The problem of profile matching in electronic social networks asks to find those offering profiles of actors in the network fitting best to a given search profile. In this article this problem is mathematically formulated as an optimization problem. For this purpose the underlying search space and the objective function are defined precisely. In particular, data structures of search and offering profiles are proposed, as well as a function measuring the matching of the attributes of a search profile with the corresponding attributes of an offering profile. This objective function, given in Equation (29), is composed of the partial matching degrees for numerical attributes, discrete non-numerical attributes, and fields of interests, respectively. For the matching degree of numerical profile attributes a fuzzy value approach is presented, see Equation (22), whereas for the matching degree of fields of interest a new measure function is introduced in Equation (26). The resulting algorithm is illustrated by a concrete example. It not only is applicable to electronic social networks but also could be adapted for resource discovery in grid computation or in matchmaking energy demand and supply in electrical power systems and smart grids, especially to efficiently integrate renewable energy resources.
Social activities in electronic networks play an increasingly important role in our every-day lives. We are exchanging important information via electronic mails, wikis, web-based forums, or blogs, and meet new friends or business contacts in Internet communities and via social network services. Parallel to this growing sociali- zation of the World Wide Web, the requirements on the electronic services become more ambitious. Huge data quantities have to be processed, user-friendly interfaces are to be designed, and more and more sophisticated computations must be implemented to offer complex solutions.
One of the most important subjects in complex networks is the search for specific items or objects in it. For instance this comprises the search for web sites which are relevant with respect to a specific term, or the request for specific resources as consumers do for electricity in smart grids. Therefore there is, and has always been, a great interest in enabling and maintaining efficient special network services which perform precisely these tasks.
This paper studies a special aspect of general electronic networks, but in particular of social network services, the profile matching problem. In essence it asks, given a search profile, for offering profiles matching it best. This problem is in principle well-known in Grid computing, where computational tasks are seeking for appro- priate resources such as CPU time and memory space on different computers. In electronic social networks, however, the problem is more general because not only specified attribute ranges such as resource sizes are to be compared but more or less vaguely describable interests. Questions of this kind have recently been under consideration, for instance to implement multiple interest matching in personel business networks [
Here, however, a different approach is presented, leaving the important but difficult problem of semantic search aside and enabling an automated matching of general types of attributes. The aim of this paper is to formulate a mathematical model for the problem of matching attribute ranges and fields of interests in electronic social networks. It tackles the following fundamental questions. How can an appropriate system and its data structures be designed? How is the mathematical formulation of a matching problem as an optimization problem? In particular, what is its search space? What is its objective function? It is obvious to use a fuzzy function to calculate the matching degree of two numerical ranges or to use the characteristic function to check for the equa- lity of discrete attribute sets, but how could a function calculating a matching degree of two fields of interest look like? One of the central results of this paper is the proposal of a precise definition of such a function computing the matching degree of a pair of profiles and the presentation of a concrete example. The applica- bility of the profile matching model is not confined to electronic social networks but can also operate to enable and control electricity resource allocation in electrical power systems or in smart grids. By this approach technological challenges of energy transition programs such as the Energiewende to integrate renewable energy into electrical power systems can be tackled.
The paper is organized as follows. After a definition of electronic social networks is given in the next section, a mathematical model of the matching problem as an optimization problem is proposed, especially the data structure of search and offering profiles, the search space, and the matching degree as the objective function. A short discussion concludes the paper.
A social network consists of a finite set of actors and the direct relations defined between them. An actor here may be an individual, a group, or an organization, and the direct relation between two actors may indicate that they directly interact with each other, have immediate contact, or are connected through social familiarities such as casual acquaintance, friendship, or familial bonds [
Since the popularization of the World Wide Web in the middle of the 1990’s and in particular around 2005 after the introduction of the Web 2.0 paradigm [
In this paper, an electronic social network is defined as a network of at least three human individuals or organizations which use essentially, albeit not exclusively, electronic devices and media to get in contact and acquaintance to each other, to meet new partners, to communicate, and to exchange information. Examples of electronic social networks are Internet social networks, as well as videoconference sessions and conference calls, especially if they serve to meet new people as in party lines, or as long as they admit spontaneous communi- cation between each network actor [
In computer science, the term matching or sometimes matchmaking in general refers to the process of evaluating the degree of similarity or agreement of two objects. Each object is characterized by a set of properties or attributes, which in many systems are given by name-value pairs [
In most matching problems, the objects under consideration take asymmetric roles, viz., some search for information or request for a service, others offer information or provide a service. A single object may naturally do both activities at a time, in electronic social networks this even is the usual case. In the sequel we will therefore more accurately consider the matching of a search profile, containing information for a request, and an offering profile presenting information for a supply or a provided service.
Given a specific search profile, the matching problem then is to find those offering profiles which match it best, in a sense to be specified in the sequel. Generalizations of this problem ask for best global matchings, given a whole set of search profiles and a set of offering profiles. For instance, the global pairwise matching problem seeks pairs of search/offering-profiles such that the entity of the pairs matches the best under the constraint that any profile is member of at most one pair. The global multiple matching problem searches for possibly multiple combinations of search and offering profiles which as a whole match the best. The pairwise version of the problem typically occurs for dating services or classical marriage matching tasks, whereas the multiple version appears in grid computing or in brokering interest groups.
