Knowledge-Augmented Induction of Complex Networks on Supply{Demand{Material Data

Abstract

We describe a method for complex network induction in a knowledge-augmented data-driven approach. For this, we match items in a database according to their attributes, using knowledge of subcontexts within the problem domain to improve the speci city and relevance of matches; this relates speci cally to the challenge of supply chain modelling for the recycled plastics industry, using heterogeneous supplydemand-material data. In our approach, knowledge of sub-contexts comes from a mixture of data-driven inference and input from experts, and is crucial in determining how best to match items to one another. We store domain-speci c knowledge in the form of patterns that describe subgroups of our data, a `case base' for use in case retrieval, and also explicit rules provided by experts. We present a system prototype, describe the conceptual modelling approach, and discuss preliminary outputs demonstrating the proposed modelling method. An e ective supply chain model can be used to support the recycled plastics industry and expand the uptake of recyclate.

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Supply chains [ 10, 29 ] can be de ned as all stages involved in producing and delivering a product from supplier to customer { historically considered as a series of steps [ 16 ]. However, recent studies have used network theory to model supply chains as complex networks [ 24, 30 ]. This requires explicit information on the supply chain elements, which is not always available, a common gap which our system aims to address in order to then model supply chain data as a complex network { in a knowledge-augmented approach.

In the context of the Di-Plast project [ 19 ], we focus on utilising industrial supply{demand{material data from the recycled plastics industry on suppliers, buyers and products with speci c material speci cations. However, supplier{ product and buyer{product information is only provided in heterogeneous form, which needs to be aligned and matched, leading to resource-induced complex networks. This requires a knowledge-augmented network induction approach. ? Both authors contributed equally to this research.

In a data-driven approach, we start with supplier{product and buyer{product speci cations, i. e., complex user{item relationships, where the item part contains complex product and/or material speci cations. The central problem we address is the matching [ 11, 38 ] of the respective entities, i. e., the complex material speci cations of a product, in order to form the complex network/graph structure. This is di cult, due to the complex alignment and the speci cation of constraints which have to be ful lled during the matching. However, this can be supported in a data-driven way { mining important parameters { while also including background knowledge of domain experts in order to guide the process. Then, with a human-in-the-loop approach, important (complex) constraints can be captured, domain knowledge e. g., on the importance of features can be provided, and the mined relations and induced networks can be inspected.

Therefore, we propose a knowledge-augmented, context-based and data-driven approach. We use background knowledge, subgroup discovery [ 4 ] as well as techniques from case-based reasoning, speci cally focusing on case-retrieval. This takes the form of a matching and similarity ranking method for creating the respective edges between buyer and seller nodes in our complex network representation. Essentially, we match them according to their product speci cations, utilising the knowledge-augmented matching method. Two special challenges in our industrial context are that many properties can be unknown and often no perfect match exists for a buyer speci cation and, further, that often the detailed target context is not known. This highlights the need to nd the hidden context and use a knowledge augmented similarity approach to nd possible alternatives.

Similar products between suppliers and buyers are matched and used for relationship modelling, leading to our desired complex network abstraction. The complex network itself is facilitated by a tripartite graph representation and/or analysing the respective bipartite projections, as discussed below. For this, we adapt analysis principles of complex networks and folksonomies [ 20, 15, 40 ]. Our contributions are summarised as follows: 1. We present a framework for inducing complex networks in order to model heterogeneous supply-demand-material data. The resulting complex networks (or graphs) can then be analysed for a variety of purposes, such as identifying important suppliers in the network, identifying gaps in the supply chain, and developing pro les of the materials required in di erent industries. For this, we propose a knowledge-augmented data-driven approach for creating the graph structure, i. e., the links between the respective tripartition of supplier{product{buyer nodes. 2. This is supplemented by a rst view on our prototypical system implementation in the context of the recycled plastics industry, for which we discuss a preliminary evaluation of our outputs with a domain expert.

The rest of the paper is structured as follows: Section 2 summarises related work. After that, Section 3 describes our proposed approach. Section 4 presents and discusses preliminary results. Finally, Section 5 concludes with a summary and interesting directions for future work.

