selection of three knowledge graphs from diferent domains, based on the availability of attributes, from KGBe2n3]c.hN[umerical attributes of entities are collected from the knowledge graph, both for the original entities and new entities, by querying the knowledge graphs. 1https://github.com/RoderickvanderWeerdt/Embedding_Estimator saref:isPropertyOf saref:relatesTo
Property saref:hasMeasurement
saref:FeatureOfInterest saref:UnitOfMeasure saref:isMeasuredIn saref:hasValue
saref:isMeasurementOf saref:isMeasured
ByDevice saref:isControlled
ByDevice saref:Property saref:relatesTo
Measurement saref:measuresProperty saref:measurement
MadeBy saref:makesMeasurement saref:accomplishes ice:hasRoundedValue ice:RoundedValue ice:measuredAtTime ice:Timestamp saref:Measurement
measurement saref:hasTimestamp timestamp ice:previousMeasurement ice:nextMeasurement saref:Measurement
For the experiments we use six diferent knowledge graphs. First we discuss the creation of the synthetic knowledge graph. Because real world knowledge graph are noisy and incomplete we also perform the same experiments with real world knowledge graphs from multiple domains. 4.2.1. Synthetic Knowledge Graph In order to test the efect of noise on the embedding estimation method we create a synthetic knowledge graph with adjustable noise levels. The noise level is a value that describes how much noise (random variation) is added to the numerical data in the knowledge graph.2Fsihgouwres the template used for the knowledge graph. The synthetic knowledge graph uses the SAREF onto2l4o]gtyo[model devices with measurements that directly correspond to the target class that we will be predicting. By adding noise (corresponding to the noise level), we gradually decrease this direct relation. The noise level is added to the measurements directly by adding random values between -noise_level and noise_level to each measurement, thereby creating increasing levels of noise to the data. We create 10 synthetic knowledge graphs, with noise levels ranging from 1 through 10. In addition to the SAREF ontology we use the extension proposed in5][(using theice prefix) to enhance the learnability of the graph.
The synthetic knowledge graph consists of 10 devices making a total of 8000 measurements, resulting in a knowledge graph of 1.2 million triples. The files that are used to create the synthetic knowledge graph are made available onli2n. e
By making the measurements (and their values) and classes directly related we expect the classification to be very accurate. By increasing the noise level this relation between the values and the classes will decrease, but the relation between the measurements and classes will remain, because the structure from the graph will not be changed. We perform the experiments on 10 variants of the synthetic graph, with noise levels increasing from 1 up to 10. 4.2.2. OPSD Household data The OPSD household dataset25[] contains the hourly energy consumption of devices in multiple residences. The dataset has been mapped to a knowledge gr2a6p]h. W[e used the data from one 2https://github.com/RoderickvanderWeerdt/Synthetic_Noisy_IoT_KG_creator residential household (household 4 in the dataset), since it is large enough to be realistic, but not so large that it takes multiple hours to train the embedding model. The attributes in the graph are: general energy export, general energy import, solar panels, dishwasher, electrical vehicle, freezer, washing machine. Each entity in the graph is a timepoint at which energy consumption measurements were taken. The graph contains 0.9 million triples.
Given the continuous source of data from hourly energy consumption updates the knowledge graph can be considered a good representation for the kind of knowledge graph for which our estimation method is intended. The classification task classifies each time point whether the outside temperature was in the warm half of the measurements, or in the cold half of the measurements. Although this classification task is not a hard task, we consider it a useful task to show the capabilities of the embedding estimation method. 4.2.3. OficeGraph Similarly to OPSD, OficeGraph contains hourly smart building measurements from devi2c7e]s. B[ut instead of only energy measurements, OficeGraph contains nine heterogeneous types of measurements made by IoT devices, such as: temperature, 2ClOevels and humidity measurements. Due to memory constrains we only use the measurements from devices on the 7th floor, which allows experiments to be performed on a consumer grade machine, instead of having to resort to a super computer or distributed computing environment. The resulting graph contains 13 devices and consists of 3.9 million triples.
Using the local outside temperature we create a similar classification task as with OPSD, predicting whether the outside weather is in the warm or cold half of the total measurements. 4.2.4. KG-Bench We use three diferent knowledge graphs from the KGBench knowledge graph benchmark repository [23], which includes benchmark tasks and train/test splits: the Amsterdam Museum Dataset (AM), the Dutch Monument Graph (DMG), and the Movie Dataset (MD). These knowledge graphs were chosen because they include numerical attributes in their knowledge graphs, as required by our estimation method. All image hashes and geodata were removed from the graph, since these would not be used in the experiments and it greatly decreases the file size.
The majority of entities lack one or more attributes, e.g. not all movies in MD have a box ofice value. more details can be found in the KGBench pap2e3r].[ Entities without any attributes were removed since our method provides no way to estimate an embedding for these entities.
