Social media filtering based on collaborative tagging in semantic space

Abstract

We propose a semantic collaborative filtering method to enhance recommendation quality derived from user-generated tags. Social tagging is employed as an approach in order to grasp and filter users’ preferences for items. In addition, we explore several advantages of semantic tagging for ambiguity, synonymy, and semantic interoperability, which are notable challenges in information filtering. The proposed approach first determines semantically similar users using social tagging and subsequently discovers semantically relevant items for each user. Experimental results show that our method offers significant advantages both in terms of improving the recommendation quality and in dealing with ambiguity, synonymy, and interoperability issues.

Appendix A

1.1 IEML language model

We present the model of the IEML language, along with the model of semantic variables. Let ∑ be a nonempty and finite set of symbols, ∑ = {S, B, T, U, A, E}. Let string s be a finite sequence of symbols chosen from ∑. The length of this string is denoted by |s|. An empty string ε is a string with zero occurrence of symbols and its length is |ε |= 0. The set of all strings of length k composed with symbols from ∑ is defined as ∑^k = {s where |s| = k}. Note that ∑⁰ = {ε} and ∑¹ = {S, B, T, U, A, E}. Although ∑ and ∑¹ are sets containing exactly the same members, the former contains symbols and the latter strings. The set of all strings over ∑ is defined as ∑^* = ∑⁰∪∑¹∪∑²∪∑³ …

A useful operation on strings is concatenation, defined as follows. For all s _i = a ₁ a ₂ a ₃ a ₄ …a _i ∈∑^* and s _j = b ₁ b ₂ b ₃ b ₄ …b _j ∈∑^*, then s _i s _j denotes string concatenation such that s _i s _j = a ₁ a ₂ a ₃ a ₄ …a _i b ₁ b ₂ b ₃ b ₄ …b _j and |s _i s _j | = i + j. The IEML language over ∑ is a subset of ∑^*, L _IEML ⊆ ∑^*:

$$ L_{{IEML}} = {\left\{ {s \in {\sum {^{*} \left\| s \right.\left| { = 3^{l} ,0 \leqslant l \leqslant 6} \right.} }} \right\}} $$

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1.2 Model of semantic sequences

Definition 3 (Semantic sequence)

A string s is called a semantic sequence if and only if s∈L _IEML .

To denote the p _n th primitive of a sequence s, we use a superscript n where 1 ≤ n ≤ 3^l and write s ⁿ. Note that for any sequence s of layer l, s ⁿ is undefined for any n > 3^l. Two semantic sequences are distinct if and only if either of the following holds: i) their layers are different, ii) they are composed from different primitives, iii) their primitives do not follow the same order: for any s _a and s _b ,

$$ {s_a} = {s_b} \Leftrightarrow \forall n,s_a^n = s_b^n \wedge |{s_a}| = |{s_b}| $$

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Let’s now consider binary relations between semantic sequences in general. These are obtained by performing a Cartesian product of two sets.⁸ For any set of semantic sequences X, Y where s _a ∈X, s _b ∈Y and using Eq. 2, we define four binary relations whole ⊆ X × Y, substance ⊆ X × Y, attribute ⊆ X × Y, and mode ⊆ X × Y as follows:

$$ \begin{array}{*{20}{c}} {{\hbox{whole}} = \left\{ {({s_a},{s_b})|{s_a} = {s_b}} \right\}} \\{{\hbox{substance}} = \left\{ {({s_a},{s_b})|s_a^n = s_b^n \wedge |{s_a}| = 3|{s_b}|,{ }1 \leqslant n \leqslant { }|{s_b}|} \right\}} \\{{\hbox{attribute}} = \left\{ {({s_a},{s_b})|s_a^{n + |{s_b}|} = s_b^n \wedge |{s_a}| = 3|{s_b}|,{ }1 \leqslant n \leqslant { }|{s_b}|} \right\}} \\{{\hbox{mode}} = \left\{ {({s_a},{s_b})|s_a^n = s_b^{n + 2|{s_b}|} \wedge |{s_a}| = 3|{s_b}|,{ }1 \leqslant n \leqslant { }|{s_b}|} \right\}} \\\end{array} $$

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Any two semantic sequences that are equal are in a whole relationship. In addition, any two semantic sequences that share specific subsequences may be in substance, attribute or mode relationship. For any two semantic sequences s _a and s _b , if they are in one of the above relations, then we say that s _b plays a role w.r.t s _a and we call s _b a seme of sequence.

Definition 4 (Seme of a sequence)

For any semantic sequence s _a and s _b , if (s _a , s _b ) ∈ whole ∪substance∪attribute∪mode, then s _b plays a role w.r.t. s _a and s _b is called a seme.

