TaxoMulti: Rule-Based Expert System to Customize Product Taxonomies for Multi-Channel E-commerce

Taxonomies are used as product categories to facilitate users navigating through an e-commerce portal with the help of hierarchically structured concepts. However, the identical taxonomy is shown to each customer regardless of the channel used. This is challenging for the customers in terms of user experience, as the screen size is rigid, and has not a flexible format like a printed catalog. Simply reducing the taxonomy as suggested in existing works is not sufficient, as it leads to semantic misrepresentation of the product domain. To overcome the inflexibility of product taxonomies, the rule-based expert system TaxoMulti is presented in this paper. The main objectives of our descriptive research are the formulation of the taxonomy over- and undersize problem in multi-channel context, before different types of flexible mediator concepts are discussed that allow overcoming these challenges. Using our novel method, marketing experts can now provide different taxonomies including the same semantics to be shown on different channels. The method is implemented using logic programming, allowing the integration of an inference engine utilizing background knowledge without changing the underlying logic of the used information (management) system. The comprehensive experiments on three public and private databases highlight the improvement when adding different types of mediator concepts for the adaption process. Compared to existing best performing works in related fields, TaxoMulti has achieved an improvement of + 26.31 % for the reduction of the taxonomy, + 60 % for the enlargement of the taxonomy, and + 21.21 % in terms of flexibility.


Introduction
During the last decade, the use of online portals has increased significantly [14,37]. The main reason is the emergence of mobile devices, leading to various channels, known as multichannel paradigm, or as omnichannel if the multi-channels are connected with each other [9,26]. Providing a multichannel e-commerce portal improves user experience, but it is complex due to its diversity [16,27,30,45,51]. This is because the online channels (e.g. desktop, mobile) are based on various device classes. Each differs according to its in-/ output capabilities, especially its screen size [38,52,59].
Regardless of the number of different channels provided, taxonomies have proven to be an indispensable method for operating information management systems like e-commerce online portals [43,44,48]. The taxonomy is used in the backend of the application to formally structure product categories in a hierarchical manner [20]. In the frontend, it is displayed to the users to support exploring product categories. However, regardless of the domain, when implementing a multi-channel portal, the focus is merely on channelspecific technical perspectives. For example, different screen sizes of device classes are considered using style sheets. The channel-specific capabilities are not considered from a semantic perspective. The taxonomy shown to the user is identical, regardless of the channel utilized. This is because the creation of the taxonomy is formal and often historically grown, as most retailers use the taxonomy additionally in other entrepreneurial perspectives (e.g. product master data, media asset management) [10,61].
Existing research paradigms aiming to customize product taxonomies are catalog segmentation, dynamic taxonomies, and personalized directories [7]. The systems for catalog segmentation are assigning the users to a pre-defined expert-generated sub taxonomy, which forms a sub catalog. Catalog segmentation played a crucial role in commercial printing. For example, a furniture retailer publishes a main catalog once a year, and provides additional sub catalogs for different seasons [12]. The latest works on catalog segmentation are using preference techniques as used in recommender systems to automate allocating users to the most related sub taxonomy (sub catalog), e.g. in [36,37,39,52,63]. However, the sub taxonomies are semantically reduced, which means that concepts not included in the sub catalog are not shown. However, the needs regarding furniture are different depending on the region, the age of the customer, and of course the personal preferences. This is a main drawback, as additionally, the preferences change over time. Techniques of personalized directories are overcoming most of the before-mentioned problems, as those are aiming to modify the taxonomy according to users' personal requirements, e.g. in [6,21,22,28,34,47,62]. The most recent technique is providing various modification rules on subsets of concepts, which allows to not semantically reduce the taxonomy. However, the flexibility of the rules provided still lacks in sufficient support for multi-channel. Each user has indeed a personalized taxonomy, but it is identical across channels. In multi-channel context, some users are singlechannel users, but most are multi-channel users [13,45,60]. The third related research paradigm named dynamic taxonomies, prunes the taxonomy according to the informal keyword given manually by the user, e.g. in [15,24,29,31,50,56,58]. Using dynamic taxonomies, the user can most directly interact with the online portal, but the domain is semantically reduced according to the keyword.
To provide a system to effectively create flexible taxonomies in multi-channel context, TaxoMulti is presented. The core motivation of the proposed system is to overcome the taxonomy oversize and taxonomy undersize challenge without suffering from semantic misinterpretation after the adaption process. This is achieved through studying two novel types of mediator concepts that are flexible and created as background knowledge resources. The contributions are as follows: • It is the first paper that discusses the problem of using taxonomies in multi-channel context from a semantic perspective. This is achieved by formulating the significance of the problems defined as taxonomy undersize and oversize. • It provides a novel method for creating flexible taxonomies by using a dynamic adaption process. This is achieved by defining different types of latent mediator concepts and various modification rules being stored as background knowledge. • It implements the method using an architecture that does not change the underlying initial logic of the information management system. This is achieved by implementing the method using a system independent inference engine.
The rest of the paper is organized as follows. Section "Backgound" formulates and discusses the taxonomy problem in a multi-channel context. The proposed rule-based expert system TaxoMulti is presented in section "Proposed system TaxoMulti". A case study for three different channels is presented in section "Case study and demonstration". In section "Experimental evaluation", the proposed system is evaluated using three databases representing retailing markets. The work concludes in section "Conclusions".