Related Work

Below, we discuss related work on matching and context-aware retrieval: We brie y summarise case-based reasoning (CBR) [ 35, 1 ] { an analogical reasoning technique used in various machine learning methods [ 35, 1 ]. Next, we introduce subgroup discovery, a technique to nd interesting subsets of of data points. Matching and Context-Aware Retrieval. The problem of matching items is closely related to that of search and recommendation in user{item interactions, where users are interested in obtaining relevant items for their queries. This has been approached in numerous ways e. g., [ 20, 21, 18, 38, 39 ]. Matches can then be analysed and processed using graph-based [ 20, 21 ] approaches, which we focus on, or using deep learning techniques [ 38 ]. Furthermore, we focus on di erent contexts and sub-contexts of the user, which we use for entity matching, as well as relationship modelling in our complex network. This is called context-aware retrieval [ 13 ], also relating to context aware queries [ 8 ]. In the context of recycled plastics, one big challenge is that producers of certain products want to nd alternatives for their non-recycled plastics. Thus, they have a working speci cation, but no exact recycled alternative exists (buyer context). By considering similar speci cations in the same application area from other buyers (hidden context) we want to identify important target attributes for adapting our results. Case-Based Retrieval. We apply an adapted case-based retrieval [ 28, 2, 12 ] method for ranking and retrieving products that match to a particular query, while in our application, the outcomes of each case are not known. [ 34 ] implemented a CBR ranking system for products over a user query which can provide suggestions on how the user could change the query to nd noteworthy products based on the selections of other users. In our case, the decision process of a buyer is rather complex, taking di erent constraints into account. Therefore, we need to have an awareness of the buyer's hidden context to understand the applied complex data. How to evaluate such a complex context was researched by [ 17 ], on which basis we decided to do an evaluation by experts. A further challenge is the high proportion of missing data. For this reason and based on the research from [ 26 ], we try to handle missing values also in a context-based manner. Subgroup Discovery. Subgroup discovery [ 4 ], aims at identifying subgroups of data instances that are interesting with respect to a certain target concept, e. g., having a high chance of some interesting attribute being present. A subgroup can be represented by a pattern which speci es rules for membership in the subgroup, typically in the form of feature{value pairs, which must hold true for a data instance in order for it to be included in the subgroup. This means that it is a data-driven process that discovers explicit and interpretable rules to associate the target concept to attributes found in the data instances. Subgroup discovery has been applied to, e. g., analyse medical knowledge [ 32 ], industrial data [ 22 ] and social media [ 3 ]. In our work, subgroup discovery is used to identify sub-contexts (hidden contexts) of buyer speci cations, where certain attributes may become more important than others in the matching process.

Method

Our method targets two objectives: First, to create a ranking of product speci cation matches, and second, to create a hypergraph using this. To do so, we match buyer property speci cations Q (also called queries) in the form of attributes to the product attributes A of di erent sellers. In many cases, no exact match be can be found, however similar products could satisfy the buyer's needs. Normally an expert would analyse the needs and make suggestions based on this. To support an increasing demand for recyclate, an automatic approach is desired. Our method includes a case-based approach to understand which deviations will be acceptable, based on the queries from previous buyers who looked for recycled materials in the same application context, i. e., we let the buyer's application context inform the matching process.

Our method is presented diagrammatically in Figure 1 (A). A complex network abstraction is the end goal of our work, which we describe in subsection 3.1. To begin the process, we describe an approach to automatically extracting information to place into the Supplier-Product and Buyer-Product databases, in subsection 3.2. Next, in subsections 3.3 and 3.4, we describe a method for matching product speci cations, leading to the relationship modelling that then forms the basis of our nal network abstraction. In subsection 3.3, we explain how subgroup discovery can infer a relevant context when matching product speci cations, leading to even greater speci city in how di erent attributes are weighted in the matching process described in subsection 3.4. The remaining steps required to match product speci cations and to create the edges for our network model are described in 3.4. This includes a step to transform the feature space according to the context of the buyer, thereby focusing the matching procedure on the most relevant attributes of the products. Concluding with subsection 3.5, we explain how our method supports interpretation, explanation and adaptation of the matching process. 3.1

Complex Network Model

Conceptual Network Modeling Process

Preparation Cleaning Preparation Cleaning ion ign t a ch erg ta ggA &M ihp gn sn li io ed ta o leR M (A) rk iton o c tew tsra N bA