We can now group distinct semantic sequences together into sets. A useful grouping is based on the layer of those semantic sequences.

1.3 Model of semantic categories

A category of L _IEML is a subset such that all strings of that subset have the same length:

$$ c = \left\{ {\forall {s_i},{s_j} \in {L_{IEML}}\,where\,\left| {{s_i}| = |{s_j}} \right|} \right\} $$

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Definition 5 (Semantic category)

A semantic category c is a set containing semantic sequences at the same layer.

The layer of any category c is exactly the same as the layer of the semantic sequences included in that category. The set of all categories of layer l is given as the powerset⁹ of the set of all strings of layer l of L _IEML :

$$ {C_l} = Powerset\left( {\left\{ {s \in {L_{IEML}}\,where\,\left| s \right| = {3^l}} \right\}} \right) $$

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Two categories are distinct if and only if they differ by at least one element. For any c _a and c _b :

$$ {c_a} = {c_b} \Leftrightarrow {c_a} \subseteq {c_b} \wedge {c_b} \subseteq {c_a} $$

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A weaker condition can be applied to categories of distinct layers (since two categories are different if their layers are different) and is written as:

$$ l({c_a}) \ne l({c_b}) \Rightarrow {c_a} \ne {c_b} $$

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where l(c _a ) and l(c _b ) denotes the layer of category c _a and c _b , respectively. Analogously to sequences, we consider binary relations between any categories c _i and c _j where l(c _i ), l(c _j ) ≥ 1. For any set of categories X, Y where c _a ∈ X, c _b ∈ Y, we define four binary relations whole _C ⊆ X × Y, substance _C ⊆ X × Y, attribute _C ⊆ X × Y, and mode _C ⊆ X × Y as follows:

$$ \begin{array}{*{20}c} {{{\text{whole}}_{{\text{C}}} = {\left\{ {{\left( {c_{a} ,c_{b} } \right)}\left| {c_{a} = c_{b} } \right.} \right\}}}} \\ {{{\text{substance}}_{{\text{C}}} = {\left\{ {{\left( {c_{a} ,c_{b} } \right)}\left| {\forall s_{a} \in c_{a} ,\exists s_{b} \in c_{b} ,{\left( {s_{a} ,s_{b} } \right)} \in {\text{substance}}} \right.} \right\}}}} \\ {{{\text{attribute}}_{{\text{C}}} = {\left\{ {{\left( {c_{a} ,c_{b} } \right)}\left| {\forall s_{a} \in c_{a} ,\exists s_{b} \in c_{b} ,{\left( {s_{a} ,s_{b} } \right)} \in {\text{attribute}}} \right.} \right\}}}} \\ {{{\text{mode}}_{{\text{C}}} = {\left\{ {{\left( {c_{a} ,c_{b} } \right)}\left| {\forall s_{a} \in c_{a} ,\exists s_{b} \in c_{b} ,{\left( {s_{a} ,s_{b} } \right)} \in {\text{mode}}} \right.} \right\}}}} \\ \end{array} $$

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For any two categories c _a and c _b , if they are in one of the above relations (c _a , c _b ) ∈ whole _C ∪ substance _C ∪ attribute _C ∪ mode _C , then we say that c _b plays a role with respect to c _a and c _b is called a seme of category.

1.4 Model of catsets

A catset is a set of distinct categories of the same layer as defined Definition 4.

Definition 6 (Catset)

A catset κ is a set containing categories such that κ ={c _n |∀i, j: c _i ≠ c _j , l(c _i )=l(c _j )}.

The layer of a catset is given by the layer of any of its members: if some c ∈ κ, then l(κ) = l(c). Note that a category c can be written as c ∈ C _l , while a catset κ can be written as κ ⊆ C _l . All standard set operations, such as union and intersection, (e.g., ∪ and ∩), can be performed on catsets of the same layer.

1.5 Model of uniform semantic locator

A USL is composed of up to seven catsets of different layers as follows:

Definition 7 (Uniform Semantic Locator, USL)

A USL υ is a set containing catsets of different layers such that υ = {κ _n | ∀i, j: l(c _i ) ≠ l(c _j )}.

Note that since there are seven distinct layers, a USL can have at most seven members. All standard set operations, such as union and intersection (e.g., ∪ and ∩) on USLs are always performed on sets of categories (and therefore on sets of sequences), layer by layer. Since at each layer l there is |C _l | distinct catsets, the whole semantic space is defined by the tuple: Ł =C ₀ × C ₁ × C ₂ × C ₃ × C ₄ × C ₅ × C ₆ .