Background
A Taxonomy ( ), as given in Fig. 1a, is a hierarchy of objects with similar properties [7], defined as technical terms representing domains [46,49] with (see Eq. 1): Fig. 1 The hierarchical structure of a sample taxonomy

SN Computer Science
where is a partially ordered set of concepts, and is a set of edges. Each edge represents a hierarchical relationship between single concepts in an acyclic graph (see Fig. 1b), referred as is-a relationships [19]. Each concept is defined by a name, i.e. the label. Using the label and the taxonomic path resulting through the is-a relationships, each concept represents a more or less generalized and in turn fine-granular semantic excerpt of the entire domain [7]. Formally, the above-mentioned is-a relationship are known as hypernym and hyponym [19]. In contrast to an Ontology, a taxonomy is only limited to this semantic relationships (summarized in Table 1) [25,57]. Whereas the ontologies are used for knowledge management (e.g. Wordnet [23]), the taxonmies are used for information management, as the is-a relationships are mostly sufficient.

Concept Types
Depending on the vertical and horizontal position of the concept, different concept types are distinguished (see Fig. 1b): sub concept, super concept, root concept, and sibling concept. A concept named Sub Concept, formally subof, is a less generalized concept that sub-ordinates another one, as given in Eq. 2, if: where D and B are two concepts of taxonomy . A concept named Super Concept, formally superof, is a more generalized concept that super-ordinates another concept, as given in Eq. 3, if: where D and B are two concepts of taxonomy .
A Root Concept A, formally rootof, is the most general concept that is not super-ordinated by another concept, as given in Eq. 4, in which: where A is a concept of taxonomy .
A concept named Sibling Concept, formally sibof, is the relationship between two concepts sharing the identical superordinated concept and have the same horizontal position, as given in Eq. 5, if (see Fig. 1c): where E and D are sub concepts of B, which are all concepts of taxonomy .
Depending on how many vertical edges inside the graph exist that are not sibling relationships, the taxonomy consists of various Levels. Our example taxonomy presented below consists of three levels (see Fig. 2): 1. The concept "Products" is the root concept. 2. The concepts "Seafood", "Meat Poultry", and "Beverages" sub-ordinate the root concept, and are sibling concepts. "Products" is their common super concept. 3. The concepts "Soft Drinks", "Coffees", "Teas", and "Beers" sub-ordinate the concept "Beverages", and are sibling concepts. Each is-a sub concept of the "Beverages", which is their super concept. The concepts "Soft Drinks", "Coffees", "Teas", and "Beers" do not superordinate another concept(s).

Problem Formulation
Taxonomies are a formal way of representing information, and are utilized for hierarchically structuring data in (enterprise) information management systems [18], e.g. enterprise resource planning, online portals, document management systems [2,3,5,18,55]. The taxonomies are generated through an expert, or by referring to a standard taxonomy, e.g. the North American Product Classification System 1 (NAPCS) [17,53]. In e-commerce, the online portal application itself mainly acts as shopping cart for representing and ordering products. The actual product information is very often maintained in another system -often in a product information management (PIM) system. The necessary data enters the e-commerce database (backend) through an interface with the PIM or an additionally system referred as middleware operating between the PIM and the shopping cart [35]. Usually, the PIM has interfaces to further applications, as the PIM system stores the information central and media neutral. This is important when the information is published in crossmedia context, meaning that the media must be visualized on multiple specific online as well as offline channels [42], but the data must be consistent across all different channels (see Fig. 3). As every single concept represents a more or less generalized semantic excerpt of the entire domain, modifying the taxonomy happens rarely [7]. Removing, adding, but also modifying (label or level) a single concept would effect that the information gain changes and the entire semantic would be misleading [54]. This intentional formality of taxonomies results in inflexibility. And, it also has significant drawbacks when the taxonomy is published in the frontend of multichannel e-commerce portals: 1. As for channels using smaller device classes, the full range of concepts can't be displayed in a user-friendly manner, it suffers from a problem which in the following is called Taxonomy Oversize. Instead of requiring massive input from the user to navigate to the concept desired (e.g. scrolling, tapping/clicks, filtering), the taxonomy should be reduced by a number of concepts , but without loosing any information about the domain, indicated with (see Eq. 6): where is the set of concepts detailing the initial taxonomy, and includes the concepts detailing the reduced taxonomy. As taxonomies usually consist of multiple levels, the desired reduction must be considered according to the level of the concepts. For sub concepts, the desired taxonomy reduction sub can be formulated as (see Eq. 7): where sub is the set of sub concepts detailing the initial taxonomy, and sub includes the sub concepts detailing the reduced one. Accordingly, for super concepts, the desired reduction super can be evaluated (see Eq. 8): where super is the set of super concepts detailing the initial taxonomy, and super only includes the super concepts detailing the reduced one. Note that both equations can of course be modified according to further levels. 2. As for channels using larger device classes, the range of concepts should be more detailed to help users more quickly finding the desired products, it suffers from a problem which in the following is called Taxonomy Oversize. Instead of requiring a good understanding of the domain by the user, the taxonomy should be represented as an enlarged taxonomy concept , but with considering the semantics of the existing concepts (see Eq. 9): where includes the concepts detailing the enhanced taxonomy. The enhancement of the number of levels level can is done by (see Eq. 10):

