InfraNodus -

Graph Language Processing Settings:

Specify the settings for your text-to-network conversion algorithm for this graph.

Lemmatizer: ?

Every word will be converted to its lemma (e.g. bricks > brick, taken > take) and will be shown on the graph as a node. Set to your language for more precise results. Switch off to turn off lemmatization and add your custom stop words list below.

Show on Graph: Double Brackets [[]]: Categories and Tags:
Stop Words: ?

List the words, comma-separated (no spaces), that should not appear in the graph, in addition to your default global stopwords list.
Example: is,the,as,to,in

Synonym Nodes: ? unmerge all

If you'd like some words to appear as one node on the graph, in addition to your default global synonyms list, list the synonyms, one per line.
Example:
machine:machine learning
learning:machine learning

Dynamic Graph Settings

See the dynamic evolution of this graph: scroll or "play" the text entries to see how the text propagated through the network graph over time.

Play the Graph

current speed of the player:

0 2000

one statement at a time

Export the Data

Network Graph Images:

The graph images for publishing on the web or in a journal. For embeds and URLs use the share menu.

PNG (Image) SVG (Hi-Res)

Visible Statements (Tagged):

Export the currently filtered (visible) statements with all the meta-data tags (topics, sentiment).

CSV (Spreadsheet) MD (e.g.Obsidian)

Text Mining Analytics:

Summary of insights from the analytics panel. For specific in-depth exports, see the download button in the Analytics panel.

TXT Analytics Report CSV Report N-Grams CSV

Network Graph Data:

The raw data with all the statistics for further analysis in another software.

JSON CSV Gexf (Gephi)

All the Text (for backup and duplicating):

Plain text used to create this graph without any meta-data

Download Plain Text (All Statements)

Share Graph Image

Share a non-interactive image of the graph only, no text:
Download Image Tweet

Share Interactive Text Graph

Save This Graph View:

Delete This Graph:

Your Project Notes

Interpret graph data, save ideas, AI content, and analytics reports.

Top keywords (global influence):

Top topics (local contexts):

Explore the main topics and terms outlined above or see them in the excerpts from this text below.

See the relevant data in context: click here to show the excerpts from this text that contain these topics below.

Tip: use the form below to save the most relevant keywords for this search query. Or start writing your content and see how it relates to the existing search queries and results.

Tip: here are the keyword queries that people search for but don't actually find in the search results.

#detrended_fluctuation_analysis or #dfa is a method for determining the statistical #self_affinity of a #signal. It is useful for analysing #time_series that appear to be long-memory processes (diverging correlation time, e.g. #power_law decaying autocorrelation function) or #1f_noise.

16029688790000000

The obtained #exponent is similar to the #hurst_exponent, except that #dfa may also be applied to signals whose underlying statistics (such as #mean and #variance) or dynamics are #non_stationary (changing with time)

16029689080000000

In #dfa the scaling exponent #alpha is calculated as the #slope of a straight line fit to the log #log graph of F(n)}F(n) using leas #squares. an exponent of 0.5 would correspond to #uncorrelated #white_noise, an exponent of 1 is #pink_noise

16029690580000000

Another way to detect #pink_noise is to build a graph where the x axis are the #events while the y axis records a #time_series estimation relative to the #standard_deviation from the #average (#mean) time interval.

16029693990000000

At its essence #pink_noise is based on #self_affinity and #self_similarity, so that no matter what scale you look at, the pattern is #similar (#scale_free)

16029694710000000

#power_spectral_analysis describes distribution of #power across #frequency components composing the #signal - for #pink_noise we have a 1/f relationship — few powerful signals with low frequency, a long tail of less powerful ones (of which there are many) (hence #1f_noise)

16029700860000000

#envelope is a smooth #curve outlining the extremes of a #signal and it is also calculated in #hilbert_transform, which, in turn is used in calculating #dfa or #detrended_fluctuation_analysis

16048776010000000

#detrended_fluctuation_analysis (#dfa) has proven particularly useful, revealing that genetic #variation, normal development, or #disease can lead to differences in the #scale_free #amplitude #modulation of oscillations https://www.frontiersin.org/articles/10.3389/fphys.2012.00450/full

16049192880000000

The reason why #chaotic #variation (#pink_noise) is indicative of a #healthy state is because it reflects #winnerless_competition behind the process. If there's a deviation in this dynamics (eg some #patterns), it could mean that one process is #dominating the rest.

