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) [1-8].
The approaches and
methods of visual analytics are constantly evolving and pro-vide users with
sufficiently reliable tools for solving many practical problems of re-searching
multidimensional data. Such tasks include the tasks of data classification,
cluster detection, identification of key determining parameters, establishing
relation-ships 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 [5–8] with
different elasticity properties. These methods allow one way or an-other to
separate the cluster structure from the initial multidimensional data volume.
Elastic maps turned out to be a useful and fairly universal tool, which allowed
them to be applied to multidimensional data volumes of various types and
different nature of origin.
This work is a continuation
of research on the development of visual analytics tools for the analysis of
multidimensional volumes of numerical and textual infor-mation. Studies on this
topic are presented in [10-14]. In the process of research, the construction of
elastic maps was tested on a large amount of data of various origins.
This work is
devoted, first of all, to experiments with a multidimensional data vol-ume,
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 [10].
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 [5–8]. A
description of the construction of elastic maps follows [7]. Such a map is a
system of elastic springs embedded in a multidimensional data space. This
approach is based on an analogy with the problems of mechanics: the principal
manifold passing through the “middle” of the data can be represented as an
elastic membrane or plate. The elastic map method is formulated as an
optimization problem involving optimization of a given functional from the
relative position of the map and data.
According to [5–8], the basis for
constructing an elastic map is a two-dimensional rectangular grid G embedded in
a multidimensional space that approximates the data and has adjustable
elasticity properties with respect to tension and bending. The location of the
grid nodes is sought as a result of solving the optimization problem of finding
the minimum functional:
|
|
(1)
|
where │X│ is the number of points in
the multidimensional data volume X; m is the number of grid nodes, λ,
μ are the elastic coefficients responsible for the tension and 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 [7] built the ViDaExpert software package [9], which
allows the processing of multidimensional data volumes, the construction of
elastic maps, and their effective visualization. Elastic mapping and
visualization of the results in this study were performed using this software
tool.
Based on the construction of elastic maps,
a number of studies of various volumes of multidimensional data were carried
out and a number of procedures for processing multidimensional data were
developed, which significantly improved the cluster picture of the studied data
volume [10-14].
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 [10-14], where similar studies were performed for
multidimensional data volumes constructed on the basis of the “verb + noun”
principle. To construct the data volume, procedures similar to those described
in [10] were used. The same basic hypothesis was used that words that are close
in meaning should occur in approximately the same context. In this regard, in
the space of features such words will be at a relatively close distance from
each other, while different words will be at a distance more distant from each
other. The models “adjective + noun” were investigated. The number of
adjectives was considered as the number of dimensions. The number of nouns was
considered as the number of points in multidimensional space. The coordinates
of these points in the space thus formed were the frequencies of joint use. In
the studies considered below, the basis of the array was a sample of such
frequencies for 300 adjectives and 300 nouns. That is, in this case we are
considering 300 points, each of which lies in a 300-dimensional space.
The filtering procedure was carried out at
the data preparation stage. Similarly to [10], to cut off the noise, all
combinations with a frequency of occurrence below a predetermined frequency
were discarded. In addition, only those main words (and their corresponding
combinations) were selected for which the power of the set of dependent words
exceeds a certain threshold value. This is necessary to filter out the noise in
the combinations extracted from the collection. The threshold value of the
frequency of occurrence allows us to get rid of combinations that accidentally
fell into the database; the number of different combinations guarantees us
sufficient statistics for comparisons.
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.
Fig.
1.
A
fragment of the constructed elastic map for the considered multidimensional
data array with annotations
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 as-cending order from
blue to red. A similar coloring is used in Fig. 2 - 8.
Fig.
2.
Extension of the
constructed elastic map for the considered multidimensional data array with
coloring by data density.
The presented visual image of a
multidimensional array consisting of joint use fre-quencies 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 cor-ner.
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 ÂÎÏÐÎÑ (QUESTION), ÏÐÎÁËÅÌÀ
(PROBLEM), ÇÀÄÀ×À (TASK). Another group, located in the middle of the picture,
contains semantically close nouns: ÌÎÌÅÍÒ (MOMENT), ÏÎËÎÆÅÍÈÅ (STATE), ÑÈÒÓÀÖÈß
(SITUATION), ÄÅËÎ (CASE), ÓÑËÎÂÈÅ (CONDITION). The leftmost subcluster in
Figure 3 contains the words ÂÐÅÌß (TIME), ÃÎÄ (YEAR), ÆÈÇÍÜ (LIFE), ÄÅÍÜ (DAY),
ÌÈÐ (PEACE).
Fig.
3.
Extension of the constructed elastic map - large plan - upper right corner.
Fig. 4 shows a similarly close-up map
fragment corresponding to the lower upper corner. Here, judging by the density
coloring in Fig. 2, there is also a weakly expressed cluster.
