Document (#35995)

Author

Egghe, L.

Title

Good properties of similarity measures and their complementarity

Source

Journal of the American Society for Information Science and Technology. 61(2010) no.10, S.2151-2160

Year

2010

Abstract

Similarity measures, such as the ones of Jaccard, Dice, or Cosine, measure the similarity between two vectors. A good property for similarity measures would be that, if we add a constant vector to both vectors, then the similarity must increase. We show that Dice and Jaccard satisfy this property while Cosine and both overlap measures do not. Adding a constant vector is called, in Lorenz concentration theory, "nominal increase" and we show that the stronger "transfer principle" is not a required good property for similarity measures. Another good property is that, when we have two vectors and if we add one of these vectors to both vectors, then the similarity must increase. Now Dice, Jaccard, Cosine, and one of the overlap measures satisfy this property, while the other overlap measure does not. Also a variant of this latter property is studied.

Similar documents (author)

1. Egghe, L.: Little science, big science and beyond (1994) 4.71

   4.7136316 = sum of:
     4.7136316 = weight(author_txt:egghe in 6883) [ClassicSimilarity], result of:
       4.7136316 = fieldWeight in 6883, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.5418105 = idf(docFreq=60, maxDocs=42306)
         0.625 = fieldNorm(doc=6883)
   

2. Egghe, L.: Expansion of the field of informetrics : the second special issue (2006) 4.71

   4.7136316 = sum of:
     4.7136316 = weight(author_txt:egghe in 7119) [ClassicSimilarity], result of:
       4.7136316 = fieldWeight in 7119, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.5418105 = idf(docFreq=60, maxDocs=42306)
         0.625 = fieldNorm(doc=7119)
   

3. Egghe, L.: Expansion of the field of informetrics : origins and consequences (2005) 4.71

   4.7136316 = sum of:
     4.7136316 = weight(author_txt:egghe in 1979) [ClassicSimilarity], result of:
       4.7136316 = fieldWeight in 1979, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.5418105 = idf(docFreq=60, maxDocs=42306)
         0.625 = fieldNorm(doc=1979)
   

4. Egghe, L.: ¬The amount of actions needed for shelving and reshelving (1996) 4.71

   4.7136316 = sum of:
     4.7136316 = weight(author_txt:egghe in 4463) [ClassicSimilarity], result of:
       4.7136316 = fieldWeight in 4463, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.5418105 = idf(docFreq=60, maxDocs=42306)
         0.625 = fieldNorm(doc=4463)
   

5. Egghe, L.: Special features of the author - publication relationship and a new explanation of Lotka's law based on convolution theory (1994) 4.71

   4.7136316 = sum of:
     4.7136316 = weight(author_txt:egghe in 5137) [ClassicSimilarity], result of:
       4.7136316 = fieldWeight in 5137, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.5418105 = idf(docFreq=60, maxDocs=42306)
         0.625 = fieldNorm(doc=5137)
   

Similar documents (content)

