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Textes et Discours comme Systèmes Dynamiques

N.B .: Cette section est uniquement disponible en anglais.

This T-LAB tool provides several integrated analysis options (see picture below) which can be used in various combinations for obtaining measures and graphical representations concerning texts treated as dynamic systems. In particular this tool allows us to verify how texts are organized in time, how the recurring themes and the sequential order of utterances relate to each other and how similarities and differences between utterances evolve in time. For these reasons – more than other T-LAB tools - this tool challenges the divide between qualitative and quantitative approaches in text analysis.

In principle the objects of this type of integrated analysis should be texts in which - like discourses and conversations - the sequence and the temporal flow of utterances is important (i.e. transcripts of focus group sessions, interviews, speeches, debates, doctor/patient iterations, novels etc.).

However, as this tool provides us with similarity measures concerning all pairs of text segments (both within the whole corpus and within its subsets), it may be also useful in other cases. Just remember that - when text segments are not in sequential order - the use of RQA Analysis and/or Sequence Analysis does not produce proper results.

To begin with, two things must be taken into consideration:
-as the granularity is important, the key-word list chosen before using this tools should contain as many items as possible;
-at the moment, this tool allows us to analyse a corpus which includes up to 30,000 text segments (i.e. about 5,000 pages), which can even be organized in two or more sub-sections (i.e. corpus subsets). However, due to some limitations concerning the visualization of recurrence plots, both the RQA Analysis and the Similarities Measures are available only for corpuses consisting of up to 3,000 text segments (i.e. about 500 pages, and a bit more when the corpus has been segmented into paragraphs).

The analysis procedure consists of the several steps, some of which are automatic and others which - when desired - can be manually performed by the user.

The initial steps performed automatically by T-LAB are the following:

a - construction of a document-term matrix, where documents are always text segments (i.e. text fragments, sentences, paragraphs) into which the corpus has been subdivided (see the T-LAB initial settings options);

b - topic analysis based on a probabilistic model which uses the Latent Dirichlet Allocation and the Gibbs Sampling (see the related information on Wikipedia);

c - use of a Naïve Bayes classifier for estimating the probability values of each topic within each text segment, and for assigning each text segment to the topic (or theme **) it most closely resembles.
(**) 'Topic' and 'Theme' will be hereafter treated as synonymous terms.

Please note that the main goal of the above automatic steps is to extract 'k' latent dimensions (where 'k' varies from 20 to 30) which determine the content structure of the analysed text and which - like a mixture model - can be used for exploring both text dynamics and similarities between text segments. For this reason the segments used for building the model are only those in which at least two key-terms included in the user list are present. Differently, after building the model, every text segment - even by maintaining the mixed nature of its content - is assigned to the topic to which it most closely resembles.

At the end of automatic steps, five options are made available, two of which correspond to two analysis tools already present in the T-LAB menu - namely the Topic Analysis (i.e. Modelling of Emerging Themes) and the Sequence Analysis of themes - and which, for this very reason, do not need further explanations. Just consult the parts of this help/manual where the main options depicted in the below section 'F' are commented.

Regarding the new tools, here is - for each of them - the required information.

A- Real Time Charts

When plotting real time charts, which allow us to dynamically visualize the time sequence of the text segments from the beginning to the end, the measures used are always the probability values that the Bayes classifier has assigned – for each of the ‘k’ topics - to each text segment.

Two complementary charts allows us to easily appreciate various types of events, including the strong recurrences of some themes or the shifts from a theme to another (see the below pictures, obtained by analysing a presidential debate between Hillary Clinton and Donald Trump which took place on October 2016. N.B.: In this case the corpus was automatically segmented into paragraphs and a multi-word list was applied).

Actually, from a semiotic point of view, we may argue that both these types of charts deal with the relationships between paradigm and syntagm or – in other words – between the synchronic and diachronic axes, where paradigm/synchronic refers to the various themes and syntagm/diachronic refers to the temporal sequence of the ‘N’ text segments.

As the information summarized by these types of charts mainly refers to formal aspects of text contents, the same charts may be regarded as some sort of musical scores where the sequence of themes and their ‘intensity’ (i.e. probability) vary in time.

Anytime, in order to check ‘who’ is speaking and about ‘what’, just click the corresponding point.