Here we can also see a number of
subclusters containing nouns that are similar in meaning. So, for example, in
the upper part of Fig. 4, we can trace the nouns
ÌÛÑËÜ
(THINK),
ÈÄÅß
(IDEA), close in meaning and close on the
elastic map. The other group contains similar semantic nouns:
ÏÀÐÅÍÜ
(GUY),
ÌÓÆ×ÈÍÀ
(MAN),
ÄÅÂÓØÊÀ
(GIRL),
ÆÅÍÙÈÍÀ
(WOMAN). A little lower in
Fig. 4 one can see a subcluster consisting of the words
ËÈÖÎ
(FACE),
ÐÓÊÀ
(HAND),
ÃËÀÇ
(EYE).
Fig.
4. Extension of the constructed elastic map - large plan - lower right corner.
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 – ÀÐÌÈß (ARMY), ÂÎÉÑÊÎ (VOYSKO), ÏÐÀÂÈÒÅËÜÑÒÂÎ
(GOVERNMENT), ÊÎÌÏÀÍÈß (COMPANY), ÂËÀÑÒÜ (AUTHORITY), and ÍÀÐÎÄ (PEOPLE). In
the upper right part of Fig. 5, we can see the group ÏÐÎÃÐÀÌÌÀ (PROGRAM),
ÒÅÕÍÈÊÀ (TECHNICS), ÈÑÑËÅÄÎÂÀÍÈÅ (RESEARCH), ÏÐÎÅÊÒ (PROJECT), ÇÀÄÀ×À (TASK).
In the middle on the left side of the figure is the ÊÎÌÈÒÅÒ (COMMITTEE), ÐÛÍÎÊ
(MARKET), ÐÅÃÈÎÍ (REGION), ÓÏÐÀÂËÅÍÈÅ (MANAGEMENT), ÏÎËÈÒÈÊÀ (POLITICS) group.
Fig.
5. Extension of the constructed elastic map - large plan - upper left corner.
Figure 6 shows the middle of the left edge
of the extension. A number of distinct word groups can also be seen here. At
the top of Figure 6, you can see the group - ÃÐÀÍÈÖÀ (BORDER), ÍÀÏÐÀÂËÅÍÈÅ
(DIRECTION), ÎÊÐÓà (DISTRICT). There is a group nearby - ÕÎÇßÉÑÒÂÎ (FARM),
ÐÀÉÎÍ (REGION). These two groups in terms of conceptual characteristics and
location on the elastic map unfolded can be combined into a common subcluster.
In the middle of the picture there is a group - ÇÎÍÀ (ZONE), Ó×ÀÑÒÎÊ (AREA). In
the lower part, a group can be distinguished - ÏËÎÙÀÄÜ (SQUARE), ÊÍßÇÜ
(PRINCE), ÎÒÐßÄ (ORDER).
Fig.
6. Extension of the constructed elastic map - close-up image - the middle of
the left edge.
The lower part of the left side of the
elastic map extension is shown in Figure 7. Here the semantic groups can also
be traced. In the upper left side of figure 7 - ÁÐÀÒ (BROTHER), ÑÛÍ (SON). In
the middle of the figure one can see the group ËÅÑÒÍÈÖÀ (LADDER), ÓËÈÖÀ
(STREET), ÎÊÍÎ (WINDOW), ÊÎÐÈÄÎÐ (CORRIDOR), ÄÂÅÐÜ (DOOR), ÑÒÅÍÀ (WALL).
Fig.
7. Extension of the constructed elastic map - close-up image - the lower part
of the left edge.
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 [10]. We studied the transposed data array, where nouns played the
role of measurements, and adjectives were considered as points in a
multidimensional data array. The role of numerical characteristics is also
played by the frequency of joint use of adjectives and nouns.
An extension of the constructed elastic map
for colorized data density is shown in Fig. 8.
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 four areas of thickening. Three areas of thickening
are located on the left edge of the map, one is located in the upper right
corner.
Fig.
8. Extension of the constructed elastic map for a transposed data array with
coloring by data density.
As in the previous case, we consider some
areas of condensation.
Fig. 9 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 – ÃÎÑÓÄÀÐÑÒÂÅÍÍÛÉ (STATE), ÍÀÖÈÎÍÀËÜÍÛÉ (NATIONAL), ÏÎËÈÒÈ×ÅÑÊÈÉ
(POLITICAL), ÌÅÆÄÓÍÀÐÎÄÍÛÉ (INTERNATIONAL), ÎÁÙÅÑÒÂÅÍÍÛÉ (PUBLIC). Nearby is a
group with na-tional-geographical characteristics – ÐÓÑÑÊÈÉ (RUSSIAN), ÅÄÈÍÛÉ
(UNIFIED), ÅÂÐÎÏÅÉÑÊÈÉ (EUROPEAN), ÀÌÅÐÈÊÀÍÑÊÈÉ (AMERICAN), ÈÍÎÑÒÐÀÍÍÛÉ
(FOREIGN), ÍÅÌÅÖÊÈÉ (GERMAN), ÔÐÀÍÖÓÇÑÊÈÉ (FRENCH), ÈÒÀËÜßÍÑÊÈÉ (ITALIAN),
ÃÅÐÌÀÍÑÊÈÉ (GERMAN).
