Citation patterns

Every vertex in a patent citation network has its publication year. Temporal received citation distributions can be constructed for each vertex (patent). As noted in Section 5.6.3, the number of citations received by a patent carries information about its importance, its usefulness, and its value for other inventions for which subsequent patents are granted. These citation counts can change as new patents are granted and added to the patent citation network. Examining the number of citations received by patents through time provides additional information about patent contents. Some patents are cited more when they are younger compared to other patents. Others are cited when they are older. The received citations for some patents grow

The indegree citation distribution for patents from 1976 with at least one citation.

Figure 5.18 The indegree citation distribution for patents from 1976 with at least one citation.

over time while those received by others decline. Of course, many other temporal patterns of received citations are possible. An interesting feature of all patents is when they are used after being noticed. Research is a very dynamic activity. As research foci in technological areas change over time, information about the distribution of received citations provide clues about the development of broad technological research areas.

Each patent has its own (changing) received citation pattern. To obtain a general sense of these patterns, it is useful to cluster them into a small set of clusters, each with a distinctive pattern. One exploratory approach is to cluster symbolic data objects as described in Section 3.10. The dataset we use here contains all patents granted in 1976: 65,054 patents received at least one citation through 2006 after each patent had existed for 31 years. Figure 5.18 shows the distribution of these patents and the number of citations they received. This distribution is almost scale-free, a typical characteristic of many distributions of received citations in citation networks (Newman 2003, 2005). As a result, our dataset disproportionately has more units with low citation levels.[1] However, seldom-cited patents are unlikely to be important: their patented inventions have little impact on subsequent inventions for which patents were granted. Attempting to get a better sense of changes in technological areas requires attention to those patents cited more often. Seldom cited patents were therefore excluded. Somewhat arbitrarily, we restricted our analysis to patents cited at least 20 times.

Given patent granting years, after which patents can be cited, a temporal citation frequency distribution can be created:

where ff represents the number of citations for patent p in z'-th year. Here, q is the number of years for which citations are observed. For this analysis, q = 31. When clustering symbolic data, such distributions need not be converted (e.g. normalized with respect to the number of citations). The count of citations received has a meaningful metric of direct interest when studying received citation distributions. To cluster these distributions we combined the adapted leader method with the hierarchical clustering approach.

Patents from 1976, cited through to 2006

Restricting attention to patents with at least 20 citations over 31 years reduced the number of units to 6774 patents. In the first step, 40 clusters were obtained with the adapted leaders algorithm (using <53 = (pj - tj)2/tj as the error measure (dissimilarity) where Pj denotes the relative size of the variable, and its component j, and tj represents the cluster representative (leader) for variable's component j). Since the adapted leaders algorithm is based on local optimization, the procedure was repeated 100 times: the best result- the clustering with the smallest error (having the lowest values of P(C))- was retained. Figures 5.19 and 5.20 show

Leaders for the first 20 clusters using leaders algorithm with <53 as the error measure.

Figure 5.19 Leaders for the first 20 clusters using leaders algorithm with <53 as the error measure.

The units are all patents from year 1976 receiving at least 20 citations over 31 years. Lines are used instead of dots for greater visual clarity

Leaders for the second 20 clusters using leaders algorithm with <53 as the error measure.

Figure 5.20 Leaders for the second 20 clusters using leaders algorithm with <53 as the error measure.

the profiles of these 40 leaders. Each box in these figures shows a profile for temporal patterns for received citations. These 40 profiles can be interpreted separately. Patents in the top left box of Figure 5.19 had an increase in citations shortly after their publication years. Thereafter, their citations dropped and remained low. In the second box on the top row of Figure 5.19, these patents had slow steady increases in citations before a sharper increase started around 2003. Moving to the next box, a steady level of citations to these patents was interrupted by a spike in the late 1980s. In the final box in the top row of this figure, the patents had a sharp jump in received citations shortly after they were granted. This level of citations was sustained for a few years before dropping sharply. The third box in the third row of Figure 5.19 has a profile for patents having a modest level of citations before the citations skyrocketed in the early 2000s. While interpreting every profile is possible, this gets to be tedious. Also, there are some commonalities across subsets of profiles. It is more efficient to cluster these profiles in a second step. More importantly, interpreting these clusters is straightforward and provides a more general (and easily digestible) summary of the patterns in the patent citation profiles.

Dendrogram for hierarchical clustering on the 40 leaders with <53 as the error measure, 1976-2006.

Figure 5.21 Dendrogram for hierarchical clustering on the 40 leaders with <53 as the error measure, 1976-2006.

The four summary leader patterns are shown below the corresponding red boxes of the dendrogram.

The 40 profiles in Figures 5.19 and 5.20 were, in the second step, clustered by using the adapted hierarchical algorithm (using the <53 error measure). The dendrogram is presented in Figure 5.21. The partition into four clusters, marked with red boxes, is very clear. For each of these clusters, the summarized profiles of the leaders are shown below the dendrogram. These profiles differ: these differences merit closer attention.