Proposed System TaxoMulti
The rule-based expert system TaxoMulti is customizing taxonomies for channel-specific requirements without misrepresenting the semantic of the underlying domain. First, the method of the underlying system is described and secondly, its implementation including the utilized architecture is presented using this section.
The core advantage of TaxoMulti compared to existing works is the usage of different types of mediator concepts operating on different levels. Through this, a highly improved flexibility regarding the adaption process is achieved. A limitation in the adaption process is now only given through the underlying initial taxonomy. Its initial size and fine-granularity define the possible adaption process.

TaxoMulti Method
As taxonomies already use different concept types to express the is-a relationships between concepts, the existing types can be used to define further concept types performing as mediator concepts. In TaxoMulti, two types of mediator concepts are used (see Sections "Taxonomic Dependencies" and "Taxonomic Collections") that can be separately asserted with different modification operations (see Section "Tax-oMulti Operations") on various taxonomic levels. The rule-based expert system allows to combine semantically similar concepts, to split semantically similar concepts, and to enlarge semantically similar concepts. Through this, the mediator concepts are flexible in its appearance and finegranularity. In addition, as the two novel concept types differ in the existing concept types they are subsuming, all existing concept types are involved. This allows to perform the customization process on taxonomies of any size.

Taxonomic Dependencies
The concept type Taxonomic Dependency relies on the fact, that the sibling concepts sub-ordinating a single concept can have a less generalized semantically sibling relationship between each other than only connecting those with one generalizing super concept (see Fig. 4a, b) [8].
A Taxonomic Dependency B1 (shortened as depof), is a mediator concept between a super concept B and a set of sub concepts in , as in Eq. 11, if: where is a further semantic relationship between the sibling concepts ∈ , is a super concept, and is the threshold provided through the provider to verify the relationship between the sibling concepts.

Taxonomic Collections
The concept type Taxonomic Collections focuses on providing more complex relationships between a root concept and its super concepts (see Fig. 5a, b). Through this, a collection concept can include multiple super concepts, depending if the super concepts are semantically similar sibling concepts. For example, the concepts "Seafood" and "Meat Poultry" are more similar compared to the concept "Beverages" (see Fig. 2). Analogues to dependencies, collections offer the possibility to perform a different kind of taxonomic modifications. Consequently, the combination of collections and dependencies ensures that various modification rules can be performed on any concept, and taxonomies of any number of levels can be customized.
The hierarchical structure of a taxonomy with dependencies A Taxonomic Collection A1 (shortened as colof), is a mediator between a root concept A and a set of super concepts in , as given in Eq. 12, if: where is a further semantic relationship between the sibling concepts ∈ , is a sub-ordinated concept of the root concept, and is the threshold provided through the provider to verify the relationship between the sibling concepts.

