=Paper=
{{Paper
|id=Vol-1178/CLEF2012wn-ImageCLEF-AbdulahhadEt2012
|storemode=property
|title=MRIM at ImageCLEF2012. From Words to Concepts: A New Counting Approach
|pdfUrl=https://ceur-ws.org/Vol-1178/CLEF2012wn-ImageCLEF-AbdulahhadEt2012.pdf
|volume=Vol-1178
}}
==MRIM at ImageCLEF2012. From Words to Concepts: A New Counting Approach ==
MRIM at ImageCLEF2012. From Words to Concepts: A New Counting Approach Karam Abdulahhad*, Jean-Pierre Chevallet**, and Catherine Berrut* * UJF-Grenoble 1, ** UPMF-Grenoble 2, LIG laboratory, MRIM group karam.abdulahhad,jean-pierre.chevallet,catherine.berrut@imag.fr Abstract. MRIM research group has participated in two tasks (ad-hoc image-based retrieval and case-based retrieval) of the ImageCLEF2012 Medical Retrieval track. In our contribution, we study the frequency shift problem that happens when using concepts instead of words as indexing terms. The main goal of our experiments is to check the validity of our new counting strategy of concepts (Relative Count), which is proposed as a solution to the frequency shift problem. In order to validate our new counting strategy, we compare the retrieval performance (represented by MAP) of some classical IR models using the classical counting strategy (count each concept as 1) with their performance using the new strategy. The results are promising, and using the new counting strategy shows a considerable gain in performance. We use in our experiments two sup- plementary resources: MetaMap as a text-to-concepts mapping tool, and UMLS as an external resource containing concepts. 1 Introduction We present in this paper the contribution of the MRIM1 research group in the ImageCLEF20122 Medical Image Retrieval task3 . The main goal of our experiments and contribution is to study the side-effects of moving from the word-space to the concept-space on the classical Information Retrieval (IR) models. In other words, to study the side-effects of using concepts instead of words as indexing terms on the classical IR models. Concepts are entry IDs in a specific external resource, and each concept is associated to a set of strings that describe it. However, in order to build a concept-based IR system, another component, for mapping documents and queries text into concepts, is needed. These mapping tools, e.g. MetaMap4 [2], are imperfect, and they could map one piece of text 1 Multimedia Information Modeling and Retrieval is a research group in LIG (Labo- ratoire d’Informatique de Grenoble) laboratory. http://mrim.imag.fr/ http://www.liglab.fr/ 2 http://www.imageclef.org/2012 3 http://www.imageclef.org/2012/medical 4 http://metamap.nlm.nih.gov/ into no or several candidate concepts. For example, MetaMap maps a text like ”x-ray” into six different UMLS5 concepts. Therefore and as classical IR models directly or indirectly depend on the shared terms d ∩ q between a document d and a query q in order to compute the Relevance Status Value RSV (d, q) [4], we have what we called a frequency shift problem, because the number of shared terms |d ∩ q| between d and q changes in a non-homogeneous way when moving from the word-space to the concept- space. For example, using a mapping tool like MetaMap and an external resource like UMLS, if d and q share one word ”x-ray” in the word-space, then they will share six different concepts in the concept-space. Whereas, if they share a noun- phrase of two words ”lung x-ray” in the word-space, then they will share only one concept ”C0581647 ” in the concept-space. One solution to this problem is the supplementary disambiguation step that is actually achieved alongside the mapping process [3]. However, in this study we follow another strategy that proposes another concept counting mechanism. We do not count a concept as 1, instead of that, we give to each concept a relative count (in R∗+ ) respecting the following two hypothesis: – concepts that correspond to a longer text should receive larger count. – the count of a concept should be inversely proportional to the ambiguity level of its corresponding text. The ambiguity level of a piece of text is determined by the number of concepts that is mapped into. The text that is mapped into a larger number of concepts is more ambiguous. The goal is to finally satisfy the following condition for a piece of text TXT : X |TXT | = count c (1) c∈map(TXT ) where, |TXT | is the number of words