Search (34 results, page 2 of 2)

0.0022374375 = product of:
  0.004474875 = sum of:
    0.004474875 = product of:
      0.00894975 = sum of:
        0.00894975 = weight(_text_:a in 2067) [ClassicSimilarity], result of:
          0.00894975 = score(doc=2067,freq=14.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.1685276 = fieldWeight in 2067, product of:
              3.7416575 = tf(freq=14.0), with freq of:
                14.0 = termFreq=14.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0390625 = fieldNorm(doc=2067)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

In this paper, for the first time, we present global curves for the measures precision, recall, fallout and miss in function of the number of retrieved documents. Different curves apply for different retrieved systems, for which we give exact definitions in terms of a retrieval density function: perverse retrieval, perfect retrieval, random retrieval, normal retrieval, hereby extending results of Buckland and Gey and of Egghe in the following sense: mathematically more advanced methods yield a better insight into these curves, more types of retrieval are considered and, very importantly, the theory is developed for the "complete" set of measures: precision, recall, fallout and miss. Next we study the interrelationships between precision, recall, fallout and miss in these different types of retrieval, hereby again extending results of Buckland and Gey (incl. a correction) and of Egghe. In the case of normal retrieval we prove that precision in function of recall and recall in function of miss is a concavely decreasing relationship while recall in function of fallout is a concavely increasing relationship. We also show, by producing examples, that the relationships between fallout and precision, miss and precision and miss and fallout are not always convex or concave.

Type

a

0.0020714647 = product of:
  0.0041429293 = sum of:
    0.0041429293 = product of:
      0.008285859 = sum of:
        0.008285859 = weight(_text_:a in 3466) [ClassicSimilarity], result of:
          0.008285859 = score(doc=3466,freq=12.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15602624 = fieldWeight in 3466, product of:
              3.4641016 = tf(freq=12.0), with freq of:
                12.0 = termFreq=12.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0390625 = fieldNorm(doc=3466)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven. They are shown to characterize functions with the scalefree property (also called seif-similarity property) as weIl as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotka's law based on the exponential growth of articles in journals and of the number of journals. His argument is reproduced here and a discrete-time argument is also given, yielding the same law as that of Lotka. This argument makes it possible to interpret the information production process as a seif-similar fractal and show the relation between Lotka's exponent and the (seif-similar) fractal dimension of the system. Lotkaian informetric systems are seif-similar fractals, a fact revealed by Mandelbrot (1977) in relation to nature, but is also true for random texts, which exemplify a very special type of informetric system.

Type

a

0.0020296127 = product of:
  0.0040592253 = sum of:
    0.0040592253 = product of:
      0.008118451 = sum of:
        0.008118451 = weight(_text_:a in 7119) [ClassicSimilarity], result of:
          0.008118451 = score(doc=7119,freq=2.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15287387 = fieldWeight in 7119, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.09375 = fieldNorm(doc=7119)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Type

a

0.0020296127 = product of:
  0.0040592253 = sum of:
    0.0040592253 = product of:
      0.008118451 = sum of:
        0.008118451 = weight(_text_:a in 1910) [ClassicSimilarity], result of:
          0.008118451 = score(doc=1910,freq=2.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15287387 = fieldWeight in 1910, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.09375 = fieldNorm(doc=1910)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Type

a

0.0020296127 = product of:
  0.0040592253 = sum of:
    0.0040592253 = product of:
      0.008118451 = sum of:
        0.008118451 = weight(_text_:a in 5154) [ClassicSimilarity], result of:
          0.008118451 = score(doc=5154,freq=8.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15287387 = fieldWeight in 5154, product of:
              2.828427 = tf(freq=8.0), with freq of:
                8.0 = termFreq=8.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=5154)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

The notions aging, obsolescence, impact, growth, utilization, and their relations are studied. It is shown how to correct an observed citation distribution for growth, once the growth distribution is known. The relation of this correction procedure with the calculation of impact measures is explained. More interestingly, we have shown how the influence of growth on aging can be studied over a complete period as a whole. Here, the difference between the so-called average and global aging distributions is the main factor. Our main result is that growth can influence aging but that it does not cause aging. A short overview of some classical articles on this topic is given. Results of these earlier works are placed in the framework set up in this article

Type

a

0.0020296127 = product of:
  0.0040592253 = sum of:
    0.0040592253 = product of:
      0.008118451 = sum of:
        0.008118451 = weight(_text_:a in 3678) [ClassicSimilarity], result of:
          0.008118451 = score(doc=3678,freq=8.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15287387 = fieldWeight in 3678, product of:
              2.828427 = tf(freq=8.0), with freq of:
                8.0 = termFreq=8.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=3678)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

In this article concentration (i.e., inequality) aspects of the functions of Zipf and of Lotka are studied. Since both functions are power laws (i.e., they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf's law and Lotka's law, we prove that Price's law of concentration is equivalent with Zipf's law. A major part of this article is devoted to the development of continuous concentration theory, based an Lorenz curves. The Lorenz curve for power functions is calculated and, based an this, some important concentration measures such as the ones of Gini, Theil, and the variation coefficient. Using Lorenz curves, it is shown that the concentration of a power law increases with its exponent and this result is interpreted in terms of the functions of Zipf and Lotka.

