This paper presents the results of numerical experiments on the study of data volumes consisting of frequencies of joint use of adjectives and nouns. The volumes of data were obtained from samples from text collections in Russian. The aim of the research is to analyze the cluster structure of the studied volume and semantic proximity of words in clusters and subclusters. The hypothesis was used that words with similar meaning should occur in approximately the same context. In this regard, in the space of features, they will be at a relatively close distance from each other, while differing words will be at a more distant distance from each other. Research is carried out using elastic maps, which are effective tools for visual analysis of multidimensional data. The construction of elastic maps and their extensions in the space of the first three principal components makes it possible to determine the cluster structure of the studied multidimensional data volumes. The analysis of the cluster structure for the considered volume of multidimensional data is carried out. The influence of transposition of the initial data array is considered.
The rapid development of the universal transition to digital technologies in the
modern world has made the task of processing, visualization and analysis of
multidimensional data extremely urgent. According to modern classifications, multidimensional
data can be considered as Big Data. The need for processing, visualization and
analysis of multidimensional data entailed the intensive development of tools for visual
analytics (Visual Analytics) [
The approaches and methods of visual analytics are constantly evolving and provide users with sufficiently reliable tools for solving many practical problems of researching multidimensional data. Such tasks include the tasks of data classification, cluster detection, identification of key determining parameters, establishing relationships between key parameters, etc.
In fact, the approaches of visual analytics are a synthesis of several algorithms for reducing the dimension and visual presentation of multidimensional data in manifolds of lower dimension embedded in the original volume.
Such algorithms include mapping the initial multidimensional volume in elastic
maps [
This work is a continuation of research on the development of visual analytics
tools for the analysis of multidimensional volumes of numerical and textual
information. Studies on this topic are presented in [
This work is devoted, first of all, to experiments with a multidimensional data
volume, which is the frequency of joint use of adjectives and nouns. With the help of
certain procedures, text corpuses and arrays of frequencies of joint use are built.
Earlier, in previous works, studies of a similar nature were carried out for arrays of the
“verb + noun” type [
In this section, we give a brief description of the elastic map construction technology
as a means of visualizing arbitrary multidimensional data. The ideology and
implementation algorithms for building elastic maps are presented in detail in [
According to [
Visual Analysis of Textual Information on the Frequencies of Joint Use of… 3 curvature of the grid, respectively; D1, D2, D3 - terms responsible for the properties of the grid.
Here D1 is a measure of the proximity of the grid nodes to the data, D2 is a measure of the extent of the grid, D3 is a measure of the curvature of the grid.
The variation of the elasticity parameters consists in constructing elastic maps with
a sequential decrease in the elastic coefficients, as a result of which the map becomes
softer and more flexible, adapting to the points of the initial multidimensional data
volume in the most optimal way. After construction, the elastic map can be turned
into a plane to observe the cluster structure in the studied data volume. On the
expanded plane, you can colorize the distribution of data density on the elastic map. In
some cases, such a coloring can be very useful. Elastic cards are especially effective
when used in conjunction with the principal component analysis (PCA). The display
of the elastic map and its sweep in the space formed by the first three principal
components can dramatically improve the results, especially in clustering and
classification problems. The construction of elastic maps and their scanning in the space of the
first three principal components allows us to determine the cluster structure of the
studied multidimensional data volumes. The author of [
Based on the construction of elastic maps, a number of studies of various volumes
of multidimensional data were conducted and a number of procedures for processing
multidimensional data were developed, which significantly improved the cluster
picture of the studied data volume [
This section presents the results of studies on the construction of elastic maps for a
multidimensional data array, which are the frequencies of joint use of adjectives and
nouns. This work is a continuation of [
The filtering procedure was carried out at the data preparation stage. Similarly to
[
According to the data obtained, elastic maps were constructed with a variation of the bending and tensile coefficients towards maximum “softness”. Let's consider some results.
Fig. 1 shows a fragment of the constructed elastic map for a multidimensional data array representing the frequencies of joint use of 300 nouns and 300 adjectives. A fragment of the map is presented in annotated form, showing nouns corresponding to each point.
The following figure (Fig.2) shows an extension of an elastic map in the space of the first two principal components with a coloring according to the data density. The density range is divided into five equal parts, which correspond to the colors in ascending order from blue to red. A similar coloring is used in Fig. 2 - 8.
Visual Analysis of Textual Information on the Frequencies of Joint Use of… 5
The presented visual image of a multidimensional array consisting of joint use frequencies for 300 adjectives and 300 nouns allows one to see 5 areas of condensation. Three areas are located on the left edge of the extended map, one is located in the upper right corner and another weakly expressed area of condensation is located in the lower left corner of the constructed image.
Let's take a closer look at them separately.
Figure 3 shows a close-up of map fragment corresponding to the upper right corner.