in TXT , map(TXT ) is the set of all candidate concepts of TXT , and count c ∈ R∗+ is the new relative count of the concept c and we will explain in the following sections the algorithm of computing it. This year, ImageCLEF2012 contains four main tracks: 1) Medical Image Classification and Retrieval, 2) Photo Annotation and Retrieval, 3) Plant Iden- tification, and 4) Robot Vision. Medical Image Classification and Retrieval track contains three tasks: 1) modality classification, 2) ad-hoc image-based retrieval which is an image retrieval task using textual, image or mixed queries, and 3) case-based retrieval: in this task the documents are journal articles extracted from PubMed6 and the queries are case descriptions. We participated in the last two tasks: ad-hoc image-based retrieval and case-based retrieval. Table 1 shows some statistics on the data collections of the two tasks that we participated in. We only use the textual data. This paper is structured as follows: Section 2 describes in details the problem that occurs when moving from the word-space to the concept-space, and it also 5 Unified Medical Language System (http://www.nlm.nih.gov/research/umls/) 6 http://www.ncbi.nlm.nih.gov/pubmed/ Table 1. Corpora statistics. avdl and avql are the average length of documents and queries. ’C’ for concepts and ’W ’ for words. ’image2012’ for ad-hoc image-based re- trieval data collection and ’case2012’ for case-based retrieval data collection. Corpus #d #q Used fields Type avdl avql W 47.16 3.55 image2012 306530 22 - C 104.26 9.41 W 160.51 24.35 title+abstract C 376.14 63.73 case2012 74654 26 W 2731.24.35 24.35 title+abstract+fulltext C - - presents our proposed solution. Section 3 presents all technical details of applying our proposed solution to ImageCLEF2012 test collections. It also shows our formal runs and the obtained results. We conclude in section 4. 2 Computing Relative Concept Count Our algorithm depends on the output of MetaMap as a mapping tool and on the UMLS as an external resource containing the concepts. However, the algorithm could be easily generalized because most mapping tools [2][5] have the same general text-to-concept mapping mechanism [3]. For a textual document d or a query q, mapping tools (e.g. MetaMap) extract noun-phrases from the text and try to map them into one or more candidate concepts of a specific external resource (e.g. UMLS). However, for a noun-phrase np, it is sometimes difficult to find concepts corresponding to the whole noun-phrase. Moreover, even if there are concepts corresponding to the whole noun-phrase np, it is useful to return some concepts corresponding to parts of np, because restricting our attention to the concepts that only correspond to the whole phrase could lead to miss some related con- cepts, or in other words, it could lead to lose in recall. Therefore, most mapping tools do not only depend on the exact match to find candidate concepts, but they also generate some variants7 of the original noun-phrase [2], and then find- ing candidate concepts of all variants instead of only the original noun-phrase. For example, Table 2 shows the variants of the noun-phrase ”lobar pneumonia x-ray” that are generated by MetaMap, their related candidate UMLS concepts, and the corresponding part of the original noun-phrase. In this study, we regroup all variants that correspond to the same part of the original noun-phrase into only one variant. Therefore, Table 2 become Table 3. 7 spelling variants, abbreviations, acronyms, synonyms, inflectional and derivational variants, or meaningful combinations of these. Table 2. Variants of ”lobar pneumonia x-ray” generated by MetaMap, their related candidate UMLS concepts, and the corresponding part of the original noun-phrase Variants Candidate concepts Corresponding part ”lobar pneumonia x-ray” - ”lobar pneumonia x-ray” ”lobar pneumonia” C0032300, C0155862 ”lobar pneumonia” ”lung x-ray” C0581647 ”pneumonia x-ray” ”lung” C0024109, C 1278908 ”pneumonia” ”pneumonia” C0032285 ”pneumonia” ”pulmonary” C2707265, C2709248 ”pneumonia” ”lobar ” C1522010 ”lobar ” ”lobe” C1428707 ”lobar ” ”lobus” C0796494 ”lobar ” C0034571, C0043299, C0043309 ”x-ray” ”x-ray” C1306645, C1714805, C1962945 Table 3. Variants of ”lobar pneumonia x-ray” after regrouping according to the cor- responding parts of the original noun-phrase Variants Candidate concepts ”lobar