16049193600000000

#self_affinity is a property of #fractal #time_series where the small parts of the whole are #similar to the whole

16049202650000000

#self_affinity processes and #self_similar structures have in common that the statistical #distribution of the measured quantity follows a #power_law function, which is the only mathematical function without a characteristic scale. Self-affine and #self_similar phenomena are therefore called "#scale_free.”

16049204010000000

In #power_law #distribution the #mean would not necessarily be the same as the #median (which is are closer to each other in #normal #distribution)

16049204950000000

A #power_law #distribution means that there is big number of #small #variation and a small number of #big #variation (hence the line with a negative #slope when expressed as a #log)

16049207830000000

In a #1f #signal the lower #frequency objects have larger #amplitude than the higher #frequency objects (#1f_noise) https://www.frontiersin.org/files/Articles/23105/fphys-03-00450-HTML/image_m/fphys-03-00450-g001.jpg

16049214350000000

the #frequency of a certain #size of flower being inversely #proportional to its #size.

16049215210000000

#time_series in which all #frequency are represented with the same #amplitude will lack the rich variability of the #scale_free #time_series and is referred to as "#white_noise”

16049216050000000

To estimate the #scale_free property we calculate the #standard_deviation (#signal in relation to #mean) over the differently sized #time_windows. If as the #time_windows size increases the #standard_deviation also increases, we're dealing with a #scale_free process. If the #scaling_effect is not there, then it's not a scale free process.

16049220900000000

a stationary #random #fluctuating process has a #signal profile, which is #self_affine with a #scaling_exponent α = 0.5

16049249650000000

when we add #memory in the sense that the #probability of an action depends on the previous actions that the walker has made — we will get a process that will exhibit #self_affinity across scales (#scale_free)

16049250440000000

Different classes of processes with #memory exist: #positive_correlation and those with #anti_correlation - anti-correlations can be seen as a #stabilizing mechanism - a future action is more likely to be opposite than the ones made before. In this case on longer windows (time scales) we will have lower #fluctuating so the coefficient will be lower (α 0 to 0.5) - has #memory, #anti_correlation. 0.5 - #random, 0.5 to 1 - has #memory and #positive_correlation (previous actions increase the likelyhood of that action taken again) https://www.frontiersin.org/files/Articles/23105/fphys-03-00450-HTML/image_m/fphys-03-00450-g003.jpg

16049257140000000

for #dfa the signal is transformed into the #cumulative_signal, then it is split into several #windows equal in size on the #log scale. then for each the data is #detrended and #standard_deviation is calculated for each #window. then #fluctuating function is calculated as the mean #standard_deviation for all the #windows. Then we plot that as a graph on #log scales. The #dfa exponent α is the #slope of the trend. If it follows a straight line 45° then it means that with every #window increase we do not have a #proportional increase in the mean of fluctuation (so it is #linear). If it is more, then it is #non_linear and shows that it is in fact #scale_free

16049268440000000

The lower end of the fitting range is at least four samples, because #linear #detrending will perform poorly with less points (Peng et al., 1994). For the high end of the fitting range, #dfa estimates for window sizes >10% of the #signal length are more noisy due to a low number of windows available for averaging (i.e., less than 10 windows). Finally, the 50% overlap between windows is commonly used to increase the number of windows, which can provide a more accurate estimate of the fluctuation function especially for the long-time-scale windows.

16049270000000000

A #brown_noise process can be obtained by successively summing data points in the #white_noise process. https://www.researchgate.net/publication/232236967_A_tutorial_introduction_to_adaptive_fractal_analysis/figures?lo=1

16190243450000000

Using the classical #dfa method, the #cumulative_sum of data are divided into segments, and the #variance of these sums is studied as a function of segment length after linearly detrending them in each segment. https://www.nature.com/articles/s41598-019-42732-7

16190250690000000

In #dfa, data are divided into segments of length L and are #linearly detrended. The #square_root of the #variance (called #fluctuation) of the detrended data is studied as a function of L. It can be shown that a #linear relationship between the #logarithm of the #fluctuation and the #logarithm of L is indicative of a #power_law behavior of the spectrum. https://www.nature.com/articles/s41598-019-42732-7

16190255840000000

If a #linear relationship between the length of a #segment or #time_windows and the strength of the #fluctuation (or the #square_root of the #variance of the #cumulative_signal) exists, the slope of the corresponding line is also referred to as #hurst_exponent.