TaxoMulti Operations
As the mediator concepts are not shown in the initial taxonomy, both above-discussed concept types provide the opportunity to perform different modifaction operations. Three operations are customizing the initial sub concepts based on the dependency concepts. Another three are used by the super concepts, and are performing on the collection concepts. The rule-based process starts by customizing the super concepts, as those are required to be used as superordinated concepts for the resulting sub concepts. Each rule for a dependency can be combined with each rule for a collection, resulting nine possibilities for each taxonomic path to create customized channel-specific taxonomies: Combine Super is reducing the super concepts to the underlying collection, instead of showing the single super concepts (see Fig. 6a, b). This affects a reduction R C of the number of super concepts, shown in Eq. 13: where R C and R i are all concepts being super-ordinated by the same concept, R C are the concepts remaining after the modification is performed, R i is the number of initial concepts super-ordinating a concept, and R N is the number of concepts being combined.
Split Super affects that each super concept of a collection is appearing as a single super concept, instead of showing the collection, see Fig. 7a, b. Consequently, this modification affects that the initial taxonomy is shown, meaning a lower reduction as above, but also a lower enlargement as the rule presented as next. Formally, the rule results as given in Eq. 14: where R S and R i are concepts being super-ordinated by one concept, but R S are the concepts remaining after the modification rule is performed, and R i is the number of initial concepts super-ordinating a concept. Enlarge Super is using itself to subsume the root concept and all super concepts assigned to it for subsuming the collection, see Fig. 8a, b. It is using the single collection to occur as sub-ordinated concept of the root concept, and the included super concepts to occur below the collection. Correspondingly, it enlarges the number of concepts by the collection, as given in Eq. 15: where R C and R i are concepts being super-ordinated by different concepts resulting in the number of concepts R E . Logically, it increases the number of levels. The number of levels increased is flexible, as it depends on with which other rules it is combined.
Combine Sub is summarizing all to the dependency assigned sub concepts, instead of showing the single sub concepts, see Fig. 9a, b. Consequently, this modification affects a reduction R K of the number of sub concepts, as given in Eq. 16: where R K and R i are all concepts being super-ordinated by the same concept, but R K are the concepts remaining after the modification rule ist performed, R i is the number of initial concepts super-ordinating a concept, and R N is the number of concepts being summarized.
Split Sub affects that all sub concepts occur as a single sub concepts, instead of combining the subset to a single dependency, see Fig. 10a, b. Consequently, this modification affects that the initial taxonomy is shown, as given in Eq. 17: where R Z and R i are all concepts being super-ordinated by the same concept, but R Z are the concepts remaining after the modification rule ist performed, and R i is the number of initial concepts super-ordinating a concept.
Enlarge Sub enhances the sub concepts through showing the dependency as additional level, and all included sub concepts, see Fig. 11a, b. It is using the single dependency to occur as sub-ordinated concept of the super concept, and the included sub concepts to occur below the dependency. Correspondingly, it enlarges the number of concepts by the collection, as given in Eq. 18: where R C and R i are concepts being super-ordinate by different concepts resulting in the total number of concepts R F . This increases the number of levels by 1. Along with the rule enlarge super concept, it doubles the number of levels.

TaxoMulti Implementation
TaxoMulti is implemented using logic programming language Prolog. Prolog is known as an effective technique for knowledge engineering and logical reasoning [40]. The reason for this area of operation is that each Prolog programm consists of two components [11]: Knowledge Base represents information using predicates in the form of facts. For example two facts: the concept "car" is-a (sub concept of) "vehicle", and the concept "vehicle is-a (sub concept of) "objects". Inference Engine represents predicates in the form of inference rules to infer new knowledge. For example: because "car" is-a (sub concept of) "car", which is-a (sub concept of) "objects", "car" is-a (sub concept of) "objects", too.
In Prolog, the predicates are written in horn clauses. Every predicate consists of a functor, which represents the name of the predicate, and arguments standing in brackets. When using the short form to represent a predicate in Prolog, the number of arguments is written behind the functor (e.g. concept/2). . 9 The modification of the taxonomy with the combine sub operation (a) (b) Fig. 10 The modification of the taxonomy with the splitting sub operation (a) (b) Fig. 11 The modification of the taxonomy with the enlarge sub operation

Architecture/Layers
The TaxoMulti architecture consists of three layers. Only the data displayed on the frontend is customized. This has the benefit that the initial data (in the backend) remains [1]. The layers are (illustrated in Fig. 12): • Publishing Layer is the frontend shown to the multichannel users. The layer can publish multiple taxonomies, according to the number of channels desired. Of course, the implementation of this layer is not part of the work at hand. This layer is provided by the frontend of the utilized online portal. • Processing Layer forms the actual implementation of TaxoMulti and consists of two components. The first component is the knowledge base named Background Knowledge. It is required for querying the initial concepts of the Storage Layer (see below), and for storing the mediator concepts and semantic relationships between those. The second component named Adaption Process is the inference engine. It is used to process different operations for customizing the channel-specific taxonomies.
Here, the operator of the multi-channel online portal can define different channels, and the above-mentioned operations as rules, which have to be performed on the mediator concepts. • Storage Layer consists of the database provided by the information management system for storing the initial taxonomy. Logically, the implementation of this layer is not part of the work at hand. This layer is provided by the backend of the utilized online portal. Consequently, our proposed system TaxoMulti does not modify the data stored on this layer. The initial taxonomy is mirrored to the processing layer.