DMG. Entities are monuments in the Netherlands, and the knowledge graph contains three attributes for each monument: “year”, “population” (of the city were the monument is located), “codeNationalMonument”. The graph contains 0.7 million triples and the classification task classifies the type of monument, out of five monument classes.
MD. The entities are movies, and knowledge graph contains three attributes: “duration”, “boxofice”, “cost”. The graph contains 2.4 million triples and the classification task classifies the genre of the movie, out of 12 genres.
AM. The entities are museum objects and the graph contains one numerical value: “dimension”, but it refers to multiple diferent dimensions which for these experiments are all considered as diferent attributes. The diferent dimensions are separated based on the units of measurement used for the dimension: “gram”, “mm”, “cm”, “ml”, “gr”, “kg”, “G”, “gr.”, “m”, “liter”. When multiple similar units are available for one entity they are all stored, and sorted on size, in order to maintain as many attributes as possible. Despite the fact that “gram” and “gr.” refer to the kind of measurement, they are not considered to be identical, as some entities have dimensions with both units. This resulted in 57 attributes. The graph contains 1.1 million triples and the classification task classifies the museum object out of eight museum object classes.
For all the used KGBench knowledge graphs we use the default subsets provided, being the training set and validation set. For DMG and MG, the training set (as defined in the benchmark) is used to create the original entities, and the validation set is used to create the new entities. For AM the original entities are created similarly, but for the new entities a subset is taken from the validation set, because the complete validation set is larger then the train set. The estimation method is intended to be used when new entities become available, but when many new entities become available the model should be retrained, instead of continuing to accumulate estimated embeddings. When this should happen should be determined per task. For our experiments we use a rule of thumb that the number of new entities should not be more than 20% of the original entities. For AM* we randomly select entities from the validation set, until their are as many entities as 20% from the training set.
In the experiment we use two metrics to determine the impact of the embedding estimation method. The first is the accuracy of the classification task of each knowledge graph, from classifying the new entities. The second is the time in seconds that the method requires to finish calculating the new embeddings. For the embedding estimator this is the time the embedding estimation takes plus the time the classifier takes. For the re-training part of the experiment this is the time it takes to retrain the embedding, retrain the classifier and perform the classification.
We present the results of our experiments in three tables and describe them in the following subsections. We first report on the experiments on the synthetic knowledge graph in se5c.t1i,5o.n2sand5.3 where we explore the efect ofk, the distance measure and time gained respectively. Then in Se5c.4t,iowne describe the same results for the five real-world domain knowledge graphs.
In order to test the efect of changing the sizke wofe perform the experiment with the synthetic knowledge graphs with increasing valueskf,orranging from 1 to 250, as can be seen in the first part of Table1, using the Euclidean distance measure. This is repeated for noise levels from 1 through 10 (as described in Sectio4n.2.1). We observe two main efects, 1) higher noise levels produce lower accuracies, and 2) synthetic knowledge graphs with higher noise levels achieve their highest accuracies at higher values fork.
By examining the highest accuracy for each noise level we see the accuracy decrease as a result of increasing the noise level. This is expected behavior, because the embedding estimation method relies on the relation between the values in the graph and the target classes. As the noise between these two increases, the accuracy drops.
When increasing the noise level, the highest accuracy is achieved for increasing vka, lsuheoswoifng a correlation between the noise level and optki.mTahlis correlation is also expected, since if the noise level is higher thek nearest neighbors of the new entity will be less likely to be similar to the new entity and by increasinkgthis is counterbalanced.
To explore the impact of changing the distance measure we repeat the same experiments, but instead of using the Euclidean distance measure, we use the Manhattan distance or the Chebyshev distance, which are described in sectio3n.2). Similarly to the Euclidean distance measure results, when the noise level increases, a higher value fokris needed to reach the highest accuracy. When examining the highest accuracies from the distance measures for each noise level (which are colored green) we see that the Manhattan distance measures achieves the highest accuracies for each noise level.
To examine the trade-of in using the embedding estimation method instead of re-training the pipeline we can compare the accuracy with time consumption for both approaches. Time consumption is the total time it takes to get a classification for a new entity. For re-training this is the time it takes to re-train the embedding, re-train the classifier, and perform the classifications. For the embedding estimation method this is the time it takes to perform the estimation and classification2.sThaobwles for each noise level the accuracy and time consumption, when using the embedding estimation method or re-training the entire pipeline. For each noise level of the synthetic knowledge graph when re-training the pipeline the accuracy remains constant, at 100%. The consistency of the accuracy is expected due to the graph structure not changing from the addition of noise. Since the graph embedding method does not consider the values of the literals. The perfect accuracy is explained by the fact that the synthetic knowledge graph was created to perform well on this task.
For the accuracy of the embedding estimator, we observe that as the noise level increases, the accuracy decreases. This indicates that the embedding estimation method is most useful when the “noise level” of a knowledge graph is low.