A.1 - Heat Map

A.2 - Waterfall

Please note that in the real time charts all text segments are present, and each of them is represented as a mixture of probability values associated with the various topics which the model consists of. In fact, when clicking the ‘Export Data’ option, all this information is made available in a data table in CSV format like the following.

B - Preliminary information about the Recurrence plots

Both the ‘Recurrence Quantification Analysis (RQA)’ and the ‘Similarity Measures’ tools use the recurrence plot technique. That is to say they build a N × N matrix, the rows and columns of which – in our case - are text segments ordered according to their temporal sequence. However in the two cases the recorded information is different. In fact, in the first case (i.e. RQA) any recurrence – marked with an unshaded dot - refers to the presence (absence in the case of white spaces) of the same theme in the ‘i’ and ‘j’ items (i.e. where the ‘X’ and ‘Y’ values are the same) and uses a categorical time series as input; differently, in the second case (i.e. Similarity Measures) any recurrence – marked with a shaded dot - refers to the similarity (i.e. Cosine) concerning the ‘i’ and ‘j’ items, the values of which are continuous (i.e. they vary from 0 to 1 ).

N.B.: In the case of recurrence plots with similarity measures the cut-off limit used by T-LAB is 0.0001 (Cosine measure). This because many scholars tend to count all nonzero entries of the similarity matrix.

Though the two types of recurrence plots may highlight similar patterns (see the below Fig. 1 and Fig. 2, which have been obtained by analysing a legislative text), by default T-LAB uses the first (i.e. Fig. 1) for computing the RQA measures and it uses the second (i.e. Fig. 2) for exploring similarities and differences concerning text segments.
However, by clicking the appropriate button, the user is also allowed to obtain the RQA measures for the recurrence plots with the similarity measures. Just remember that, as in this case the percentage of recurrent points is higher, all RQA measures are somehow inflated.

The fact remains that, like the 2D barcodes used for marketing purposes, both the below recurrence plots can be seen as unique fingerprints of the analysed text.

Fig. 1 - Time Series
Fig. 2 - Similarities

N.B. The time series used for the recurrence plot in Fig. 1 is the following:

Both when clicking 'Similarity Measures' and 'Recurrence Quantification Analysis (RQA)' the default T-LAB chart shows a 100x100 recurrence plot which however can be zoomed in and out by using the mouse wheel. Moreover in both cases six different options allow us to perform different operations (see pictures below).

In particular:
-options ‘1’ and ‘2’ allow us to visualize the general measures (‘1’) or the transcript of the selected segment (‘2’);
-options ‘3’ and ‘4’ allow us to visualize the complete recurrence plot (‘3’) or a subsection of it (‘4’);
-options ‘5’ and ‘6’ allow us to export the image in different formats (‘5’) or to export a data table with all the analysed values (‘6’).
Please note:
-in the RQA case the magic wand button ( ) allows us to check some characteristics which will be explained in below section ‘D’. Differently, in the case of similarities, the same button may be used for obtaining the RQA measures for the shown recurrence plot;
-when exporting the similarity data, all measures concerning ‘Self-Similarity’ and ‘Other-Similarity’ are included (see table below);

C - Similarity Measures

When choosing ‘Similarity Measures’, several options are made available (see picture below) which allow the user to select both the vectors to be used for the similarity computation and the reference context to be analysed (i.e. either the entire corpus or a subset of it).

N.B.: The difference between ‘conceptual’ (1) and ‘term-based’(2) similarities is that in the first case (1) each text segment is represented by a feature vector concerning topics, whereas in the second case (2) each text segment is represented by a feature vector concerning words. In both cases the similarity measure used is the Cosine coefficient.

According to the design of the user interface, in this case - like in the RQA analysis (see section 'D' below) - the user can choose between visualizing the global measures or the transcripts of recurrent segments (see picture below). Moreover, when a corpus subset is selected, two further measures are provided concerning the 'self-similarity' (i.e. averaged cosine similarity) between all pairs of text segments within the chosen corpus subset, one (1) with and the other (2) without zero values included. Other measures concerning similarities between all pairs of corpus subsets can be exported by clicking the 'Export Data' button.

Please remember that, unlike the RQA, the 'Similarity Measures' option considers only those text segments in which at least two key-terms included in the user list are present. This is in order to reduce biases in the Cosine computation.

D - Recurrence Quantification Analysis (RQA)

RQA is a method of nonlinear data analysis for the investigation of dynamical systems which quantifies the information contained in a recurrence plot and detects the transitions in the systems by analysing time series (see https://en.wikipedia.org/wiki/Recurrence_quantification_analysis ).