Background Knowledge
The background knowledge is the first component of the processing layer. It is used for querying the information about the initial taxonomy, storing the information about the mediator concepts and the semantic relationships, as well as about the channels. The initial taxonomy is queried from the storage layer. Each concept regardless of its type (root, super, sub) is mirrored using the same type of fact. This is done to not limit the proposed system to a fixed number of taxonomic levels. The fact to mirror the concepts is named concept/2 (see Listing 1). It uses its label (CCL), along with the unique identifier of a concept (CCI). The is-a relationship is expressed using the fact isa/2.
The fact dependency/2 is storing the information about the dependencies using its unique identifier (DPI), along with its label (DPL) (see Listing 2). A mapping between the dependencies and the super and sub concepts is achieved using the fact dependencymapping/3. It uses the unique identifier of the super-ordinated concept (SPI), DPI, and the unique identifier of the sub-ordinated concept (SBI). Analogous to the dependencies, another two facts are used for storing the information about the collections and its mappings. The fact collection/2 is storing the information about the collections using its unique identifier (COI), along with its label (COL). A mapping between the collections and the super and sub concepts is achieved using the fact collectionmapping/3. It uses the unique identifier of the root concept (ROI), COI, and the unique identifier of the super concept (SPI).

Adaption Process
The adaption process is the second component of the processing layer. It is necessary to finally create channel-specific taxonomies. Doing so, different channels can be defined, and the rules can be applied to the concepts of the initial taxonomy by using the in the previous section explained mediator concepts. Before finally processing the channel-specific taxonomies, three different facts are needed. The different channels and its operations are stored as fact channel/2, where each channel is having a unique identifier (CNI), and a name (CNN) (see Listing 3). Each channel is having rules to describe the operations to be performed for each collection and dependency: collectionrule/3, dependencyrule/3. Each fact includes the identifier of the channel, of the mediator concept, and an identifier for the desired operation (OPP, or OPB).
The final processing of the channel-specific taxonomies is done in four steps (see Listing 4). It starts with asking the user for the channel ( user_input(CNI) ) to be modified. Afterwards, the rule isa_operation is performed, which creates maximum paths in the form isa(ROI, COI, SPI, DPI, SBI). Based on those, the final modifications are performed using the rule modification(CNI). Depending on the rule for a specific mediator concept, the paths are modified accordingly.

Case Study and Demonstration
As an illustration of the proposed rule-based expert system TaxoMulti, let us consider the retailing market Northwind. 2 The retailing market operates a multi-channel e-commerce online portal. In total, three digital channels with the accompanying device classes are distinguished according to the underlying screen size (summarized in Table 2): • Mobile is the channel used by most customers for quick browsing. However, many customers are terminate the browsing. The goal is to reduce the taxonomy published on this channel to allow a more comfortable browsing experience. • Tablet is the channel recently used by many customers for placing orders. The goal is that this channel is using the initial taxonomy. No change should be made as the channel operates successful. • Desktop is the channel used by some customers. Customers looking for specific things are mainly using this channel. The goal is that this channel is using the maximum taxonomy to allow a detailed navigation for all customers.
Based on the initial taxonomy, mediator concepts are created (see Fig. 13).

Mobile Channel-Specific Taxonomy
As the complete range of concepts is too large to be shown on a mobile device, the taxonomy published in the frontend should be reduced. To do so, mediator concepts performing on the different levels (super and sub concepts) are assigned with corresponding rules. The collections performing on the super concepts are assigned with the rule combining similar super concepts, see Table 3. The dependencies performing on the level of sub concepts are assigned with the rule combining similar sub concepts, see Table 4.
Based on the initial taxonomy, in total eight super concepts exist. Depending on the semantic similarity between the super concepts, a different number of super concepts can sub-ordinate the different collections. The super concept "Confections" for example and "Beverages" have no similar super concepts. In contrast, the super concept "Produce" for example sub-ordinates the new collection "Preperation", as well as its sibling concepts "Grains Cereals", "Dairy Products", and "Condiments". Same for the super concept "Seafood". Along with its sibling concept "Meat Poultry" it is classified into the collection "Meat and Seafood". The new labels for the collections indicate that it has a less semantic meaning compared to the super concepts. For example, the label "Meat and Seafood" is more general than to split the concept along with its label into "Seafood" and "Meat Poultry". Correspondingly, having different semantic weights for one level would not be meaningful, as it hampers the interpretation of the domain by the user. For this reasons, the super concepts having no similar sibling concept are also categorized into a collection carrying a more general label. For this reason, "Confections" sub-ordinates the collection "Sweet food", and "Beverages" sub-ordinates the collection "Drinking". In total, the number of super concepts can be halved ( super = 8 − 4 ). On the level of the sub concepts, in total 22 less generalized concepts exist. Again, a different number of sub concepts can sub-ordinate the different dependencies, due to the semantic similarity between the sub concepts. Hereby, the number of sub concepts subordinate a dependency goes from one to three. In total, the number of sub concepts can be reduced by six concepts ( sub = 22 − 16 ). In the end, the complete number of concepts (except the root concept) can be reduced by ten concepts ( = 30 − 20 ), which indicates a relative minimum reduction by 33.33 %, see Fig. 14.
(a) (b) Fig. 13 The taxonomy of Northwind including mediator concepts