16190283930000000

For #white_noise the #hurst_exponent or the relation between the #time_windows and the #fluctuation (square root of #variance) will be #linear: when we double the #time_windows the #fluctuation (or #variance of the #cumulative_sum) will also double.

16190320820000000

For #pink_noise #1f_noise the #hurst_exponent will equal #1 and will mean that for #time_windows twice longer the #fluctuation will increase about 4 times. In other words, the the longer is the #time_windows the more #fluctuation occurs (#positive_correlation).

16190325510000000

#hurst_exponent in this context is #alpha_exponent, because we use #alpha_exponent for #non_stationary processes

16190326350000000

if #alpha_exponent is more than 1, it means that for every increase of scale (#time_windows) the cumulative_sum of #fluctuation increases a lot. That means, the longer we look at the process, the more likely it is to have big #fluctuation — there is a tendency in the #short_term to be #small and in the #long_term there's a tendency to be #big.

16190328080000000

the #cumulative_sum of the difference from the #average of a #time_series will be #brown_noise (#random_walk) for the #white_noise

16190339070000000

[accessed_apr_21_2021]

In contrast, #0.5 < #hurst_exponent < #1 indicates a #correlated process for #f_gn or what is termed a #persistent process for #f_bm. In this case, #increases in the signal (for #f_gn) or increments of the signal (for #f_bm) are likely to followed by further #increase, and #decrease are likely to be followed by #decreases (i.e., a #positive #long_term #correlation). Anti-#persistent and #persistent processes contain #structure that distinguishes them from truly #random sequences of data. (2) (PDF) A tutorial introduction to adaptive fractal analysis. Available from: https://www.researchgate.net/publication/232236967_A_tutorial_introduction_to_adaptive_fractal_analysis [accessed Apr 21 2021].

16190379890000000

The difference between the #exponent or #exponential_decay and the #power_law #decay is that #power_law #decay is slower: there are more values with a low #amplitude in the case of the #power_law https://math.stackexchange.com/questions/164436/difference-between-power-law-distribution-and-exponential-decay

16195411410000000

Show Nodes with Degree > 0:

0 0

Total Nodes Shown:
extend

Filter Graphs:

Filter Time Range

from: 0
to: 0

update metrics live

Recalculate Metrics Reset Filters

Show Labels for Nodes > 0 size:

0 0

Default Label Size: 0

0 20

labels size = nodes size
labels color = nodes color

Edges Type:

Layout Type:

Reset to Default

Semantic Variability Score

— modulates diversity of the discourse network how it works?

The score is calculated based on how modular the structure of the graph is (> 0.4 means the clusters are distinct and separate from one another = multiple perspectives). It also takes into account how the most influential nodes are dispersed among those clusters (higher % = lower concentration of power in a particular cluster).

Actionable Insight:

N/A

We distinguish 4 states of variability in your discourse. We recommend that a well-formed discourse should go through every stage during its evolution (in several iterations).

1 - (bottom left quadrant) — biased — low variability, low diversity, one central idea (genesis and introduction stage).
2 - (top right) - focused - medium variability and diversity, several concepts form a cluster (coherent communication stage).
3 - (bottom right) - diversified — there are several distinct clusters of main ideas present in text, which interact on the global level but maintain specificity (optimization and reflection stage).
4 - (left top) — dispersed — very high variability — there are disjointed bits and pieces of unrelated ideas, which can be used to construct new ideas (creative reformulation stage).

Read more in the cognitive variability help article.

Your Workflow Variability:

Shows to what extent you explored all the different states of the graph, from uniform and regular to fractal and complex. Read more in the cognitive variability help article.

You can increase the score by adding content into the graph (your own and AI-generated), as well as removing the nodes from the graph to reveal latent topics and hidden patterns.

Phases to Explore:

Main Topical Clusters & High-Level Ideas

The topical clusters are comprised of the nodes (words) that tend to co-occur together in the same context (next to each other).