Re-training the pipeline takes almost 24 minutes (1437 seconds, as seen in2T),awblheile using the embedding estimator for a new instance takes less then a second. This shows that the embedding estimation method is less resource intensive, providing users with a clear trade-of between accuracy and time.
Table 2 visualises the results of the experiments with the domain knowledge graphs. For all knowledge graphs time is saved, being at least 1000 times faster, up to 3300 times, when using the estimation method compared to retraining the embedding model.
Table 3 show a clear distinction between the smart building knowledge graphs and the other domain knowledge graphs. OPSD and OficeGraph reach their highest accuracy with akl,owwhile DMG, AM* and MD require a higkh to reach their highest accuracy. When we compare this with1T,able where the synthetic knowledge graphs with higher noise levels reached their highest accuracy with larger values fokr, we could argue that this indicates that DMG, AM* and MD have a higher noise level, then OPSD and OficeGraph. which would make sense, since the numerical attributes of OPSD and OficeGraph are measurement data, directly representing their entities. While DMG, AM* and MD have only indirect numerical attributes.
With DMG, the estimation method is not able to create embeddings that outperform the baseline. The accuracy of attributes for DMG are also below the baseline, indicating that the attributes were not at all representative for the entities of DMG. We analysed the knowledge graph and found that for the available numerical attributes: “year”, “population” and “codeNationalMonument” only the “codeNationalMonument” is present for every entity, and this is an identification number, so it is not useful for comparisons with other entities. For this graph the embedding estimation method is not efective.
The results for both MD and AM show that there is a decrease in accuracy when comparing the estimation method with retraining. This result is expected, since these are, after all, estimates based on the limited information from the numerical attributes. However, both outperform the baseline of k=N, showing that a meaningful representation is still learned for the entities. Combined with the time gain of using the embedding estimation method we consider this a useful situation for the embedding estimation method.
Table 2 shows that with OPSD and OficeGraph the accuracy of the estimation method outperforms the accuracy of retraining. When we consider T3awbelesee that OPSD and OficeGraph also difer in that they reach their highest accuracy with a small vaklu(eeiftohrer 1 or 5) as opposed to the other knowledge graphs, which require high values fko. rWe explain this by examining the classifier, which only in the case of OPSD and OficeGraph was overfitted on the training data. Because the classifier is not retrained we are using the same embeddings in the embedding estimator which are used in training the (overfitted) classifier, therefor resulting in “better” embeddings than the ones that are kept in the training set, during the re-training of the models. As future research we suggest investigating what the efect is of re-training the classifier with the new entities, as compared to only using the test set for the estimation process.
The results from OPSD, OficeGraph and DMG show that the estimation method has requirements from the knowledge graph and entities in order to estimate useful embeddings. The attributes related to the entities that are queried from the knowledge graph need to be representative enough to be able to find the similar entities. When the usage scenario fits these requirements, as it does with MD and AM, the estimation method can be useful as an interim solution, to use new data before having to retrain the pipeline. As mentioned in Sectio4n.2.4, many entities in the knowledge graphs from KGBench are missing one or more numerical attributes. Additionally, we use all available numerical attributes for the entities in each knowledge graph. This results in the inclusion of possibly less desirable numerical attributes, for example with “codeNationalMonument” from DMG. Future research should delve into the selection process of numerical attributes.
For the experiments we compare the resulting accuracies from re-training the models and from using the embedding estimator. In future research we can broaden the scope of the scenario to be able to include more methods, creating the possibility to use diferent methods, such as the ones discussed in Section2.
In this implementation we have not applied normalization to the numerical attributes of the entities, which means that attributes with bigger numerical ranges can disproportionately influence the calculated distances between entities. Future research should explore the efects of normalization of the numerical attributes on the estimation quality. Future research could determine where the cut-of point for specific knowledge graphs and tasks will be and at which point it will become necessary to re-train the entire pipeline. Additional future research could explore the possibility of using the embedding estimation method instead as a measure onfoaise k for a classification task. Where the nokisies the noise between the values of a knowledge graph and the (classification) target. The higher the vka,lutheeomfore noise exists between the data and the targets.
In this paper, we present a method for estimating knowledge graph embeddings, which estimates an embedding for a new entity in a graph for which an embedding model was already created.
The experiments show that the estimation method can result in useful estimated embeddings, which, although they have a lower accuracy, performs between 1,004-4,635 times faster. From the synthetic knowledge graph results, we conclude that the accuracy is a good indicator of how well embedding estimation method performs the estimation, since the increase of noise requires an inkcrteoase of achieve the “best possible” accuracies. Using the Manhattan distance measure consistently resulted in the highest accuracies for the synthetic knowledge graphs, but not for the real world knowledge graphs. The creation process of the synthetic knowledge graphs and the implementation of the noise values may have contributed to this. In future research other synthetic knowledge graph benchmarks, such as GraphWorld2[8], can provide more insight into the efect of distance measure selection.
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