Suppliers tsc u d o r P

Buyers

Suppliers

Buyers (B)

Products (C)

To model the supply chain, we consider networks modelled as graphs GS ; GB; G, with the bipartite supplier and buyer graphs GS = (VS ; VP ; ES ); GB = (VB; VP ; EB, where VS and VB indicate suppliers and buyers and VP indicates products (with heterogeneous textual/numeric/nominal material speci cations from a set A = fa1; a2; : : : ; ang, attributed to a node), ES VS VP ; EB VB VP , and nally the induced tripartite hypergraph G = (VS ; VB; VP ; E), where E VS VB VP captures ternary supply{demand relationships between suppliers and buyers for speci c products. We thus aim at a tripartite hypergraph between suppliers, products, and buyers. Figure 1 { part (B) { shows an example graph. This graph can then also be projected onto bipartite graphs, as shown in part (C), similar to procedures in folksonomies [ 20 ] such that according methods like search, recommendation and ranking can also be directly applied on the graph. This augments the capabilities of our system to adapt based on accumulated knowledge. 3.2

Sources of Data

The data we use to construct our model of the recycled plastics supply chain is taken from our `Matrix Tool', created in collaboration between Osnabruck University and industrial partner Polymer Science Park (PSP). This contains a database of plastic recyclate suppliers, speci cations of the recyclate products they o er, plus potential buyers and the speci cations of the products they make from recyclate.

For obtaining supplier{ pMraotdruixct{tbouoylerrdealiteas, tohne DocPuDmFents Images DocuAmneanlytsLiasyout data extracted from PDF data sheets containing PrToidtluect PSurobdtiutclet DePsrcordiputciton . . . Table product speci cations. tThheiscsoplde-csitacratllyprtoabrlgeemts, Doc DesTcirtilpetion itad.lvaeeat).,ailuawbsselhheree.enintOsfnonrowmteha(eotiaroPpnDpliltiFys- rDweailtathatiheoixnetsrrhaaircpcthioicnal .Ta.ble. rrooww cceell intDegartaatsetdordaagteabinase document layout analysis, to identify and to analyse the physical and Fig. 2. Overview of data extraction and data integration logical document struc- pipeline (adapted from [ 33 ]). ture to extract relevant information [ 27, 37 ] and also extract information from other heterogeneous data sources. Figure 2 illustrates the extraction process. Supplier-Product and BuyerProduct is stored in an appropriate database, and becomes the basis for inferring Supplier-Product-Buyer edges in our network abstraction. 3.3

Subgroup Discovery

Our method aims to match buyers and products in a context-aware manner. When matching a buyer speci cation, we use subgroup discovery to nd a relevant context, speci ed through other similar buyer speci cations in the database. Subgroup discovery [ 4 ], aims at identifying subgroups of data instances (in our case buyer speci cations) that are interesting with respect to a certain target concept, e. g., regarding a speci c processing technology such as injection moulding. Using a binary target concept such as this, we are interested in large subgroups with a high share of instances for which the target concept is true, e. g., being very predictive of a speci c production process.

Subgroups are described by a symbolic pattern which is typically given by a conjunction of feature{value pairs in the case of nominal features and selections on intervals in the case of numeric features. In our work, this is performed on the set of product attributes, so that we obtain conjunctions of constraints on the attributes. An example in our application context is given by `MFI Minimum' < 1:0 AND `Elongation at Break' = NA AND `MFI Maximum < 1:500. Here, MFI indicates a speci c property of a material. A pattern can thus also be interpreted as the body of a rule. The rule head then depends on the target concept. In a top-k setting, a subgroup discovery algorithm returns the topk subgroups according to a selectable interestingness measure, c. f., [ 4 ]. For a binary target concept, e. g., the size of a subgroup described by the pattern (its support ), and the share of the target concept in the subgroup, (its con dence), are combined by one of the standard interestingess measures.

Finding subgroups that, for example, have a high probability of being appropriate for a certain manufacturing process, we can identify contexts consisting of highly relevant product speci cations. These sub-contexts can then be used to normalise the data in a way that is more relevant to what the buyer is looking for, leading to better matches, as described in subsection 3.4, next. 3.4

Creation of Tripartite Supplier{Product{Buyer Edges

An edge in our tripartite hypergraph model represents a match between a \buyer query" Q A of a node VB speci ed via a set of attribute constraints (our query on material attributes from the set of parameter attributes A) and the according attributes of a node VP of a supplier node VS , as de ned above. We aim to build a similarity ranking to indicate matches between queries and product attributes for constructing our graph model. To create edges, we can then take the top-n elements in the ranking, or just the top-1 match for a simple graph.