Desktop Channel-Specific Taxonomy
As nowadays, desktop computers usually have extra-large screens, users using this channel should see the most enlarged taxonomy to better filter for the concepts they require. As the goal is to achieve the maximum size of the taxonomy, it is the one inlcuding all of our defined mediator concepts (see Fig. 13b). For this reason, the modification rules to enlarge the taxonomy should be enlarged for all levels. The collections performing on the level of super concepts are assigned with the rule to enlarge the super concepts, see Table 5. The dependencies performing on the level of sub concepts are assigned with the rule enlarging similar sub concepts, as given in Table 6. As explained in the previous section, in total eight super concepts exist. Such super concepts are assigned to the collections as described above, namely to four collections. The difference to the mobile taxonomy is that now the super concepts are not combined. The super concepts are displayed as single concepts, in total eight. In addition, the four collections are also displayed to the user below the root concept. Similar is the modification for the sub concepts. In contrast to the mobile taxonomy, the sub concepts are not reduced to dependency. The dependencies are used as an additional level between the super and sub concepts. Correspondingly, the sub concepts remain as single sub concepts. In the end, the complete enhanced taxonomy includes 20 more concepts ( = 50 − 30 ) and two additional levels ( level = 5 − 3 ). Through this, the complete relative enhancement is 66.67 % with respect to the number of concepts. And 66.67 % of  Fig. 14 The reduced taxonomy used for the channel "mobile"

Experimental Evaluation
The evaluation of rule-based attempts is often considered as challenging and differs significantly compared to other disciplines [33,41]. Often, the standard quality metrics (e.g. accuracy, f-measure) are not in the focus because of different reasons [32]. First, the rule-based systems are implemented to support or automate a single task. So, the rules to be included heavily depend on the human expert. Second, the implementation consists not only of an algorithm, but of a knowledge base and an inference engine forming the background knowledge [11]. So, a mutual supplementation of both components is decisive. However, both components significantly depend on the domain and the experts opinion, which is not qualitatively measurable. Because of the mentioned reasons, the evaluation of the proposed rule-based expert system TaxoMulti is multi-faceted and intense. In detail, the following metrics are used: • Reduction Efficiency is measured to verify the reduction of the taxonomy for channels requiring a reduced taxonomy. Hereby, the system is evaluated against the provided problem formulation (see Sect. 2.2). To do so, each taxonomy is firstly investigated against its initial number of sub ( sub ) and super ( super ) concepts. Secondly, the number of sub ( sub ) and super ( sub ) concepts for the reduced taxonomy are measured. This results in the reduction of sub ( sub ) and super ( super ) concepts, and finally the reduction of the complete taxonomy ( ), respectively. The reduction efficiency is in addition compared with the latest work on personalized directories, presented by [6], in the following named Personalized Directories. We do this by comparing their proposed operations to reduce the taxonomy, with the operations proposed in the work at hand. • Enlargement Efficiency is computed to verify the enlargement of the taxonomy for channels requiring a larger taxonomy. We investigate the system against the provided problem formulation (see Sect. 2.2). First, the initial number of super and sub concepts is measured ( ), which is compared with the enhanced number of concepts ( ) to result in the enhancement with respect to the number of concepts ( concept ). In addition, the enhancement with respect to the number of levels is computed ( level ). To do so, the enhanced number of levels ( level ) is compared with the initial number of levels ( level ). Both final metrics are compared against the most recent operations presented in Personalized Directories.
• Analytical Comparison of the rule-based system is performed with the help of the related research paradigms aiming to modify taxonomies: dynamic taxonomies, catalog segmentation, and personalized directories. The work at hand and the mentioned paradigms are investigated according to four criteria: if a taxonomy reduction can be performed by the techniques if the reduction is performed without changing the domain, if the taxonomy enhancement can be performed, and if the enlargement is performed without changing the domain. • Quantitative Comparison is performed based on the analysis above, for all techniques being capable to reduce the taxonomy, respectively to enlarge the taxonomy. This is done by firstly analyzing the minimal possible relative reduction ( min ), with (see Eq. 19): where min is the remaining number of concepts if a minimal subset of the taxonomy is reduced, respectively enlarged. Correspondingly, the maximum possible relative reduction and enlargement ( max ) is also measured, with (see Eq. 20): where max is the remaining number of concepts the maximum reduction or enlargement capability is performed. For both, min and max , the remaining domain is investigated. Namely, if the performed reduction/enlargement is changing the semantics of the domain ( ), with (see Eqs. 21 and 22): where min is the relative remaining domain if the minimal reduction/enlargement is performed, min is the remaining domain if the maximal possible reduction/enlargement is performed, and is the complete domain. Finally, both metrics, and are multiplied resulting , the efficiency of the technique with respect to the remaining domain, with (see Eq. 23): where min is the minimum efficiency, and max is the maximum efficiency. Consequently, the higher (0 to 1), the more capable the technique is to be used for To ensure that all the above-mentioned analysis are investigated in different directions, the proposed rule-based expert system is applied to different databases. In detail, two open (AdventureWorks, 3 Northwind), and one database provided by a German company (Festool 4 are used. The characteristics of the databases are summarized in Table 7.

