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Fig. 10. The 5 most significant normalized semantic relations sequences for those HBC association: that map onto a path of two and three steps in WN.

Figure 10 The 5 most significant normalized semantic relations sequences for those HBC association: that map onto a path of two and three steps in WN.

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Fig. 1. Graphical representation of the word association network obtained from the HBC dataset. Labeled nodes represent the first 5,000 words entered in the system while arcs represent word associations. Label colors distinguish different parts of speech (nouns, verbs, etc). Arcs’ width codes the weight of the corresponding association, i.e., how many people ever made that association.
Fig. 1. Graphical representation of the word association network obtained from the HBC dataset. Labeled nodes represent the first 5,000 words entered in the system while arcs represent word associations. Label colors distinguish different parts of speech (nouns, verbs, etc). Arcs’ width codes the weight of the corresponding association, i.e., how many people ever made that association.
Fig. 2. The log-binned degree distributions for the word association networks of HBC and SF, in log-log scale. Since we are matching datasets of different sizes we divided the degree by the average degree value. In red, the in-degree distributions for HBC (filled circles) and for SF (empty circles). In blue, the out-degree distributions for HBC (filled squares) and for SF (empty squares). Both in-degree distributions show a power law form (a straight line in log-log). Both out-degree distributions have a scale-rich shape. The different in shape at lower degrees is a consequence of the filtering procedure described in Appendix A. associations were present in the HBC dataset. To deepen our analysis, we consider for each word w the set of associations in which w was proposed as a cue word to players, and define the out-strength sou4(w) of the corresponding node as the total number of associations in which w was the cue, and the out-degree kou:(w) as the number of distinct target words answered in response to w. Analogously, we define the in-strength s;,(w) and the in-degree k;,(w) by referring to the associations in which w was answered as target: $;n(w) is the total number of times that w appears as a target, and k;,(w) is the number of distinct other words which yielded w as an answer. the in-strength s;,(w) and the in-degree kj,(w) by referring to the associations in
Fig. 2. The log-binned degree distributions for the word association networks of HBC and SF, in log-log scale. Since we are matching datasets of different sizes we divided the degree by the average degree value. In red, the in-degree distributions for HBC (filled circles) and for SF (empty circles). In blue, the out-degree distributions for HBC (filled squares) and for SF (empty squares). Both in-degree distributions show a power law form (a straight line in log-log). Both out-degree distributions have a scale-rich shape. The different in shape at lower degrees is a consequence of the filtering procedure described in Appendix A. associations were present in the HBC dataset. To deepen our analysis, we consider for each word w the set of associations in which w was proposed as a cue word to players, and define the out-strength sou4(w) of the corresponding node as the total number of associations in which w was the cue, and the out-degree kou:(w) as the number of distinct target words answered in response to w. Analogously, we define the in-strength s;,(w) and the in-degree k;,(w) by referring to the associations in which w was answered as target: $;n(w) is the total number of times that w appears as a target, and k;,(w) is the number of distinct other words which yielded w as an answer. the in-strength s;,(w) and the in-degree kj,(w) by referring to the associations in
Fig. 3. The log-binned strength distributions for the word association networks of HBC and SF, in log-log scale. Since we are matching datasets of different sizes we divided the strength with the average strength value. In red, the in-strength distributions for HBC (filled circles) and for SF (empty circles). In blue, the out-strength distributions for HBC (filled squares) and for SF (empty squares). Both in-strength distributions show a power law form (a straight line in log-log). The different shape at lower degrees is a consequence of the filtering procedure described in Appendix A. The out-strength distributions have a peaked but different shape, because of the different ways in which cue words were chosen.
Fig. 3. The log-binned strength distributions for the word association networks of HBC and SF, in log-log scale. Since we are matching datasets of different sizes we divided the strength with the average strength value. In red, the in-strength distributions for HBC (filled circles) and for SF (empty circles). In blue, the out-strength distributions for HBC (filled squares) and for SF (empty squares). Both in-strength distributions show a power law form (a straight line in log-log). The different shape at lower degrees is a consequence of the filtering procedure described in Appendix A. The out-strength distributions have a peaked but different shape, because of the different ways in which cue words were chosen.
Fig. 4. Average (kout) as a function of Sout (red), obtained by averaging the kout values of all those cue words with the same Sout value. The fitted curve obtained from Eq. (2) is shown in black (parameters: V ~ 74 and B ~ 0.92). Inset: same data in log-log scale together with a fit to a pure sub-linear power-law, to highlight the deviation from such a law at large Sout. contrary, the out-degree shows a Gammaz-like distribution peaked around a typical value kout & 28, corresponding therefore to a well-defined characteristic number of distinct words obtained as targets for each word inserted in the game as a cue. The distribution drops very rapidly at large kouz with a sharp cut-off around 100, indi- cating that the number of distinct words that humans spontaneously associate to a given cue is quite restricted. For a better understanding of the origin of this kout scale, we can study the average growth of kouz as a function of Ssouz, i.e., the average number of different target words obtained from a given cue word as a function of the number of times the given cue was extracted for a game (see Fig. 4).