In this T-LAB tool, both in the case of the RQA Analysis and in the case of the Sequence Analysis (i.e. Markovian Analysis), a time series is represented by a categorical vector where each element is an integer which corresponds to the topic assigned to the 'i' text segment. However only in the case of the RQA a square matrix is built where the time series is both in rows and in columns.

When using the RQA tool, two main options are made always available (see pictures below):

1-Show the RQA Measures;
2-Show the Selected Item.

In the first case, the standard measures of RQA are provided (e.g. %REC, %DET, ENTR etc.**). In the second case the excerpts of recurring text segments are displayed.
In both cases, the mouse wheel allows zooming in and out. Moreover two buttons allow the user to export both the picture and the analysed data.
(**) For more information about the RQA measure see section ‘E’ below.

Please note that in the recurrence plot analysed with RQA the representation is symmetric across the main diagonal and two types of lines are particularly important: the diagonals parallel to the main diagonal and the vertical lines (**). In fact these lines mark the transitions present in the system and they are the base for obtaining the various RQA measures.

(**) In any recurrence plot vertical lines and horizontal lines mirror each other. In fact vertical lines in the upper part of the plot correspond to horizontal lines in the lower part, and vice versa.

In particular, the distribution of diagonal lines allows for the investigation of determinism (i.e. predictability of the system) and the distribution of vertical lines allows for the investigation of intermittency (i.e. sequences which are interspersed by erratic breaks).

As an example, just consider the above fictitious time series. In it the same sequence of nine points/themes is repeated two times in different time spans (see the above red rectangles), respectively from t-12 to t-20 and from t-28 to t-36, where each ‘t’ stands for a different text segment. In the same series there is also a sequence – from t-54 to t-61 - in which the same theme which appears at t-44 is repeated eight times (see the above green rectangle).

The corresponding recurrence plot (RP) - which has the same time series on the ‘X’ and the ‘Y’ axes - is that depicted in the image below.
Please note that in the case of diagonal line each point on the ‘X’ axis (i.e. from t-12 to t-20) recurs with the corresponding point on the ‘Y’ axis (i.e. from t-28 to t-36); differently the eight points which form the vertical line recur with just one point (i.e. t-44).
Accordingly, in musical terms we may say that diagonal lines refer to a restatement of a motif (i.e. a pattern is repeated), whereas vertical lines refer to a repetition of a single note which somehow breaks the thematic variation.

Please note that when a monothematic sequence like that form t-54 to t-61 is repeated two or more times, usually in the recurrence plot it is represented by a square or by a rectangle.

Regarding the rectangular block structures – which actually include both vertical and diagonal lines - they can be seen as referring to recurrences of the same topics in sub sections of the time series, i.e. to groups of overall similar feature vectors. In fact each dot in the graph represents a revisit of the same state and there is a correspondence between the rectangular blocks of the recurrence plot, the rectangles highlighted in the real time heat map and the chart of the time series (see pictures below). In other words we may say that in this cases speakers are repeatedly engaged on the same topic/theme, which appears to be ‘hot’.

As stated above, in the RQA outputs the longest diagonals parallel to the main diagonal allow us to detect interesting repetitions of the same thematic sequence. However their shapes are not so evident as the rectangular block structures, also because sometimes they can be hidden inside one of them (see the below case marked with ‘2’). For this reason T-LAB includes a specific option (see the magic wand below) which automatically detects the longest diagonal, informs the user about the sequence of repeated themes included in it and automatically positions the cursor in the corresponding X-Y coordinates.

N.B.: Soon after the longest diagonal is detected T-LAB allows the user to export a file with the most frequent repeated sequences, each one of them including at least three concatenated themes. Such a file can be considered a sort of summary of the main themes - and of the corresponding variations - present in the corpus.

N.B.: In the case of the above diagonal '1', one of the corresponding patterns on the heat map is the following.

Regarding the vertical/horizontal lines they can be easily checked by exploring the heat map first (see case '1' in the image below) and then the recurrence plot (see case '2' in the image below).

E - Some notes about the RQA measures

When talking about the RQA measures, we have to make a clear distinction between their technical definitions (1) and their relevance in a thematic text analysis (2).