Here we can see a number of subclusters containing nouns that are similar in meaning. So, for example, in the left part of Fig. 3, one can trace closely related nouns ВОПРОС (QUESTION), ПРОБЛЕМА (PROBLEM), ЗАДАЧА (TASK). Another group, located in the middle of the picture, contains semantically close nouns: МОМЕНТ (MOMENT), ПОЛОЖЕНИЕ (STATE), СИТУАЦИЯ (SITUATION), ДЕЛО (CASE), УСЛОВИЕ (CONDITION). The leftmost subcluster in Figure 3 contains the words ВРЕМЯ (TIME), ГОД (YEAR), ЖИЗНЬ (LIFE), ДЕНЬ (DAY), МИР (PEACE). A complete presentation of all the resulting clusters and subclusters in the resulting picture for nouns takes up too much space, so in the following presentation we will restrict ourselves to the most characteristic places. So, Fig. 5 shows the top-most area of condensation on the left edge in close-up. Here one can trace the following groups of concepts closely located on the fragment of the sweep. In the upper left corner there is a group of words – АРМИЯ (ARMY), ВОЙСКО (VOYSKO), ПРАВИТЕЛЬСТВО (GOVERNMENT), КОМПАНИЯ (COMPANY), ВЛАСТЬ (AUTHORITY), and НАРОД (PEOPLE). In the upper right part of Fig. 5, we can see the group ПРОГРАММА (PROGRAM), ТЕХНИКА (TECHNICS), ИССЛЕДОВАНИЕ (RESEARCH), ПРОЕКТ (PROJECT), ЗАДАЧА (TASK). In the middle on the left side of the figure is the КОМИТЕТ (COMMITTEE), РЫНОК (MARKET), РЕГИОН (REGION), УПРАВЛЕНИЕ (MANAGEMENT), ПОЛИТИКА (POLITICS) group. Thus, the constructed elastic map makes it possible to single out a number of subclusters and groups uniting words that are semantically related. This opens up a number of possibilities, including searching for words by related words from such group.
The considered data array was transposed similarly to [
An extension of the constructed elastic map for colorized data density is shown in Fig. 6.
Here the picture is very similar to that shown in Fig. 2, with the difference that the weakly expressed region of condensation in the lower right corner practically disappears. The presented visual image allows one to see 4 areas of thickening. Three areas of thickening are located on the left edge of the map, one is located in the upper right corner.
As in the previous case, we consider some areas of condensation.
Fig. 7 shows a close-up of the thickening region in relation to the data density in the upper right corner of the sweep of the elastic map for the transposed data array. Here traced groups of adjectives that are similar in characteristics. For example, in the upper right corner – ГОСУДАРСТВЕННЫЙ (STATE), НАЦИОНАЛЬНЫЙ (NATIONAL), ПОЛИТИЧЕСКИЙ (POLITICAL), МЕЖДУНАРОДНЫЙ (INTERNATIONAL), ОБЩЕСТВЕННЫЙ (PUBLIC). Nearby is a group with national-geographical characteristics – РУССКИЙ (RUSSIAN), ЕДИНЫЙ (UNIFIED), ЕВРОПЕЙСКИЙ (EUROPEAN), АМЕРИКАНСКИЙ (AMERICAN), ИНОСТРАННЫЙ (FOREIGN), НЕМЕЦКИЙ (GERMAN), ФРАНЦУЗСКИЙ (FRENCH), ИТАЛЬЯНСКИЙ (ITALIAN), ГЕРМАНСКИЙ (GERMAN). We also give an example of a group of words located in the lower right corner of the constructed extension of an elastic map for a transposed array. This fragment is shown in Fig. 8. At the bottom of the figure, one can distinguish a group of adjectives with size characteristics – ОГРОМНЫЙ (HUGE), БОЛЬШОЙ (BIG), МАЛЕНЬКИЙ (SMALL), КРУПНЫЙ (LARGE), НЕБОЛЬШОЙ (LITTLE), МЕНЬШИЙ (LESS), БОЛЬШИЙ (LARGE), ДЛИННЫЙ (LONG), УЗКИЙ (NARROW), ШИРОКИЙ (WIDE).
Thus, summing up the experiments and the results obtained, it can be argued that the original hypothesis of this study was justified. Recall that we assumed that words that are close in terms of meaning in terms of frequency characteristics should be located close to each other.
The implemented approach makes it possible to process volumes of textual information and highlight groups that are similar in semantic characteristics to nouns and adjectives. 4
To analyze the “visual portrait” of a multidimensional data volume, elastic map construction technologies were used. These technologies are methods for mapping points of the initial multidimensional space onto manifolds of smaller dimension embedded in this space. The development of such a map, displayed in the space of the first principal components, allows us to get a "visual portrait" of a multidimensional data volume. Such an image can be organically supplemented by a coloring displaying data density.
This work contains a description of the results of constructing elastic maps for analyzing data volumes consisting of frequencies of joint use of adjectives and nouns. The analysis of the cluster structure for the considered volume of multidimensional data is carried out. A study of the effect of of the source data transposition is performed. The initial hypothesis about the proximity in space of signs of words that are close in meaning is confirmed. 5
This work was supported by RFBR grants 19-01-00402 and 20-01-00358.