Information Retrieval on social network: An Adaptive Proof

Information Retrieval has become one of the areas for studying to get the trusty information, with which the recall and precision become the measurement form that represents it. Nevertheless, development in certain scientific fields make it possible to improve the performance of the Information Retrieval. In this case, through social networks whereby the role of social actor degrees plays a role. This is an implication of the query in which co-occurrence becomes an indication of social networks. An adaptive approach we use by involving this query in sequence to a stand-alone query, it has proven the relationship among them.


Introduction
Information Retrieval (IR) is a part of computer science that systematically examines the relevance of information required with information sources, which mathematically derives and proves the measurement formulation of the relevance of information resources and information required. It is from models to methods [1]. In information era with such a large and change information source dynamically [2], also continue to grow, the role of IR is crucial for generating trusty information [3]. This is based on the work of the search engine, which logically means that the document ω is relevant to the query q if it means query or ω ⇒ q, ω ∈ Ω, where Ω is a space information [4].
One way of obtaining information is through the extraction of information or data mining, such as the extraction of social networks from the Web, or the mining of social structure from information sources by involving social network analysis (SNA) [5]. On the other hand, social networks obtained either by extracted (semi)-automatically or manually [6], or social networks either by document or in real terms are present in everyday life [7]. It technologically presents IR methods based on social networks [8]. Because after all the source of information such as the Web has always been a shadow of the actual state of the events [20]. However, little interest has been made to prove the existence of social network links with IR [10]. Therefore, this paper aims to reveal an IR formula adaptively based on social networks.

Basic Concept and Problem Definition
To be a conceptual bridge toward the problem definition, we disclose the basic concepts and related works of various literature as follows [11,12] A document d consists of the words w k , k = 1, . . ., K or contains some vocabularies (sometimes it expressed as tokens) i.e. w l , l = 1, . . ., L where L ≤ K if every word has a weight |w l | = k j i=1 p(w k ) = k i /L where |w k | = p(w k ) = 1/K and k i the number of the same words for the word w k or k i is the word frequency of w k .

Definition 2.
A set of documents D is a collection of documents d i , i = 1, . . ., I arranged in such a way that each document has a weight |d| and every vocabulary or word has a weight |w|.

Information Retrieval
To model IR approach required the standard data as the comparison for results returned by the access method toward information source. Therefore, based on Definition 2, a document-set D r serves as the comparative standard data for document generated by an access tool (search engine) whereby it depends on the query q (we call it as the evaluation document or D e ). The document comparison result will be stated in the mutual document D r ∩ D e [4,13].

Definition 4. Evaluation document D e is a collection of documents that is accessed whereby each document has id uniquely based on the information source.
In general, to estimate the trusty information we use the measurement referred to as recall and precision as follows [14].
where D r is a set of relevant documents and D e is a set of the retrieved documents, and |D r ∩D e | is the size of D r ∩ D e and |D r | is the size of D r . Definition 6. Precision (prec) is a measurement to the retrieved documents that is relevant to real documents based on tool, i.e.
where D r is a set of relevant documents and D e is a set of the retrieved documents, and |D r ∩D e | is the size of D r ∩ D e and |D e | is the size of D e .

Social Network
To develop the social network, we have a set of social actors A = {a i |i = 1, . . ., I} and we determine the relationship between social actors in pairs based on a set of relation clues C = {c j |j = 1, . . ., J}. Therefore, social network can be defined as follows [15,16].
where R is a set of relation between social actors, i.e. r j = c(a k , a l ), r j ∈ R, j = 1, . . ., J, a k , a l ∈ A. We notify a social network as < V, E, A, R, C, γ 1 , γ 2 .

An Approach
To be get information we use cognitive structures as an approach in some of implications as follows [4,1].

Lemma 2.
If D r and D e each contains uniquely document id that may be the same between two sets, then the same two id are based on the iteration of id i ∈ D r againts id j ∈ D e . Proof. Suppose id i ∈ D r and id j ∈ D e . id j ∈ D e is generated based on the ω ⇒ q implication which is true value if the content q is in the Ω, in other case it is false. While D r contains a set of documents with specified id, and ω ⇒ id is true if q ⇒ id. Because D r contains a set of id j , so q ⇒ id j has to round every id i ∈ D e , and looping id ∈ D r done to id ∈ D e . Lemma 3. If D r and D e each contains a document id that might be the same so as to form D r ∩ D e , looping id i ∈ D r against id j ∈ D e generates a sequance number of D e . Proof. Based on the assumptions and consequences of the Lemma 1 and Lemma 2. Suppose id j ∈ D e with id 1 , id 2 , . . ., id m , j = 1, . . ., m, as a result sequence of ω ⇒ q. Therefore, by doing iteration id i ∈ D r against one by one against from id j ∈ D e from the sequence 1 to m.

Adaptive Proof
Later in this paper, we reveal the interpretive outlines involving the above approach to prove adaptively Theorem 1.
Assuming that each query stands alone, based on Algorithm 1 the recall and precision calculations can be expressed as Fig. 1, although the query contains the co-occurrence of two names of the social actor [17]. However, since any query involving co-occurrence becomes a clue of the relationship between two social actors, so it is possible that one of the social actor names is the same actor on each query [18]. Thus, the queries produce social networks that are generally the form of star graph with one social actor as the center [19].
Suppose that there is a query sequence q 1 , . . ., q k whereby each query contains q 1 ← a 1 , a 2 ; q 2 ← a 1 , a 3 ; . . .; q k ← a 1 , a k . So we get a list of D e 1 , D e 2 , . . ., D e k , or a sequence of D r ∩ D e 1 , D r ∩ D e 2 , . . ., D r ∩ D e k , and a set of documents is a collection of evaluation documents as follows whereby |D es | ≤ |D e 1 | + |E e 2 | + . . . + |D e k |. Whereas, a collection of documents comes from the comparison between id of 2 sets of documents is D r ∩ D es = ∪ k l=1 D r ∩ D e l , and based on Eq. ( whereby In general, in Eqs. (1) and (2), the value of |D e 1 | + |D e 2 | + · · ·+ |D e k | and the value of |D r ∩ D e 1 | + |D r ∩ D e 2 | + · · · + |D r ∩ D e k | each has been reduced to | ∪ k l=1 D e l | and |D r ∪ k l=1 D e l |. This reduction as a result of merging the set of documents where the same documents to be listed once so that the value of |D es | close to the value of |D r | or |D r ∩ D es | ≤ |D r |, but the number of documents in D es has potential to exceed the number of documents in D r . This causes a low precision value even if recall value is high. Taking into account that the keyword can reduce unsuitable documents, each query with a form of co-occurrence (one of the social actor names being the keyword for the other) lifts the appropriate document up to the surface [20]. Randomly assigned queries such that every D e l , l = k, |D e l | has the highest value in accordance with |D r ∩ D e l | in sequence, where in the next sequence the value of |D e l | does not come from the same document in the previous query, while in the last query or for |D e k | involves all possible documents, see Fig. 2. Thus by involving the same query as Fig. 1, taking into account the precise measurements consecutively. The query results, except the last query, are considered only to the extent that the last document is appropriate. In other words, if Eqs. (1) and (2) are restated based on Eqs. (3) and (4) as follows [1] and As the implementation of the Eqs. (5) and (6) can be seen in Fig. 2. Theorem is proven.

Conclusion
The involvement of social actors can be used to improve the performance of recall and precision through effective approaches. An effective approach is made to the use of queries in sequence via a stand-alone query. However, implementation needs to be done by involving data and search 6 1234567890''"" engines, in addition to providing more definitive proof of the relation existence between the extracted social networks and IR.