pneumonia x-ray” - ”lobar pneumonia” C0032300, C0155862 ”pneumonia x-ray” C0581647 C0024109, C1278908, C0032285 ”pneumonia” C2707265, C2709248 ”lobar ” C1522010, C1428707, C0796494 C0034571, C0043299, C0043309 ”x-ray” C1306645, C1714805, C1962945 2.1 Definitions Our algorithm locally works at the level of noun-phrases not at the level of documents. Each noun-phrase np is a sequence of words or a set of 2-tuples, where each tuple (w, i) contains a word w ∈ W and the position i ∈ N∗ of w in np. Any variant v of np is also supposed to be a noun-phrase. By this way, it is possible to attach to each noun-phrase np, a set Vnp : Vnp = {np} ∪ {v1 , . . . , vj } where, {v1 , . . . , vj } are the variants of np that are generated by the mapping tool. We define the function wrd that returns the set of word-position tuples of a specific variant. ∗ wrd : Vnp → 2W ×N For example, suppose the variant v =”pneumonia x-ray” of the phrase ”lobar pneumonia x-ray”, then: wrd (v) = {(pneumonia, 2), (x − ray, 3)} We also define for any variant v ∈ Vnp , |v| = |wrd (v)| the number of words in v. We define the function map that returns the candidate concepts of a variant v ∈ Vnp . map : Vnp → 2C where C is a set of concepts. For example, suppose the variant v =”pneumonia x-ray” of the phrase ”lobar pneumonia x-ray”, then: map(v) = {C0581647} We will remove from Vnp all members v that do not have any candidate concepts map(v) = φ. For example, in the case of ”lobar pneumonia x-ray” noun-phrase, we will remove the noun-phrase itself because it is not mapped into any concept. Finally, Vnp becomes: Vnp ={”lobar pneumonia”, ”pneumonia x-ray”, ”pneumonia”, ”lobar ”, ”x-ray”} It is possible to define a partial order < relation on the set Vnp as follow: ∀v1 , v2 ∈ Vnp , v1 < v2 iff wrd (v1 ) ⊂ wrd (v2 ) Therefore, it is possible to define a hierarchy HR np on Vnp ∪ {R}, where: – v ∈ Vnp ∪ {R} are the nodes. – R is an abstract root satisfying: ∀v ∈ Vnp , v < R. Moreover, |R| = 0. – The direct children ch(v) of any node v ∈ Vnp ∪ {R} is defined as follow: ∀v1 , v2 ∈ Vnp ∪ {R}, v1 ∈ ch(v2 ) iff v1 < v2 and 6 ∃v3 ∈ Vnp , v1 < v3 < v2 – The direct parents pr (v) of any node v ∈ Vnp ∪ {R} is defined as follow: ∀v1 , v2 ∈ Vnp ∪ {R}, v1 ∈ pr (v2 ) iff v2 ∈ ch(v1 ) For example, Fig. 1 shows the hierarchy of the noun-phrase ”lobar pneumonia x-ray”. 2.2 The Algorithm The main goal of the algorithm is to compute the relative count of candidate concepts, as follow: for a noun-phrase np, distributing the number of words |np| of this noun-phrase on the candidate concepts of np and its variants. The algorithm respects two hypothesis: – the relative count of a concept is directly proportional to the number of words in the corresponding variant. Fig. 1. The hierarchy of the noun-phrase ”lobar pneumonia x-ray”. – the relative count of a concept is inversely proportional to the ambiguity level of the corresponding variant. The variant that is mapped into a larger number of concepts is more ambiguous. The input is the set Vnp that contains all variants of np, and the number of words |np| in np. The output will be a set CC np of 2-tuples, and each tuple contains one of the candidate concepts and its associated relative count. The detailed algorithm is shown in Algorithm 1. 2.3 Example Assume np is the noun-phrase ”lobar pneumonia x-ray”. The list of variant Vnp is: Vnp = {v1 , v2 , v3 , v4 , v5 } (see Fig. 1). Figure 1 also shows the hierarchy HR np of the set Vnp ∪ {R}. Initially, we have αR = |np| = 3 and ∀v ∈ Vnp , αv = 0. We scan the nodes in breadth-first order, that means, nodes will be scanned in the following order < R, v1 , v2 , v3 , v4 , v5 >. By following the Algorithm P 1, Table 4 shows the output set CC np . By con- sulting Table 4, we can see: (c,count c )∈CC np count c = |np| = 3. 3 Experiments The main goal of our experiments is to show the validity of our new way of counting. We check this validity through comparing the retrieval performance of some classical IR models using classical concept counting method, to their performance using our new way of counting. We use the Mean Average Precision (MAP) metric as an indicator to the retrieval performance of IR models. 