Type

a

0.0020296127 = product of:
  0.0040592253 = sum of:
    0.0040592253 = product of:
      0.008118451 = sum of:
        0.008118451 = weight(_text_:a in 2011) [ClassicSimilarity], result of:
          0.008118451 = score(doc=2011,freq=8.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.15287387 = fieldWeight in 2011, product of:
              2.828427 = tf(freq=8.0), with freq of:
                8.0 = termFreq=8.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=2011)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

In an earlier paper [Egghe, L. (2004). A universal method of information retrieval evaluation: the "missing" link M and the universal IR surface. Information Processing and Management, 40, 21-30] we showed that, given an IR system, and if P denotes precision, R recall, F fallout and M miss (re-introduced in the paper mentioned above), we have the following relationship between P, R, F and M: P/(1-P)*(1-R)/R*F/(1-F)*(1-M)/M = 1. In this paper we prove the (more difficult) converse: given any four rational numbers in the interval ]0, 1[ satisfying the above equation, then there exists an IR system such that these four numbers (in any order) are the precision, recall, fallout and miss of this IR system. As a consequence we show that any three rational numbers in ]0, 1[ represent any three measures taken from precision, recall, fallout and miss of a certain IR system. We also show that this result is also true for two numbers instead of three.

Type

a

0.0018909799 = product of:
  0.0037819599 = sum of:
    0.0037819599 = product of:
      0.0075639198 = sum of:
        0.0075639198 = weight(_text_:a in 5157) [ClassicSimilarity], result of:
          0.0075639198 = score(doc=5157,freq=10.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.14243183 = fieldWeight in 5157, product of:
              3.1622777 = tf(freq=10.0), with freq of:
                10.0 = termFreq=10.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0390625 = fieldNorm(doc=5157)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

Measurement of the degree of interconnectedness in graph like networks of hyperlinks or citations can indicate the existence of research fields and assist in comparative evaluation of research efforts. In this issue we begin with Egghe and Rousseau who review compactness measures and investigate the compactness of a network as a weighted graph with dissimilarity values characterizing the arcs between nodes. They make use of a generalization of the Botofogo, Rivlin, Shneiderman, (BRS) compaction measure which treats the distance between unreachable nodes not as infinity but rather as the number of nodes in the network. The dissimilarity values are determined by summing the reciprocals of the weights of the arcs in the shortest chain between two nodes where no weight is smaller than one. The BRS measure is then the maximum value for the sum of the dissimilarity measures less the actual sum divided by the difference between the maximum and minimum. The Wiener index, the sum of all elements in the dissimilarity matrix divided by two, is then computed for Small's particle physics co-citation data as well as the BRS measure, the dissimilarity values and shortest paths. The compactness measure for the weighted network is smaller than for the un-weighted. When the bibliographic coupling network is utilized it is shown to be less compact than the co-citation network which indicates that the new measure produces results that confirm to an obvious case.

Type

a

0.0018909799 = product of:
  0.0037819599 = sum of:
    0.0037819599 = product of:
      0.0075639198 = sum of:
        0.0075639198 = weight(_text_:a in 194) [ClassicSimilarity], result of:
          0.0075639198 = score(doc=194,freq=10.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.14243183 = fieldWeight in 194, product of:
              3.1622777 = tf(freq=10.0), with freq of:
                10.0 = termFreq=10.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0390625 = fieldNorm(doc=194)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

In the first part of this article the author defines the n-overlap vector whose coordinates consist of the fraction of the objects (e.g., books, N-grams, etc.) that belong to 1, 2, , n sets (more generally: families) (e.g., libraries, databases, etc.). With the aid of the Lorenz concentration theory, a theory of n-overlap similarity is conceived together with corresponding measures, such as the generalized Jaccard index (generalizing the well-known Jaccard index in case n 5 2). Next, the distributional form of the n-overlap vector is determined assuming certain distributions of the object's and of the set (family) sizes. In this section the decreasing power law and decreasing exponential distribution is explained for the n-overlap vector. Both item (token) n-overlap and source (type) n-overlap are studied. The n-overlap properties of objects indexed by a hierarchical system (e.g., books indexed by numbers from a UDC or Dewey system or by N-grams) are presented in the final section. The author shows how the results given in the previous section can be applied as well as how the Lorenz order of the n-overlap vector is respected by an increase or a decrease of the level of refinement in the hierarchical system (e.g., the value N in N-grams).