Fig.
9. Extension of the constructed elastic map - large plan - upper right corner.
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. 10. At the bottom of
the figure, one can distinguish a group of adjec-tives with size
characteristics – ÎÃÐÎÌÍÛÉ (HUGE), ÁÎËÜØÎÉ (BIG), ÌÀËÅÍÜÊÈÉ (SMALL), ÊÐÓÏÍÛÉ
(LARGE), ÍÅÁÎËÜØÎÉ (LITTLE), ÌÅÍÜØÈÉ (LESS), ÁÎËÜØÈÉ (LARGE), ÄËÈÍÍÛÉ (LONG),
ÓÇÊÈÉ (NARROW), ØÈÐÎÊÈÉ (WIDE).
Fig.
10. Extension of the constructed elastic map - close-up - lower right corner.
Let's move on to the left side of the
extension, where three areas of data condensation are located, determined by
density coloring. Let's consider them one by one.
Figure 11 is a partial flat pattern showing
the top left corner. A group of adjectives can be traced here - ÏÐÎØËÛÉ (PAST),
ÑËÅÄÓÞÙÈÉ (NEXT), ÏÐÅÄÛÄÓÙÈÉ (PREVIOUS), ÀÍÀËÎÃÈ×ÍÛÉ (SIMILAR), ÑÎÎÒÂÅÑÒÂÓÞÙÈÉ
(APPROPRIATE), ÂÎÇÌÎÆÍÛÉ (POSSIBLE), ÏÎËÎÆÈÒÅËÜÍÛÉ (POSITIVE), ÏÐÀÂÈËÜÍÛÉ
(RIGHT), ÑÅÊÐÅÒÍÛÉ (SECRET). Below - ÑËÅÄÑÒÂÅÍÍÛÉ (INVESTIGATIVE), ÑÓÄÅÁÍÛÉ
(JUDICIAL). Even lower - ÏÐÀÂÎÎÕÐÀÍÈÒÅËÜÍÛÉ (LAW ENFORCEMENT), ÓÃÎËÎÂÍÛÉ
(CRIMINAL). A group is located nearby - ÐÅÇÊÈÉ (SHARP), ÃÐÎÌÊÈÉ (LOUD).
Fig.
11. Extension of the constructed elastic map - close-up - top left corner.
The following figure 12 shows the middle
section of the elastic map for the transposed array. Here one can trace the
group - ×ÓÄÅÑÍÛÉ (WONDERFUL), ÐÅËÈÃÈÎÇÍÛÉ (RELIGIOUS), ÓÄÈÂÈÒÅËÜÍÛÉ (AMAZING).
Also we can see a group with national and geographic characteristics -
ÊÈÒÀÉÑÊÈÉ (CHINESE), ÏÎËÜÑÊÈÉ (POLISH), ßÏÎÍÑÊÈÉ (JAPANESE).
Fig.
12.
Extension of the constructed elastic map - close-up – middle of the
left edge.
Figure 13 shows the lower part of the left
side of the constructed elastic map extension. A number of groups are quite
clearly expressed here. A group reflecting the characteristics of the direction
- ÑÅÂÅÐÍÛÉ (NORTH), ÞÆÍÛÉ (SOUTH), ÇÀÏÀÄÍÛÉ (WESTERN), ÂÎÑÒÎ×ÍÛÉ (EAST). Group
- ÃÎËÛÉ (NAKED), ÃÐßÇÍÛÉ (DIRTY). Group - ÁËÅÄÍÛÉ (PALE), ÌßÃÊÈÉ (SOFT), ÍÅÆÍÛÉ
(TENDER). The group of adjectives characterizing the temperature is ËÅÄßÍÎÉ
(ICE), ÒÅÏËÛÉ (WARM), ÃÎÐß×ÈÉ (HOT), ÕÎËÎÄÍÛÉ (COLD). Group with material characteristics
- ÊÀÌÅÍÍÛÉ (STONE), ÆÅËÅÇÍÛÉ (IRON).
Fig.
13.
Extension of the constructed elastic map - close-up - bottom part of
the left edge.
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.
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 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.
The implemented approach allows one to
select groups that are similar in semantic characteristics of nouns and
adjectives. It should be noted that such an analysis can be useful in the tasks
of confronting negative verbal influences such as fake news, hidden propaganda,
involvement in sects, verbal manipulation, etc.
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