The first (leftmost) pattern is for patents being very popular soon after they were granted: they had an early impact. Thereafter, interest in them decayed slowly over time. Even so, they were still being cited at a modest level 31 years after they were granted. The second pattern differs dramatically. Patents with this profile did not have a dramatic early impact. Yet the

Example profiles of patents in each identified 1976 patent cluster.

Figure 5.22 Example profiles of patents in each identified 1976 patent cluster.

growth of interest in them was maintained over a longer period before dropping. However, despite this drop, interest in them in 2006 was above the interest in patents of the first cluster.

Patents in the third cluster had an early rise in interest, reaching a peak between the peaks in early interest for the first two clusters. The salient feature of this profile is that interest in these patents was sustained at a high level for longer than the patents in the second cluster. In contrast to the patents in the second cluster, starting shortly before 2000, interest in these patents plummeted to near zero levels. Patents in the fourth cluster enjoyed the same rise in initial interest. But interest stayed at a lower level, even dropping slightly, before taking off to finish at a high level of interest. This takeoff coincided with the drop of interest in the patents of the second cluster.

Figure 5.22 shows the actual temporal profiles of four patents with one from each 1976 patent cluster in the same order of the clusters shown in Figure 5.21. The profiles are more jagged than the smoothed profiles shown in Figure 5.21. The first patent, number 3,940,941, was issued for the invention of new anchor bolts and a new method for installing them in order to strengthen the roofs of underground mines. It belongs to the broad method category and the two-digit mechanical area. Issued to a French company, it had high citation volumes shortly after it was granted with the citations to it diminishing thereafter. The second patent, number 3,995,216, shown in Figure 5.22, was granted to IBM for an apparatus designed to measure the number of surface states at or near the insulator-semiconductor interface in a metal-insulator semiconductor. It belongs to the method and computers and communication categories. It had two separated spikes in received citations during the time period considered.

The third profile is patent number 3,955,280 issued to an Israeli inventor for a new type of dental implant capable of absorbing the shocks associated with chewing. It belongs to the articles of manufacture and drugs and medical categories. This invention had a single spike of received citations coupled to citations around this peak. The final patent in this figure, number 3,987,580, was granted for a separably connective toy with separate geometric flexible parts. This patent belongs to the articles of manufacture the others (as an amusement device) categories. It had a moderate citation level before spiking at the end of this time period.

Utilizing supplementary variables for 1976 patents

The clusters obtained in Section 5.7.1 can be further characterized by using supplementary materials in the form of patent variables. We examined differences between the variable distribution of the whole dataset and the variable distributions within each cluster. We present results for using 1) the two-sample Kolmogorov-Smirnov test (Bickel and Doksum, 1977) for numerical variables, and 2) Pearson's x1 test °f independence for the categorical variables. We note some potential drawbacks. Using the Pearson's x1 test with more than

Table 5.4 p-values for Kolmogorov-Smirnov statistical tests for the four final 1976 clusters.

p-values for Kolmogorov-Smirnov statistical tests for the four final 1976 clusters

Citations received and generality for the four clusters of Figure 5.21.

Figure 5.23 Citations received and generality for the four clusters of Figure 5.21.

Left panel: citation distributions for the four clusters and overall (black solid line), Right panel: empirical cumulative distribution functions for generality in all four cluster and overall (black solid line).

two categories has the risk of leading often to significant differences. Having large clusters can lead also to significant results. With the Kolmogorov-Smirnov test, small deviations between two variables can be deemed significant. Caution is merited in interpreting these results to avoid over-interpreting them.[2]

Variables available in the patent dataset (Section 5.3) include the number of citations received and measures of generality. Unfortunately, for patents granted in 1976, information about citations made, measures of heterogeneity, and the percentage of self-citation did not exist.36 Table 5.4 shows the p-values for eight statistical tests (four for the number of citations and four for generality). For judging significance, a = 0.005. All four clusters differ significantly in the overall number of received citations (Table 5.4). The left panel of Figure 5.23 show similarities in the sense of having peak citation levels of 30 or more. Cluster 3 has the highest relative frequency at 31 citations, Cluster 1 has it at 33, with the other two clusters having their peaks at 30. However, interpreting these profiles is better done in conjunction with the profiles in Figure 5.21. Cluster 1 has patents with the largest received number of citations which came mainly in the first half of 1976-2006. Cluster 3 also includes many more well-cited patents distributed more evenly over time. Given the results in Table 5.4, this is the only cluster where generality needs to be considered. According to the right panel of Figure 5.23 it was less general: it has the only line slightly above the overall line.[3] This may be related to the sharp drop of citations over the last eight years.

  • [1] This holds also for patents granted in other years.
  • [2] Also, when making multiple statistical tests with the same dataset, the chances of getting at least one statistically significant result increase. Since the issue is not a standard multiple comparison test, one possibility to use is the idea of the Bonferroni correction and use much smaller a values than a = 0.05 or a = 0.01. We use a = 0.005. 36 In Section 5.7.2, we do include these additional variables for patents granted in 1987.
  • [3] From the result of the statistical test alone, the direction of the deviation was not known.
 
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