1. Egghe, L.: New relations between similarity measures for vectors based on vector norms (2009) 1.00

   1.0001072 = sum of:
     1.0001072 = product of:
       2.0835567 = sum of:
         0.020039216 = weight(abstract_txt:while in 528) [ClassicSimilarity], result of:
           0.020039216 = score(doc=528,freq=1.0), product of:
             0.056735855 = queryWeight, product of:
               1.1588502 = boost
               4.5209856 = idf(docFreq=1250, maxDocs=42306)
               0.0108292205 = queryNorm
             0.353202 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.5209856 = idf(docFreq=1250, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.006032237 = weight(abstract_txt:that in 528) [ClassicSimilarity], result of:
           0.006032237 = score(doc=528,freq=1.0), product of:
             0.032106973 = queryWeight, product of:
               1.2328583 = boost
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0108292205 = queryNorm
             0.18787934 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.060405686 = weight(abstract_txt:measure in 528) [ClassicSimilarity], result of:
           0.060405686 = score(doc=528,freq=3.0), product of:
             0.082088426 = queryWeight, product of:
               1.3939252 = boost
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.0108292205 = queryNorm
             0.7358612 = fieldWeight in 528, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.059858885 = weight(abstract_txt:vector in 528) [ClassicSimilarity], result of:
           0.059858885 = score(doc=528,freq=1.0), product of:
             0.11767644 = queryWeight, product of:
               1.6689497 = boost
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.0108292205 = queryNorm
             0.5086735 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.07495717 = weight(abstract_txt:constant in 528) [ClassicSimilarity], result of:
           0.07495717 = score(doc=528,freq=1.0), product of:
             0.13671386 = queryWeight, product of:
               1.7988907 = boost
               7.0179553 = idf(docFreq=102, maxDocs=42306)
               0.0108292205 = queryNorm
             0.54827774 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.0179553 = idf(docFreq=102, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.10887873 = weight(abstract_txt:overlap in 528) [ClassicSimilarity], result of:
           0.10887873 = score(doc=528,freq=1.0), product of:
             0.20072258 = queryWeight, product of:
               2.6695757 = boost
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.0108292205 = queryNorm
             0.5424339 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.30411148 = weight(abstract_txt:cosine in 528) [ClassicSimilarity], result of:
           0.30411148 = score(doc=528,freq=4.0), product of:
             0.25078568 = queryWeight, product of:
               2.983977 = boost
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.0108292205 = queryNorm
             1.2126349 = fieldWeight in 528, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.32213697 = weight(abstract_txt:jaccard in 528) [ClassicSimilarity], result of:
           0.32213697 = score(doc=528,freq=2.0), product of:
             0.32833555 = queryWeight, product of:
               3.414311 = boost
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0108292205 = queryNorm
             0.9811212 = fieldWeight in 528, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.27499235 = weight(abstract_txt:dice in 528) [ClassicSimilarity], result of:
           0.27499235 = score(doc=528,freq=1.0), product of:
             0.37226135 = queryWeight, product of:
               3.635533 = boost
               9.45546 = idf(docFreq=8, maxDocs=42306)
               0.0108292205 = queryNorm
             0.7387078 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.45546 = idf(docFreq=8, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.25684676 = weight(abstract_txt:measures in 528) [ClassicSimilarity], result of:
           0.25684676 = score(doc=528,freq=6.0), product of:
             0.24662843 = queryWeight, product of:
               4.1848574 = boost
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.0108292205 = queryNorm
             1.041432 = fieldWeight in 528, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.44605607 = weight(abstract_txt:vectors in 528) [ClassicSimilarity], result of:
           0.44605607 = score(doc=528,freq=3.0), product of:
             0.42247695 = queryWeight, product of:
               5.0 = boost
               7.8025365 = idf(docFreq=46, maxDocs=42306)
               0.0108292205 = queryNorm
             1.0558116 = fieldWeight in 528, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               7.8025365 = idf(docFreq=46, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
         0.14924103 = weight(abstract_txt:similarity in 528) [ClassicSimilarity], result of:
           0.14924103 = score(doc=528,freq=1.0), product of:
             0.32851255 = queryWeight, product of:
               5.2168517 = boost
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0108292205 = queryNorm
             0.45429325 = fieldWeight in 528, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.078125 = fieldNorm(doc=528)
       0.48 = coord(12/25)
   