We suggest a buyer context aware ranking approach to compare multiple related products to one query Q. A context is described by C A n Q, which consists of several similar buyer speci cations. At rst an initial limitation of the context is provided from the buyer, but via subgroup discovery we next want to nd the most suitable hidden context Ch. An example for a context could be the attribute product=pipes, where a more speci c unknown hidden context Ch exists e. g., underground pipes, which we need to discover via subgroup discovery. Inside subgroup Ch, di erent degrees of variance for the individual attributes can be observed. We argue that a smaller variance of an attribute inside a subgroup means that this attribute is especially important for the context Ch. Concluding, an attribute with a lower variance is more important compared to one with a higher variance. This further highlights the importance to nd the correct sub-context via subgroup discovery. Compared to traditional methods, we decide the importance of features according to previous buyer speci cations rather than product speci cations, and achieve this by discovering a detailed (hidden) context for the matching on a case-by-case basis (see subsection 3.3).

After nding the hidden context, we normalise the data (product, query), by transforming the attribute value space into a Gaussian form based on Ch to achieve a normal distribution and stabilised variances. In this way, we implicitly include the weight/importance of an attribute into the according normalised value space.

This is similar to other work 0 10 20 30 40 50 60 70 on CBR problems that has used a mfi_minimum weighting based on Gaussian distributions [ 25, 31 ]. An example of this 4 transformation for the attributes MFI 2 (smhoewltningin oFwig uinrdeex3), adnedmodnesntsriatytinigs itsyen 0 the resulting normalised distribution. d 2 We now compute the Euclidean dis- 4 tances between a query and potentially matching products within this 4 2mfi_mi0nimum 2 4 transformed space. This normalisation provides a data-driven adapta- Fig. 3. Example distribution of the attion of the matching procedure to the tribute Density and the attribute MFI context at hand. Hence, an adapted Minimum before (top) and after (bottom) query can now be better assessed in- the Gaussian transformation, showing the side the normalised feature space. Ad- shifted distances based on the variance. ditionally, our method adapts according to knowledge that has been captured from experts. To return to the example of product=pipes, when constructing piping, there is a need for su cient rigidity to prevent the pipe from bending. In this instance, expert knowledge may inform the matching procedure by adding the constraint that an e-modulus higher than stated in the query is acceptable while a lower e-modulus is not. We capture this type of knowledge as complex constraints for the relevant context. Using domain knowledge also makes it possible to de ne partial matches for non-numeric attributes, e. g., HDPE is a sub-material of PE, which is handled as a match rather than being penalised with an error of 1 in our distance calculations. Alternatively, non-numeric attributes can be included as constraints in the de nition of a context C, thus impacting the data subset which normalises the attribute space. 3.5

Interpretation, Explanation, Adaptation

The steps described so far provide a matching between suppliers, products and buyers, that then can provide tripartite edges in a hypergraph. Using this graph structure, as well as the case information contained in the ranking we can provide an explanation on why a product is ranked as it is. We can perform this on di erent levels: First, we can show related cases. Second, we can visualise the discovered subgroups for a given context C and show how each attribute space is transformed and why. In this space the distance can be visualised and easily interpreted by a human. Further we can give examples based on older searches which illustrate the deviation in the given context to explain the base idea of the weights. Finally, we can also apply techniques of CBR for case-based explanation [ 14, 23 ]. In particular, we can also adapt cases utilising the top-n matches of a query utilising the adaptation step in the CBR cycle [ 1 ], such that we can, e. g., merge cases into prototypical cases for both summarising cases as well as provide explainable candidate cases to the user, c. f., [ 9, 5 ]. 4

First Results

In this section we present the results from subgroup discovery, evaluate a preliminary example of rankings according to the knowledge from a domain expert and showcase a portion of the induced hypergraph structure. 4.1