3.1 Retrieval Models In order to check the validity of our new way of counting, we use several classical IR models: Algorithm 1: RelativeCount input : Vnp , |np| output: CC np ⊆ C × R∗+ 1 CC np = {}; 2 construct the hierarchy HR np of the set Vnp ∪ {R}; 0 3 attach to each node n in HR np a value αn0 , where αn0 is the total amount that 0 is received from pr (n ) and should be distributed on the candidate concepts of n0 and its children ch(n0 ), starting by αn0 = 0; 4 n is the current node, starting by n = R; 5 set αR = |np|; 6 scan HR np in a breadth-first way, starting from the current node n = R; 7 begin 8 for each child n0i ∈ ch(n) do 9 compute the amount αn0i that should be transferred from n to n0i : α ×|n0i | αn0i = αn0i + |n|+P n0 0 ; n ∈ch(n) |nj | j 10 end 11 if n 6= R then 12 compute the amount an that should be distributed on the candidate concepts map(n) of the current node n: an = |n|+Pαn0 ×|n| |n0 | ; n ∈ch(n) j j 13 for each candidate concept ci ∈ map(n) do 14 compute the relative count: count np an ci = |map(n)| ; np 15 CC np = CC np ∪ {(ci , count ci )}; 16 end 17 end 18 change n to the next node according to the breadth-first scan order; 19 go to line 7; 20 end – from probabilistic framework: we choose BM25 (2) [7]. – from language models framework: we choose Dirichlet model DIR (3) [9], and Jelinek-Mercer model JM (4) [9]. – from vector space framework: we choose Pivoted Normalization Method PIV (5) [8], and a version of TFIDF model (6) [1]. where, tf t,d is the term frequency of the indexing term t in the document d, tf t,q is the term frequency of the indexing term t in the query q, |d| is the document length, |q| is the query length, avdl is the average document length, N is the total number of documents in the corpus D, nt is the number of documents that contain the indexing term t, d ∩ q are the shared indexing terms between d and q, and p(t, D) is the probability of t given the corpus language model D. s, k1 , b, k3 , λ, and µ are all parameters. They usually have the following values: s = 0.2 [8]. k1 = 1.2, b = 0.75, and k3 = 1000 [6]. λ = 0.1 for short queries or λ = 0.7 for long queries and µ = 2000 [9]. Table 4. The output set CC np of the noun-phrase ”lobar pneumonia x-ray” Vnp CC np v1 =”lobar pneumonia” (C0032300,0.375), (C0155862,0.375) v2 =”pneumonia x-ray” (C0581647,0.75) v3 =”lobar ” (C1522010,0.125), (C1428707,0.125), (C0796494,0.125) (C0024109,0.15), (C1278908,0.15), (C0032285,0.15) v4 =”pneumonia” (C2707265,0.15), (C2709248,0.15) (C0034571,0.0625), (C0043299,0.0625), (C0043309,0.0625) v5 =”x-ray” (C1306645,0.0625), (C1714805,0.0625), (C1962945,0.0625) P N −nt +0.5 (k1 +1)×tf t,d RSV (d, q) = t∈d∩q ln nt +0.5 × k1 ×((1−b)+b× |d| )+tf avdl t,d (2) (k +1)×tf × 3k3 ×tf t,q t,q tf t,d µ X RSV (d, q) = |q| × ln + tf t,q × ln 1 + (3) |d| + µ µ × p (t, D) t∈d∩q tf t,d X 1−λ RSV (d, q) = |q| × ln(λ) + tf t,q × ln 1 + × (4) λ |d| × p (t, D) t∈d∩q X 1 + ln 1 + ln tf t,d N +1 RSV (d, q) = |d| × tf t,q × ln (5) (1 − s) + s avdl nt t∈d∩q X tf t,d N RSV (d, q) = |d ∩ q| × tf t,q × |d| × (6) tf t,d + avdl nt t∈d∩q There are two different views for documents and queries. The first one is the classical view, where both documents and queries are bags of indexing terms (e.g. words or concepts). The classical way of counting (count each concept or word as 1) is compatible with this view, and the previous definitions of IR model components correspond to this classical view. We will present the second view, which is convenient to the relative count of concepts. In this view, some components of IR models should be redefined. Most mapping tools extract noun-phrases from the text of documents and queries. Therefore, any document d or query q is a sequence of noun-phrases: d =< np1 , . . . , npnd > q =< np1 , . . . , npnq > We redefine the set CC np on the level of documents and queries instead of the noun-phrase level: [ [ CC d = CC npi CC q = CC npi npi ∈d npi ∈q CC d∩q = {(c, r)|(c, r) ∈ CC q , ∃(ci , ri ) ∈ CC d , c = ci } According to our way of counting (Relative Count), the components of the IR models become: X X X tf c,d = ri tf c,q = ri tf c,D = tf c,di (c,ri )∈CC d (c,ri )∈CC q di ∈D X X X |d| = ri |q| = ri |D| = |di | (ci ,ri )∈CC d (ci ,ri )∈CC q di ∈D X |d ∩ q| = ri (ci ,ri )∈CC d∩q 3.2 Data We only use the textual part of the data collections of ad-hoc image-based re- trieval and case-based retrieval tasks of the ImageCLEF 2012 Medical Image Classification and Retrieval track. Table 1 shows some statistics about these two data collections. We use two types of indexing terms: – words (W): we eliminate the stop words and stem the remaining words using Porter algorithm to finally get the list of words that indexes documents and queries. – concepts (C): we use MetaMap for mapping the documents and queries text content into UMLS concepts. 