In fact the technical definitions correspond to formulas and are the same in all sciences using RQA for the study of dynamic systems and their time series (e.g. physics, physiology, meteorology, finance, etc.). Differently, the relevance – and also the meaning – of the RQA measures in text analysis is a matter of debate.

Starting with the technical definitions (1), here is a table which summarizes the relevant information for the most used RQA measures.

Measure Definition
%REC - Recurrence Rate The percentage of recurrence points in a Recurrence Plot which fall within a specified radius.
%DET - Determinism The percentage of recurrence points which form diagonal line structures, main diagonal not included (N.B.: In RQA the main diagonal is also called LOI, i.e. Line of Identity, because in it each point recurs with itself).
RATIO The ratio between %DET and %REC.
L The average length of the diagonal lines.
LMAX The length of the longest diagonal line.
DIV - Divergence The invrs of MAX
ENTR - Entropy The Shannon entropy of all diagonal line lengths distributed over integer bins in a histogram (Webber, C. L., & Zbilut, J. P. , 2005, p. 48). Accordingly, if there are lots of diagonal lines with varying lengths, the entropy will be high. Please note that, as in the RQA case entropy reflects the complexity of the RP in respect of the diagonal lines, here the definition of entropy does not correspond to the entropy of physical systems, where the higher the entropy the greater the disorder.
TREND The degree of system stationarity . Accordingly, when recurrent points are homogeneously distributed across the recurrence plot, TREND value will be close to zero. Differently, when points 'fade away' from the central diagonal, the trend will have a negative value.
%LAM - Laminarity The percentage of recurrence points which form vertical lines.
VMAX The length of the longest vertical line.
TT - Trapping time The average length of the vertical lines.

Regarding the relevance of RQA measures in text analysis (2) both %DET and TREND deserve special attention. In fact higher determinism (%DET) values indicates that the same thematic patterns are repeated more often and that – accordingly – the dynamic of analysed system is somehow more predictable. On the other hand TREND can be interpreted as a measure referring to how quick the transitions are from some themes to others, where lower TREND values indicate quicker transitions.
For example, when comparing RQA measures obtained by analysing a scientific essay (‘a’) and a novel (‘b’), we can find out that in the first case (‘a’) the %DET value is higher than ‘b’ and that in the second case (‘b’) the TREND value is very low (often below zero).

Below is a comparison of the RQA measures obtained by analysing the essay ‘On the Origin of Species’ (C. Darwin) and the novel ‘The adventures of Pinocchio’ (C. Collodi).

On the Origin of Species (a) The adventures of Pinocchio (b)
%REC = 8.201%
%DET = 16.474%

RATIO = 2.009
L = 2.093
LMAX = 6
DIV = 0.167
ENTR (base2) = 0.460
TREND = 4.705
%LAM = 30.717%
VMAX = 7
TT = 2.263
REC = 3.525%
%DET = 9.676%

RATIO = 2.745
L = 2.089
LMAX = 5
DIV = 0.2
ENTR (base2) = 0.435
TREND = -5.599
%LAM = 23.194%
VMAX = 6
TT = 2.267

Here are the two corresponding recurrence plots.

On the Origin of Species (a)
The adventures of Pinocchio (b)


N.B.: A table which summarizes the meanings of typical patterns in recurrence plots can be found at page 251 of the following article:
N. Marwan, M. Romano, M. Thiel and J. Kurths, “Recurrence Plots for the Analysis of Complex Systems", Phys. Rep. 438, 240-329 (2007).

F - Topic Analysis and Sequence Analysis

The below pictures summarize the main options of two tools already present in the T-LAB menu, which are integrated with the new ones and which are explained in the corresponding sections of this manual/help, i.e. Modeling of Emerging Themes and Sequence and Network Analysis.

-Any variable selected in the above forms (see the label highlighted by a red rectangle) will be used in the outputs provided by the various tools (Please note that only categorical variables with up to 20 values are made available) ;
-The ‘Export/Import Dictionary’ option, which is no longer available after performing a Sequence Analysis, is intended to allow the user to save time when repeating the same analysis by using topic labels manually assigned previously. In other words: just export the topic dictionary after completing - if desidered - all renaming operations and import the same dictionary when repeating the same analysis with the same corpus, the same key-word list and the same parameters;
-While the Correspondence Analysis option allows us to explore the relationships between the various topics and the various speakers, the 'Graph Maker' tool allows us to explore the relationships between key-terms within each selected topic (see pictures below).