Reduction Efficiency
When summarizing the results for the taxonomy reduction, the taxonomies were reduced with the proposed system by on average 50%, see Table 8.
The results obtained reveal that the possible reduction does not depend on the general size of the taxonomy. The efficiency mainly depends on the fine-granularity of the taxonomy for the different levels of the initial taxonomy. The more similar the concepts for a single super-ordinate concept are, the higher the taxonomy can be reduced. Through this, there is no linear correlation between the size of the initial taxonomy and the reduction. Small, as well as very large taxonomies can be reduced with the same high efficiency. A higher efficiency can be further achieved when using more general mediator concepts, which is also possible with the proposed system.
Compared to the taxonomy operations presented in Personalized Directories, a further decrease of 9.93% is performed, see Fig. 15. This is achieved through using the novel concept type collection, which is acting as a mediator concept between the root and a set of super concepts. The works in Personalized Directories lack a mediator concept acting  between the root and super concepts. In the case of requiring a very reduced taxonomy as in our experiment, the different sets of super concepts are reduced to the underlying collections. A further reduction or a lower reduction could have only been achieved if the initial taxonomy is already bigger or smaller so that the size of the sets change completely. However, manipulating the initial taxonomy is not the scope of this work, as the taxonomy is often used in other entrepreneurial perspectives for other tasks as well (e.g. product master data) [10,61].

Taxonomy Enlargement
When summarizing the results corresponding to the taxonomy enlargement, an efficiency greater 50% was achieved for the number of concepts, and an efficiency of almost 67% for the number of levels, see Table 9. The resulted value for enlarging the number of concepts is analogues to the subtraction of the reduction, which shows the simplicity of the proposed operations, as the mediator concepts can be used in multiple directions. Compared to the operations presented in Personalized Directories, an increase of 17.29% was measured with respect to the number of concepts, see Fig. 16. This is achieved through allowing the flexible combination of two types of mediator concepts, whereas the works on Personalized Directories only adapt each concept type separately. In the case of requiring a very large taxonomy as in our experiment, the different sets of super concepts that are bound to one collection are shown, including its superordinated concept. Additionally, the different sets of sub concepts that are bound to one dependency are shown, including its super-ordinated concept. A further increase or a lower increase could have only been achieved if the initial taxonomy is already bigger or smaller, so that the size of the sets change. However, as discussed, changing the initial taxonomy is not expedient.

Analytical Comparison
For demonstrating the strength and weakness of TaxoMulti regarding the adaption of taxonomies, the systems main criteria are compared against other research paradigms aiming to adapt taxonomies: dynamic taxonomies, catalog segmentation, and personalized directories To give the reader the most comprehensive comparison, we first explain the different paradigms in more detail, before identifying the strength and weakness of TaxoMulti.

Analytical Techniques Paradigms
A dynamic taxonomy prunes itself in response to the request and so considers the significance of a user-query [50]. These paradigm has been proposed as a solution to combine navigation and querying, offering both  expressivity and interactivity, e.g. in [15,24,29,31,50,56,58]. However, as the (semi)-automatic technique is until now always based on the initial taxonomy, this paradigm is not capable to enlarge the taxonomy. In addition, as not detected matches against the provided keyword are not displayed inside the dynamic taxonomy, the domain is reduced accordingly. Catalog segmentation is also based on a (static) taxonomy, but proposes to create a variety of different sub-taxonomies for different segments of users, e.g. in [4,36,37,39,52,63]. Its capabilities lie on a high effective reduction of the taxonomy, but the computed sub-taxonomies are loosing information about the domain. Logically, enlarged taxonomies are not considered in this paradigm.
Personalized directories are using different taxonomy modification rules, i. a. operations to represent the taxonomy according to a user-specific requirement, e.g. in [6,21,22,28,34,47,62]. Hereby, the main focus is to effectively reduce the distance of preferred concepts to the root distance. This paradigm does not loose information about the domain, and the enlargement would be possible if the in this work presented mediator concepts are used.