2. Egghe, L.: Properties of the n-overlap vector and n-overlap similarity theory (2006) 0.40

   0.40207884 = sum of:
     0.40207884 = product of:
       1.005197 = sum of:
         0.045575056 = weight(abstract_txt:concentration in 1320) [ClassicSimilarity], result of:
           0.045575056 = score(doc=1320,freq=1.0), product of:
             0.090368815 = queryWeight, product of:
               1.034172 = boost
               8.069165 = idf(docFreq=35, maxDocs=42306)
               0.0108292205 = queryNorm
             0.5043228 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.069165 = idf(docFreq=35, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.08983698 = weight(abstract_txt:lorenz in 1320) [ClassicSimilarity], result of:
           0.08983698 = score(doc=1320,freq=2.0), product of:
             0.11276142 = queryWeight, product of:
               1.1552175 = boost
               9.013627 = idf(docFreq=13, maxDocs=42306)
               0.0108292205 = queryNorm
             0.7966996 = fieldWeight in 1320, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               9.013627 = idf(docFreq=13, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.0048257895 = weight(abstract_txt:that in 1320) [ClassicSimilarity], result of:
           0.0048257895 = score(doc=1320,freq=1.0), product of:
             0.032106973 = queryWeight, product of:
               1.2328583 = boost
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0108292205 = queryNorm
             0.15030347 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.014678399 = weight(abstract_txt:both in 1320) [ClassicSimilarity], result of:
           0.014678399 = score(doc=1320,freq=1.0), product of:
             0.0612388 = queryWeight, product of:
               1.4745431 = boost
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.0108292205 = queryNorm
             0.23969117 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.09577421 = weight(abstract_txt:vector in 1320) [ClassicSimilarity], result of:
           0.09577421 = score(doc=1320,freq=4.0), product of:
             0.11767644 = queryWeight, product of:
               1.6689497 = boost
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.0108292205 = queryNorm
             0.8138776 = fieldWeight in 1320, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.04715394 = weight(abstract_txt:increase in 1320) [ClassicSimilarity], result of:
           0.04715394 = score(doc=1320,freq=1.0), product of:
             0.13332744 = queryWeight, product of:
               2.1757245 = boost
               5.658723 = idf(docFreq=400, maxDocs=42306)
               0.0108292205 = queryNorm
             0.35367018 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.658723 = idf(docFreq=400, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.24636444 = weight(abstract_txt:overlap in 1320) [ClassicSimilarity], result of:
           0.24636444 = score(doc=1320,freq=8.0), product of:
             0.20072258 = queryWeight, product of:
               2.6695757 = boost
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.0108292205 = queryNorm
             1.2273878 = fieldWeight in 1320, product of:
               2.828427 = tf(freq=8.0), with freq of:
                 8.0 = termFreq=8.0
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.2577096 = weight(abstract_txt:jaccard in 1320) [ClassicSimilarity], result of:
           0.2577096 = score(doc=1320,freq=2.0), product of:
             0.32833555 = queryWeight, product of:
               3.414311 = boost
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0108292205 = queryNorm
             0.78489697 = fieldWeight in 1320, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.0838858 = weight(abstract_txt:measures in 1320) [ClassicSimilarity], result of:
           0.0838858 = score(doc=1320,freq=1.0), product of:
             0.24662843 = queryWeight, product of:
               4.1848574 = boost
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.0108292205 = queryNorm
             0.34013027 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
         0.119392835 = weight(abstract_txt:similarity in 1320) [ClassicSimilarity], result of:
           0.119392835 = score(doc=1320,freq=1.0), product of:
             0.32851255 = queryWeight, product of:
               5.2168517 = boost
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0108292205 = queryNorm
             0.3634346 = fieldWeight in 1320, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0625 = fieldNorm(doc=1320)
       0.4 = coord(10/25)
   

3. Eck, N.J. van; Waltman, L.: How to normalize cooccurrence data? : an analysis of some well-known similarity measures (2009) 0.39