Subgroup discovery

As stated in section 3.4, we use subgroup discovery as a way to detect possible unknown sub-contexts within a larger context, such as sub-contexts of the automobile industry. As outlined above, subgroup discovery operates by rst specifying a variable of interest (the `target variable'), and then applying a discovery algorithm that identi es sets of membership criteria, also known as `patterns', such that the membership criteria identify a collection of instances with some atypical average value, as determined by a quality function. The discovered sub-contexts identify a selection of data points that are closely related and are particularly relevant for the query at hand. Using the VIKAMINE system [ 6 ], subgroups were identi ed within the di erent markets in the business domain. Below are examples taken from the construction market, where each subgroup is represented by a pattern of membership criteria: { `Elongation at Break' = NA AND `OIT' = NA AND `MFI Maximum' < 1:5 { `MFI Maximum' < 1:5 { `MFI Minimum' < 1:0 AND `Elongation at Break' = NA AND `MFI Maximum' < 1:5 { `MFI Minimum' < 1:0 AND `Elongation at Break' = NA AND `OIT' = NA { `MFI Minimum' < 1:0 AND `MFI Maximum' < 1:5

These patterns indicate that there is a sub-context of the construction market in which elongation at break and OIT (oxidative induction time) are not relevant, and in which MFI values should be low. Similarity Material Processing MFI-Min MFI-Max Density E Modulus TYS TYE OIT Query: HDPE extrusie Subgroup discovery helped us to

nd smaller clusters in our given context. For enabling a knowledge- s1 s2 s3 augmented approach, we also included some initial expert knowl- b3 edge for the selection of important features. In further steps and with more data we want to develop a b2 semi-automatic selection of the important product features. b1

Table 1 depicts an example ranking for a given query. The rows indi- m1 m2 m3 m4 cate di erent product speci cations.

According to inspection by a domain expert, the produced top rows are Fig. 4. Tripartite HyperGraph example from relevant, in particular rows 1-5 all our dataset where blue nodes are materials include relevant speci cations. How- (m), green are buyers (b) and red are suppliever, rows 3-5 are slightly more rele- ers (s). vant than the others, since for some parameters, the deviations between query and provided values should only deviate in one direction. So, ultimately the ranking needs to be reordered using some additional domain constraints.

This is an example of the domain knowledge that needs to be incorporated into our knowledge augmented approach. It is important to note, however, that the domain knowledge required to match products to buyers is quite complex, and further work is needed to capture and exploit this knowledge. In our approach, we can either incorporate this using domain knowledge, or by enriching the graph using multi-edges for capturing a larger set of matched options. Finally, Figure 4 shows an example visualisation of the hypergraph created from a subset of the real-world data.

Conclusions and Future Work

In this work, we focused on utilising complex industrial supply{demand{material data for context-based search and ranking, which we also implemented in a system prototype. We presented a framework for knowledge-augmented induction of complex networks for modeling complex relationships in the context of heterogeneous data. Our hypergraph modelling approach can be generally applied on supply chains with Supplier-Product-Buyer relations. Our proposed matching process is suited to domains where previous buyer requests are informative about (hidden) buyer contexts which in turn are informative about the importance and availability of attributes used for matching. In the application domain of recycled plastics, our proposed knowledge-augmented data driven approach showed rst promising results according to the assessment of domain experts.

Future steps include further domain speci c ne-tuning of the matching, incorporating data about the selection step of real users to enable a ne-grained application of CBR approaches, in particular taking the adaptation step of CBR into account. This also concerns the further formalisation and inclusion of domain knowledge into the proposed framework, in order to enable a rened human-centred knowledge-based approach using speci c constraints of real users. In addition, we intend to investigate further re nements of the hypergraph model, as well as augment the hypergraph model further, leading to knowledge graph structures, such that both knowledge modeling as well as application can be integrated into the same structural representation, e. g., [ 7, 36 ].

Last but not least, we aim to analyse the industrial data with multiple complex network methods. For example, (1) link prediction could be performed on the supply-demand-material graph to infer new edges, and (2) community detection can help with identifying new subgroups in the data. In addition, (3) global graph metrics such as density and the average degree of the nodes in the hypergraph could provide further insights into the characteristics of the data.

Acknowledgements

This work has been supported by Interreg NWE, project Di-Plast - Digital Circular Economy for the Plastics Industry (NWE729).

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