Analytical Strength and Weakness Comparison
The proposed rule-based system could outperform all existing paradigms according to the studied criteria, see Table 10, whereby the paradigm of personalized directories is closest to our proposed system. However, the above-provided comparison of the related works offers to identify the strength of the system at hand, but also its possible further extensions: • None of the other recent techniques provides an effective solution to adapt taxonomies for supporting taxonomies in omni-channel. The main difference to other works relies on the usage of the mediator concepts. Those are flexible in its appearance, and can be used to reduce the taxonomy, as well as to enlarge the taxonomy. Hereby, both different cases can be achieved without missing semantically information about the domain. • The other related paradigms offer techniques to adapt the taxonomy according to user feedback. The most recent work on personalized directories includes a recommender system to automatically perform the taxonomical operations. In TaxoMulti, the operation is automatically performed, but the status for the mediator concepts to perform the rule has to be provided by the expert.

Quantitative Comparison
Based on the above studied analytical comparison, a quantitative comparison can be performed for the techniques being capable to reduce and/or enlarge the taxonomy. The techniques being capable to reduce the taxonomy are: Tax-oMulti, Personalized Directories, Catalog Segmentation, and Dynamic Taxonomies, see Fig. 17. The techniques being capable to enlarge the taxonomy are: TaxoMulti, and Personalized Directories. However, a comprehensive comparison of these both techniques is already presented above. The ter results compared to TaxoMulti regarding the minimal reduction of the taxonomy. This is, because it is assumed, that the minimum reduction for catalog segmentation techniques is performed for a minimum one super concept including the sub concepts, but TaxoMulti still shows the semantics of all super concepts, including the sub concepts. Compared to the latest techniques on personalized directories, a further improvement was performed using TaxoMulti instead. The improvement is again affected, because of TaxoMulti can reduce the taxonomy for each level. For all three databases, TaxoMulti resulted in a maximum reduction of the taxonomy with respect to the remaining of the domain, of on average 8%, the personalized directories technique of 5%, the catalog segmentation technique of 18%, and dynamic taxonomies of 0%. Compared to currently best performing existing works, TaxoMulti has achieved an improvement of + 60,00 %. 3. TaxoMulti shows the best performance regarding flexibility. Catalog segmentation fully lacks with respect to flexibility. The reason is, the more the number of concepts of the taxonomy is reduced, the more, the domain is also reduced semantically. Similar for dynamic taxonomies, where the techniques are reducing the taxonomy regarding the precision of a provided keyword. However, the more precise the keyword is, the more the taxonomy is also reduced semantically. In contrast, the more vague the keyword is, the bigger the semantics of the taxonomy is, but without any reduction. For all three databases, on average, TaxoMulti resulted in a range of 40%, the techniques of personalized directories a range of 33%, the techniques of catalog segmentation a range of 4%, and the technique of dynamic taxonomies, a range of 2%.
So compared to the currently best performing existing works, TaxoMulti has achieved an improvement of + 21,21 %.

Conclusions
This work has presented TaxoMulti, the first rule-based expert system to customize product taxonomies for multichannel e-commerce. Contrary to previous work on catalog segmentation, dynamic taxonomies, or personalized directories, TaxoMulti is not reducing the taxonomy in a semantically manner. This progress is achieved by using flexible mediator concepts. Through the adaption of the taxonomy according to the channels' specification, the rule-based system remedies three major drawbacks the formal taxonomies suffer from. Firstly and foremost, the system provides an environment to flexible customize taxonomies. This is achieved through providing various and combinable taxonomic operations, which perform on the different levels of the taxonomy. The flexibility of these operations is achieved by performing on mediator concepts. Those are flexible in its appearance and can be asserted with channel-specific rules. The efficiency of the mediator concepts has been evident by an evaluation performed on three databases. For channels requiring a smaller taxonomy (e.g. mobile), the taxonomy can be reduced by on average almost 50%. For channels requiring a larger taxonomy (e.g. desktop), the taxonomy can be enlarged by over 50% in the number of concepts. In addition, an enlargement for the number of levels of on average almost 67% was achieved. Compared to the currently best performing existing works, TaxoMulti has achieved an improvement of + 26,31 % for the reduction of the taxonomy, + 60 % for the enlargement of the taxonomy, and + 21,21 % in terms of flexibility.
Future work on TaxoMulti can be divided in two directions. By applying recommender system techniques, the taxonomy can be adapted automatically according to the channel and users' preferences. And, by combining the adapted taxonomy with user interface design, so-called mixed-reality scenarios could be investigated, e.g. in [38].
Funding Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest
The authors declare that they have no conflict of interest.

SN Computer Science
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