   0.39352095 = sum of:
     0.39352095 = product of:
       1.229753 = sum of:
         0.020039216 = weight(abstract_txt:while in 762) [ClassicSimilarity], result of:
           0.020039216 = score(doc=762,freq=1.0), product of:
             0.056735855 = queryWeight, product of:
               1.1588502 = boost
               4.5209856 = idf(docFreq=1250, maxDocs=42306)
               0.0108292205 = queryNorm
             0.353202 = fieldWeight in 762, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.5209856 = idf(docFreq=1250, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.008530871 = weight(abstract_txt:that in 762) [ClassicSimilarity], result of:
           0.008530871 = score(doc=762,freq=2.0), product of:
             0.032106973 = queryWeight, product of:
               1.2328583 = boost
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0108292205 = queryNorm
             0.2657015 = fieldWeight in 762, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.06975049 = weight(abstract_txt:measure in 762) [ClassicSimilarity], result of:
           0.06975049 = score(doc=762,freq=4.0), product of:
             0.082088426 = queryWeight, product of:
               1.3939252 = boost
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.0108292205 = queryNorm
             0.8496994 = fieldWeight in 762, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.018348 = weight(abstract_txt:both in 762) [ClassicSimilarity], result of:
           0.018348 = score(doc=762,freq=1.0), product of:
             0.0612388 = queryWeight, product of:
               1.4745431 = boost
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.0108292205 = queryNorm
             0.29961395 = fieldWeight in 762, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.21503928 = weight(abstract_txt:cosine in 762) [ClassicSimilarity], result of:
           0.21503928 = score(doc=762,freq=2.0), product of:
             0.25078568 = queryWeight, product of:
               2.983977 = boost
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.0108292205 = queryNorm
             0.85746235 = fieldWeight in 762, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.32213697 = weight(abstract_txt:jaccard in 762) [ClassicSimilarity], result of:
           0.32213697 = score(doc=762,freq=2.0), product of:
             0.32833555 = queryWeight, product of:
               3.414311 = boost
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0108292205 = queryNorm
             0.9811212 = fieldWeight in 762, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.27742618 = weight(abstract_txt:measures in 762) [ClassicSimilarity], result of:
           0.27742618 = score(doc=762,freq=7.0), product of:
             0.24662843 = queryWeight, product of:
               4.1848574 = boost
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.0108292205 = queryNorm
             1.1248751 = fieldWeight in 762, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
         0.29848206 = weight(abstract_txt:similarity in 762) [ClassicSimilarity], result of:
           0.29848206 = score(doc=762,freq=4.0), product of:
             0.32851255 = queryWeight, product of:
               5.2168517 = boost
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0108292205 = queryNorm
             0.9085865 = fieldWeight in 762, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.078125 = fieldNorm(doc=762)
       0.32 = coord(8/25)
   

4. Rorvig, M.: Images of similarity : a visual exploration of optimal similarity metrics and scaling properties of TREC topic-document sets (1999) 0.28

   0.2826516 = sum of:
     0.2826516 = product of:
       1.00947 = sum of:
         0.008445132 = weight(abstract_txt:that in 4768) [ClassicSimilarity], result of:
           0.008445132 = score(doc=4768,freq=1.0), product of:
             0.032106973 = queryWeight, product of:
               1.2328583 = boost
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0108292205 = queryNorm
             0.26303107 = fieldWeight in 4768, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.04882534 = weight(abstract_txt:measure in 4768) [ClassicSimilarity], result of:
           0.04882534 = score(doc=4768,freq=1.0), product of:
             0.082088426 = queryWeight, product of:
               1.3939252 = boost
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.0108292205 = queryNorm
             0.59478956 = fieldWeight in 4768, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.438076 = idf(docFreq=499, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.08380244 = weight(abstract_txt:vector in 4768) [ClassicSimilarity], result of:
           0.08380244 = score(doc=4768,freq=1.0), product of:
             0.11767644 = queryWeight, product of:
               1.6689497 = boost
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.0108292205 = queryNorm
             0.7121429 = fieldWeight in 4768, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.5110207 = idf(docFreq=170, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.15243022 = weight(abstract_txt:overlap in 4768) [ClassicSimilarity], result of:
           0.15243022 = score(doc=4768,freq=1.0), product of:
             0.20072258 = queryWeight, product of:
               2.6695757 = boost
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.0108292205 = queryNorm
             0.75940746 = fieldWeight in 4768, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.943154 = idf(docFreq=110, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.21287803 = weight(abstract_txt:cosine in 4768) [ClassicSimilarity], result of:
           0.21287803 = score(doc=4768,freq=1.0), product of:
             0.25078568 = queryWeight, product of:
               2.983977 = boost
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.0108292205 = queryNorm
             0.84884447 = fieldWeight in 4768, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.20760675 = weight(abstract_txt:measures in 4768) [ClassicSimilarity], result of:
           0.20760675 = score(doc=4768,freq=2.0), product of:
             0.24662843 = queryWeight, product of:
               4.1848574 = boost
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.0108292205 = queryNorm
             0.8417795 = fieldWeight in 4768, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.4420843 = idf(docFreq=497, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
         0.29548216 = weight(abstract_txt:similarity in 4768) [ClassicSimilarity], result of:
           0.29548216 = score(doc=4768,freq=2.0), product of:
             0.32851255 = queryWeight, product of:
               5.2168517 = boost
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0108292205 = queryNorm
             0.8994547 = fieldWeight in 4768, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.109375 = fieldNorm(doc=4768)
       0.28 = coord(7/25)
   