3.3 Formal Runs The initial of our runs in the formal campaign is ”LIG MRIM xxx”. However, Tables 5 and 6 show the name and the description of our runs. The best MAP in the ad-hoc image-based retrieval task (only text) is 0.2182, and the best MAP in the case-based retrieval task (text only) is 0.1690. 3.4 Results and Discussion In this section we show the validity of our new method of concept counting (RelativeCount), through comparing the retrieval performance of IR models with or without using the relative count. The only type of indexing terms that is used in this section is concepts. We count concepts in two ways: the classical count (count each concept as 1) and the relative count (Algorithm 1). Table 7 shows the results of applying IR models to the image2012 collection (see Teble 1). Table 8 shows the results of applying IR models to the case2012 collection (see Teble 1). We only map the title and the abstract parts of documents into concepts Table 5. Our formal runs in the ad-hoc image-based retrieval task. (TFIDF*) means the TFIDF model after removing |d ∩ q|. (TFIDF**) means the TFIDF model after removing |d ∩ q| and avdl run name IR model term type count type MAP IB TFIDF W avdl DintQ TFIDF W - 0.1586 IB FUSION TFIDF W TB C avdl DintQ TFIDF W+C relative 0.1432 IB FUSION JM01 W TB C JM(λ = 0.1) W + C relative 0.1425 IB TB PIVv2 C PIV C relative 0.1383 IB TFIDF C avdl DintQ TFIDF C classic 0.1345 IB TB JM01 C JM(λ = 0.1) C relative 0.1342 IB TB BM25 C BM25 C relative 0.1165 IB TB TFIDF C avdl TFIDF* C relative 0.1081 IB TB DIR C DIR C relative 0.0993 IB TB TFIDF C TFIDF** C relative 0.0900 Table 6. Our formal runs in the case-based retrieval task. (TFIDF*) means the TFIDF model after removing avdl. (TFIDF**) means the TFIDF model after removing |d ∩ q|. (TFIDF***) means the TFIDF model after removing |d ∩ q| and avdl. The concepts are extracted from the title and abstract of each document run name IR model term type count type MAP CB FUSION DIR W TA TB C DIR W+C relative 0.1508 CB FUSION JM07 W TA TB C JM(λ = 0.7) W + C relative 0.1384 CB TFIDF W DintQ TFIDF* W - 0.1036 CB TA TB JM07 C JM(λ = 0.7) C relative 0.0908 CB TA TB BM25 C BM25 C relative 0.0895 CB TA TB DIR C DIR C relative 0.0893 CB TA TB PIVv2 C PIV C relative 0.0865 CB TA TFIDF C DintQ TFIDF* C classic 0.0789 CB TA TB TFIDF C avdl TFIDF** C relative 0.0692 CB TA TB TFIDF C TFIDF*** C relative 0.0646 Tables 7 and 8 show that we have a considerable gain in retrieval performance when using the relative count instead of the classical one. The gain is clearer in the case of short documents and queries (image2012) than the case of long documents and queries (case2012). Tables 5 and 6 show that using words as indexing terms is still more effective (from the retrieval performance point of view) than using concepts. Concerning our formal contribution in the ad-hoc image-based retrieval task, we got a middle-rank. We still far from the best formal run. However, our con- tribution in the case-based retrieval task was more encouraging. We are ranked the second in the final list. We made a late fusion between two result set: 1- one resulting from applying DIR model to the case2012 corpus using words as index- ing terms, and 2- another one resulting from applying DIR model to case2012 corpus using concepts as indexing terms. Table 7. Comparing the retrieval performance of IR models using the classical count with their performance using the relative count (Algorithm 1). The corpus is image2012. The last column shows the gain in performance when using the relative count comparing to the performance of using the classical count IR model count type MAP Gain classic 0.1071 PIV +27% relative 0.1360 classic 0.1034 BM25 +10% relative 0.1142 classic 0.0861 DIR +13% relative 0.0969 classic 0.1022 JM(λ = 0.1) +29% relative 0.1318 classic 0.1322 TFIDF +7% relative 0.1410 4 Conclusion We present in this paper the contribution of the MRIM research group in the ImageCLEF2012 Medical Image Retrieval task. We describe the frequency shift problem that happens when moving from the word-space to the concept-space. The source of this