Fig. 4. Average (kout) as a function of Sout (red), obtained by averaging the kout values of all those cue words with the same Sout value. The fitted curve obtained from Eq. (2) is shown in black (parameters: V ~ 74 and B ~ 0.92). Inset: same data in log-log scale together with a fit to a pure sub-linear power-law, to highlight the deviation from such a law at large Sout. contrary, the out-degree shows a Gammaz-like distribution peaked around a typical value kout & 28, corresponding therefore to a well-defined characteristic number of distinct words obtained as targets for each word inserted in the game as a cue. The distribution drops very rapidly at large kouz with a sharp cut-off around 100, indi- cating that the number of distinct words that humans spontaneously associate to a given cue is quite restricted. For a better understanding of the origin of this kout scale, we can study the average growth of kouz as a function of Ssouz, i.e., the average number of different target words obtained from a given cue word as a function of the number of times the given cue was extracted for a game (see Fig. 4).
Fig. 5. For each cue word we calculate the frequency-rank (FR) plot of its target words. Each curve in the picture corresponds to an averaged FR plot obtained by averaging the FR curves corresponding to cue words with the same out-strength value. When sout is sufficiently large (i.e., we have sufficiently large statistics) we obtain a power-law with an exponent close to (minus) unity, followed by a flat tail. Heaps’ law is symptomatic of an underlying generalized Zipf’s law [24], which in our case should appear in the marginal distribution of the target word frequencies, given a fixed cue word. Figure 5 shows the average frequency ranks for different values of Sout, confirming the presence of a Zipf’s law, which becomes better defined as Sout grows.
Fig. 5. For each cue word we calculate the frequency-rank (FR) plot of its target words. Each curve in the picture corresponds to an averaged FR plot obtained by averaging the FR curves corresponding to cue words with the same out-strength value. When sout is sufficiently large (i.e., we have sufficiently large statistics) we obtain a power-law with an exponent close to (minus) unity, followed by a flat tail. Heaps’ law is symptomatic of an underlying generalized Zipf’s law [24], which in our case should appear in the marginal distribution of the target word frequencies, given a fixed cue word. Figure 5 shows the average frequency ranks for different values of Sout, confirming the presence of a Zipf’s law, which becomes better defined as Sout grows.
Fig. 6. The mapping of HBC onto WN: given a couple of words linked by an association in the HBC graph (the blue arrow) we consider for the shortest path (black arrows and nodes) between the same words in the WN graph (gray graph in the background). In this example a HBC association maps into a 3-steps WN path.
Fig. 6. The mapping of HBC onto WN: given a couple of words linked by an association in the HBC graph (the blue arrow) we consider for the shortest path (black arrows and nodes) between the same words in the WN graph (gray graph in the background). In this example a HBC association maps into a 3-steps WN path.
Fig. 7. Red bars represent (in logarithmic scale) the normalized distribution of the semantic relations characterizing those HBC associations that map into a one step path on the WN network. Blue bars represent the semantic relations distribution in the whole WN graph.
Fig. 7. Red bars represent (in logarithmic scale) the normalized distribution of the semantic relations characterizing those HBC associations that map into a one step path on the WN network. Blue bars represent the semantic relations distribution in the whole WN graph.
Fig. 8. Normalized “effective” probabilities of the different types of WN semantic relations with error bars. The dashed line represents the probabilities of the associations in WN. So, if the semantic relation occurrences in the mapped HBC were exactly the same as in WN, all symbols would lie on the dashed line. To give an idea of the significance of the values, for each value we draw two triangles whose colors indicate the logarithm of the number of relations of the given type and therefore give an idea of the measure accuracy (blue and violet values correspond to smaller sample sizes than yellow and red ones). Upward triangles refer to the mapped HBC with unity length paths, while downward triangles refer to the whole WN.
Fig. 8. Normalized “effective” probabilities of the different types of WN semantic relations with error bars. The dashed line represents the probabilities of the associations in WN. So, if the semantic relation occurrences in the mapped HBC were exactly the same as in WN, all symbols would lie on the dashed line. To give an idea of the significance of the values, for each value we draw two triangles whose colors indicate the logarithm of the number of relations of the given type and therefore give an idea of the measure accuracy (blue and violet values correspond to smaller sample sizes than yellow and red ones). Upward triangles refer to the mapped HBC with unity length paths, while downward triangles refer to the whole WN.
These results confirm the existence of preferential patterns of exploration of hier- archical structures in the process of word association, in a way that most often maintains the same level of specificity between cue and target. Note that we limit the analysis to paths of up to three steps because the distribution for longer paths is practically equal to the distribution occurring in an uncorrelated artificial system built associating randomly extracted words.
These results confirm the existence of preferential patterns of exploration of hier- archical structures in the process of word association, in a way that most often maintains the same level of specificity between cue and target. Note that we limit the analysis to paths of up to three steps because the distribution for longer paths is practically equal to the distribution occurring in an uncorrelated artificial system built associating randomly extracted words.
Fig. 9. The top ten occurrence ranking of the semantic relations sequences for those HBC associations that map onto a path of two (top chart) and three (bottom chart) steps in WN.
Fig. 9. The top ten occurrence ranking of the semantic relations sequences for those HBC associations that map onto a path of two (top chart) and three (bottom chart) steps in WN.
Here we report a list of the semantic relations recognized by Wordnet with their abbreviation. For further information we refer to the Wordnet documentation [15, 17, 16]. Appendix C. Wordnet semantic relations abbreviations
Here we report a list of the semantic relations recognized by Wordnet with their abbreviation. For further information we refer to the Wordnet documentation [15, 17, 16]. Appendix C. Wordnet semantic relations abbreviations
Related topics:
Applied MathematicsComputer ScienceNatural Language ProcessingSemantics (Computer Science)Semantic NetworkWord associationLanguage Dynamics
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