5. Ku, C.-H.; Leroy, G.: ¬A crime reports analysis system to identify related crimes (2011) 0.26

   0.2579257 = sum of:
     0.2579257 = product of:
       0.9211632 = sum of:
         0.017614914 = weight(abstract_txt:then in 1630) [ClassicSimilarity], result of:
           0.017614914 = score(doc=1630,freq=1.0), product of:
             0.060413055 = queryWeight, product of:
               1.1958147 = boost
               4.665194 = idf(docFreq=1082, maxDocs=42306)
               0.0108292205 = queryNorm
             0.29157463 = fieldWeight in 1630, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.665194 = idf(docFreq=1082, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.006824697 = weight(abstract_txt:that in 1630) [ClassicSimilarity], result of:
           0.006824697 = score(doc=1630,freq=2.0), product of:
             0.032106973 = queryWeight, product of:
               1.2328583 = boost
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0108292205 = queryNorm
             0.2125612 = fieldWeight in 1630, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4048555 = idf(docFreq=10381, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.014678399 = weight(abstract_txt:both in 1630) [ClassicSimilarity], result of:
           0.014678399 = score(doc=1630,freq=1.0), product of:
             0.0612388 = queryWeight, product of:
               1.4745431 = boost
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.0108292205 = queryNorm
             0.23969117 = fieldWeight in 1630, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.8350587 = idf(docFreq=2483, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.121644594 = weight(abstract_txt:cosine in 1630) [ClassicSimilarity], result of:
           0.121644594 = score(doc=1630,freq=1.0), product of:
             0.25078568 = queryWeight, product of:
               2.983977 = boost
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.0108292205 = queryNorm
             0.485054 = fieldWeight in 1630, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.760864 = idf(docFreq=48, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.1822282 = weight(abstract_txt:jaccard in 1630) [ClassicSimilarity], result of:
           0.1822282 = score(doc=1630,freq=1.0), product of:
             0.32833555 = queryWeight, product of:
               3.414311 = boost
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0108292205 = queryNorm
             0.55500597 = fieldWeight in 1630, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.8800955 = idf(docFreq=15, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.21999387 = weight(abstract_txt:dice in 1630) [ClassicSimilarity], result of:
           0.21999387 = score(doc=1630,freq=1.0), product of:
             0.37226135 = queryWeight, product of:
               3.635533 = boost
               9.45546 = idf(docFreq=8, maxDocs=42306)
               0.0108292205 = queryNorm
             0.5909662 = fieldWeight in 1630, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.45546 = idf(docFreq=8, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
         0.35817853 = weight(abstract_txt:similarity in 1630) [ClassicSimilarity], result of:
           0.35817853 = score(doc=1630,freq=9.0), product of:
             0.32851255 = queryWeight, product of:
               5.2168517 = boost
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0108292205 = queryNorm
             1.0903039 = fieldWeight in 1630, product of:
               3.0 = tf(freq=9.0), with freq of:
                 9.0 = termFreq=9.0
               5.814954 = idf(docFreq=342, maxDocs=42306)
               0.0625 = fieldNorm(doc=1630)
       0.28 = coord(7/25)