In this paper we will focus on the local version of the matching problem, i.e., finding an optimum offering profile to a specified search profile. Thus the matching problem is an optimization problem, and to formulate it precisely we have to specify the search space and the objective function. The search space will turn out to be the set of pairs of the fixed search profile and the offering profiles, and the objective function will be a function measuring the “matching degree”. We will work out these notions in the next sections.
A profile consists of its owner corresponding to an actor of the electronic social network, a list of attributes of a given set
In principle, there are two different types of attributes, subsumed in the two disjoint sets
The set
Correspondingly, the stencil of an attribute is determined by the attribute’s name and its range, being of a
certain set called type
where
denotes the set of ranges for the numerical attributes, and
denotes the set of possible value sets for discrete non-numerical attributes. That is,
On the other hand, a field of interest is a name-value pair specifying the field itself as well as its level ranging on a scale from ‒1 to 1, coded by the interpolation of the following table,
The set of fields of interests is denoted by
Usually,
Example 1. In grid computing, a main matching problem is resource discovery and resource allocation [
In each column of a profile there is listed its owner and some attributes and their values. Then a solution to the global matching problem is obviously given by the matchings (194.94.2.21, Haegar) and (194.1.1.3, Bond). ,
Let be a set
where
problem is given by all pairs of search and offering profiles, i.e.,
considering the local matching problem, given a single search profile
where
denote the set of searched numerical attributes, the set of discrete non-numerical attributes, and the set of fields of interests, respectively, specified by the search profile. Then a search profile
where
is the set of attribute-range pairs, with the given mapping
numerical attributes to their associated desired ranges (
interval
is the set of attribute-set pairs, with the mapping
is the set of searched fields of interest with their desired levels, with the given mapping
that for a usual software system each of the pairs
table or a hash map. Analogously, an offering profile is given by
where the three sets are defined the same way as in the search case, but with the index “s” (for “search”) replaced by “o” (for “offering”).
Example 2. Assume a small social network for pooling interest groups, consisting of three persons, Alice, Bob, and Carl, who provide search and offering profiles according to the following tables.
In each column of a profile there is listed its owner, some attributes and their values, and the fields of interests with their levels. For instance, Alice looks for someone between 20 and 40 years of age being enthusiastic in tennis and having some penchant to chess, whereas Carl seeks a tall person in the 20’s with highest preference for basketball. Looking at the offering profiles in this social network, one sees that Alice may contact Bob, but Carl cannot find an ideal partner in this community. On the other hand, Alice would be a “better” partner for Carl than Bob, since she is partly interested in basketball. Formally Alice’s search profile, for instance, is given as follows. The sets for the searched attributes and fields of interest are
the mapping
and the mapping
The mapping
Note in particular that
where
With the definitions
the search space
The matching degree of a search profile and an offering profile is a real number
To determine the matching degree of a searched value range
The parameter
For instance, if the searched attribute is “height > 180” and an offered attribute is “height = 165” then for a fuzzy level of
i.e., the matching degree is 16.7%. Then the matching degree of two numerical ranges
If the values of specific attribute are constrained to be of a finite set, or an enum, say
If the searched attribute, for instance, is “name Î {‘Smith’, ‘Taylor’}” and the offered attribute is “name = ‘Tailor’” then “E = {‘Smith’, ‘Taylor’}” and “
First we notice that the matching degree as a function of the levels of interest
greater than 0, but if the search requires
case, the searcher is indifferent about the field of interest, in the second case he demands high interest.
Definition 3. An interest matching degree function is a function
conditions are satisfied.
The first condition expresses the perfect matching of the diagonal, the second the search indifference, and the last the search necessity. ,
A possible matching degree function is given by
where
with
By construction,
function.
It is asymmetric with respect to its arguments, since we have
the other hand, it is an even function, i.e.,
Putting together all partial matching degrees considered above, i.e., the matching degree (22) for numerical attributes, the matching degree (24) for numerical attributes, the matching degree (26) of fields of interest, we construct a function
where
Thus for the computation of the matching degree, the attributes and fields of interest of the search profile
Example 2 (revisited). For Alice’s search space we have the two solutions (19), i.e.,
and
Hence Bob’s offering profile has a matching degree of 73.15% with Alice’s search profile, whereas Carl’s matches it only by 54.36%. ,
Notice that the objective function (29) is constructed in such a way that each searched item
where
of all weights
Let
A simple algorithm to solve this maximum problem is to exhaustively compute the matching degrees of all possible profile pairs
In this paper, a mathematical model of the matching of search and offering profiles in electronic social networks is proposed. Basing on the data structure described by
The applicability of a profile matching algorithm is not restricted to electronic social networks but could be adapted for resource discovery in grid computation or in matchmaking energy resources in grids. In particular energy transition projects aiming to integrate renewable energy into electrical power systems have to solve the problem of matching energy supply and demand, caused by the high variability of renewable energy supply such as wind or solar power ( [
I am indebted to Thomas Kowalski for valuable discussions.