problem is the heterogeneous change in the frequency of indexing terms when moving from the word-space to the concept-space. We propose a solution to the frequency shift through a new counting strategy. Our counting strategy (Algorithm 1) depends on the hierarchy that could be built from the output of mapping tools. It also depends on the following two hypotheses: – the relative count of a concept is directly proportional to the number of words in the corresponding text. – the relative count of a concept is inversely proportional to the ambiguity level of the corresponding text. For validating the effectiveness (from the retrieval performance point of view) of our new counting strategy, we participated in the ImageCLEF2012 campaign, more precisely, in the ad-hoc image-based retrieval and case-based retrieval tasks. Our experiments only depend on the textual data. For mapping text into con- cepts, we use MetaMap as a mapping tool and UMLS as an external resource containing concepts. In the case-based retrieval task, we only map the title and abstract of each document (we do not map the fulltext). In the ad-hoc image-based retrieval task, we got a middle-rank. We still far from the best formal run. However, our contribution in the case-based retrieval task was more encouraging. We are ranked the second in the final list. Moreover, the supplementary results that we present in this paper show a considerable gain in retrieval performance when applying our counting strategy Table 8. Comparing the retrieval performance of IR models using the classical count with their performance using the relative count (Algorithm 1). The corpus is case2012. The last column shows the gain in performance when using the relative count comparing to the performance of using the classical count IR model count type MAP Gain classic 0.0789 PIV +10% relative 0.0865 classic 0.0847 BM25 +7% relative 0.0895 classic 0.0825 DIR +8% relative 0.0893 classic 0.0863 JM(λ = 0.7) +5% relative 0.0908 classic 0.0830 TFIDF +2% relative 0.0847 (Algorithm 1) comparing to the classical counting strategy (count each concept as 1). References 1. Karam Abdulahhad, Jean-Pierre Chevallet, and Catherine Berrut. The Effective Relevance Link between a Document and a Query. In 23rd International Conference on Database and Expert Systems Applications (DEXA 2012), Vienna, Austria, pages 206–218, sep 2012. 2. Alan R. Aronson. Metamap: Mapping text to the umls metathesaurus, 2006. 3. Jean-Pierre Chevallet, Joo Hwee Lim, and Thi Hoang Diem Le. Domain knowledge conceptual inter-media indexing, application to multilingual multimedia medical reports. In ACM Sixteenth Conference on Information and Knowledge Management (CIKM 2007), Lisboa, Portugal, November 6–9 2007. 4. Stéphane Clinchant and Eric Gaussier. Information-based models for ad hoc ir. In Proceedings of the 33rd international ACM SIGIR conference on Research and development in information retrieval, SIGIR ’10, pages 234–241, New York, NY, USA, 2010. ACM. 5. Christopher Dozier, Ravi Kondadadi, Khalid Al-Kofahi, Mark Chaudhary, and Xi Guo. Fast tagging of medical terms in legal text. In Proceedings of the 11th international conference on Artificial intelligence and law, ICAIL ’07, pages 253– 260, New York, NY, USA, 2007. ACM. 6. Hui Fang, Tao Tao, and ChengXiang Zhai. A formal study of information retrieval heuristics. In Proceedings of the 27th annual international ACM SIGIR conference on Research and development in information retrieval, SIGIR ’04, pages 49–56, New York, NY, USA, 2004. ACM. 7. S. E. Robertson and S. Walker. Some simple effective approximations to the 2- poisson model for probabilistic weighted retrieval. In Proceedings of the 17th annual international ACM SIGIR conference on Research and development in information retrieval, SIGIR ’94, pages 232–241, New York, NY, USA, 1994. Springer-Verlag New York, Inc. 8. Amit Singhal, Chris Buckley, and Mandar Mitra. Pivoted document length normal- ization. In Proceedings of the 19th annual international ACM SIGIR conference on Research and development in information retrieval, SIGIR ’96, pages 21–29, New York, NY, USA, 1996. ACM. 9. Chengxiang Zhai and John Lafferty. A study of smoothing methods for language models applied to ad hoc information retrieval. In Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval, SIGIR ’01, pages 334–342, New York, NY, USA, 2001. ACM.