Type

a

0.001757696 = product of:
  0.003515392 = sum of:
    0.003515392 = product of:
      0.007030784 = sum of:
        0.007030784 = weight(_text_:a in 1878) [ClassicSimilarity], result of:
          0.007030784 = score(doc=1878,freq=6.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.13239266 = fieldWeight in 1878, product of:
              2.4494898 = tf(freq=6.0), with freq of:
                6.0 = termFreq=6.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=1878)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

In this article, for any group of authors, we define three different h-indices. First, there is the successive h-index h2 based on the ranked list of authors and their h-indices h1 as defined by Schubert (2007). Next, there is the h-index hP based on the ranked list of authors and their number of publications. Finally, there is the h-index hC based on the ranked list of authors and their number of citations. We present formulae for these three indices in Lotkaian informetrics from which it also follows that h2 < hp < hc. We give a concrete example of a group of 167 authors on the topic optical flow estimation. Besides these three h-indices, we also calculate the two-by-two Spearman rank correlation coefficient and prove that these rankings are significantly related.

Type

a

0.001674345 = product of:
  0.00334869 = sum of:
    0.00334869 = product of:
      0.00669738 = sum of:
        0.00669738 = weight(_text_:a in 2531) [ClassicSimilarity], result of:
          0.00669738 = score(doc=2531,freq=4.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.12611452 = fieldWeight in 2531, product of:
              2.0 = tf(freq=4.0), with freq of:
                4.0 = termFreq=4.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0546875 = fieldNorm(doc=2531)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

It is shown that vector information retrieval (IR) and general fuzzy IR uses two types of fuzzy set operations: the original "Zadeh min-max operations" and the so-called "probabilistic sum and algebraic product operations". The universal IR surface, valid for classical 0-1 IR (i.e. where ordinary sets are used) and used in IR evaluation, is extended to and reproved for vector IR, using the probabilistic sum and algebraic product model. We also show (by counterexample) that, using the "Zadeh min-max" fuzzy model, yields a breakdown of this IR surface.

Type

a

0.0014351527 = product of:
  0.0028703054 = sum of:
    0.0028703054 = product of:
      0.005740611 = sum of:
        0.005740611 = weight(_text_:a in 4384) [ClassicSimilarity], result of:
          0.005740611 = score(doc=4384,freq=4.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.10809815 = fieldWeight in 4384, product of:
              2.0 = tf(freq=4.0), with freq of:
                4.0 = termFreq=4.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=4384)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

One aim of science evaluation studies is to determine quantitatively the contribution of different players (authors, departments, countries) to the whole system. This information is then used to study the evolution of the system, for instance to gauge the results of special national or international programs. Taking articles as our basic data, we want to determine the exact relative contribution of each coauthor or each country. These numbers are brought together to obtain country scores, or department scores, etc. It turns out, as we will show in this article, that different scoring methods can yield totally different rankings. Conseqeuntly, a ranking between countries, universities, research groups or authors, based on one particular accrediting methods does not contain an absolute truth about their relative importance

Type

a

0.0014351527 = product of:
  0.0028703054 = sum of:
    0.0028703054 = product of:
      0.005740611 = sum of:
        0.005740611 = weight(_text_:a in 3464) [ClassicSimilarity], result of:
          0.005740611 = score(doc=3464,freq=4.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.10809815 = fieldWeight in 3464, product of:
              2.0 = tf(freq=4.0), with freq of:
                4.0 = termFreq=4.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046875 = fieldNorm(doc=3464)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, ... items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.

Type

a

8.4567186E-4 = product of:
  0.0016913437 = sum of:
    0.0016913437 = product of:
      0.0033826875 = sum of:
        0.0033826875 = weight(_text_:a in 4217) [ClassicSimilarity], result of:
          0.0033826875 = score(doc=4217,freq=2.0), product of:
            0.053105544 = queryWeight, product of:
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.046056706 = queryNorm
            0.06369744 = fieldWeight in 4217, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              1.153047 = idf(docFreq=37942, maxDocs=44218)
              0.0390625 = fieldNorm(doc=4217)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Type

a