We use a combination of clustering and graph community detection algorithm (Blondel et al based on Louvain) to identify the groups of nodes are more densely connected together than with the rest of the network. They are aligned closer to each other on the graph using the Force Atlas algorithm (Jacomy et al) and are given a distinct color.

please, add your data to display the stats...

Most Influential Keywords & Concepts

The most influential nodes are either the ones with the highest betweenness centrality — appearing most often on the shortest path between any two randomly chosen nodes (i.e. linking the different distinct communities) — or the ones with the highest degree.

We use the Jenks elbow cutoff algorithm to select the top prominent nodes that have significantly higher influence than the rest.

Click the Reveal Underlying Ideas button to remove the most influential words (or the ones you select) from the graph, to see what terms are hiding behind them.

please, add your data to display the stats...

Network Structure:

N/A

The network structure indicates the level of its diversity. It is based on the modularity measure (>0.4 for medium, >0.65 for high modularity, measured with Louvain (Blondel et al 2008) community detection algorithm) in combination with the measure of influence distribution (the entropy of the top nodes' distribution among the top clusters), as well as the the percentage of nodes in the top community.

Download: TXT Report CSV Report More Options

Structural Gap Insight

(topics to connect)

A structural gap shows the two distinct communities (clusters of words) in this graph that are important, but not yet connected. That's where the new potential and innovative ideas may reside.

This measure is based on a combination of the graph's connectivity and community structure, selecting the groups of nodes that would either make the graph more connected if it's too dispersed or that would help maintain diversity if it's too connected.

N/A

Discourse Entrance Points

(concepts with the highest influence / frequency ratio)

These nodes have unusually high rate of influence (betweenness centrality) to their frequency — meaning they may appear not as often as the most influential nodes but they are important narrative shifting points.

These are usually effective entrance points into the discourse, as they link different topics together and have high inlfuence, but not too many connections, which makes them more accessible.

N/A

Emerging Keywords

N/A

Evolution of Topics

(number of occurrences per text segment)

↻

The chart shows how the main topics and the most influential keywords evolved over time. X-axis: time period (split into 10% blocks). Y-axis: cumulative number of occurrences.

Drag the slider to see how the narrative evolved over time. Select the checkbox to recalculate the metrics at every step (slower, but more precise).

Main Topics

(according to Latent Dirichlet Allocation):

loading...

LDA stands for Latent Dirichlet Allocation — it is a topic modelling algorithm based on calculating the maximum probability of the terms' co-occurrence in a particular text or a corpus.

We provide this data for you to be able to estimate the precision of the default InfraNodus topic modeling method based on text network analysis.

Most Influential Words

(main topics and words according to LDA):

loading...

We provide LDA stats for comparison purposes only. It works with English-language texts at the moment. More languages are coming soon, subscribe @noduslabs to be informed.

Sentiment Analysis

positive: | negative: | neutral:
reset filter

We analyze the sentiment of each statement to see whether it's positive, negative, or neutral. You can filter the statements by sentiment (clicking above) and see what kind of topics correlate with every mood.

The approach is based on AFINN and Emoji Sentiment Ranking

Use the Bert AI model for English, Dutch, German, French, Spanish and Italian to get more precise results (slower). Standard model is faster, works for English only, is less precise, and is based on a fixed AFINN dictionary.

Concept Relation Analysis:

please, select the node(s) on the graph or in the table below to see their connections...

Use this feature to compare contextual word co-occurrences for a group of selected nodes in your discourse. Expand the list by clicking the + button to see all the nodes your selected nodes are connected to. The total influence score is based on betweenness centrality measure. The higher is the number, the more important are the connections in the context of the discourse.

Top Relations in 4-grams

(bidirectional, for directional bigrams see the CSV table below):

The most prominent relations between the nodes that exist in this graph are shown above. We treat the graph as undirected by default. Occurrences shows the number of the times a relationship appears in a 4-gram window. Weight shows the weight of that relation.

As an option, you can also downloaded directed bigrams above, in case the direction of the relations is important (for any application other than language).

Text Statistics:

Word Count	Unique Lemmas	Characters	Lemmas Density
0	0	0	0

Text Network Statistics:

Discourse Network Structure Insights

mind-viral immunity:

N/A

stucture:

N/A

The higher is the network's structure diversity and the higher is the alpha in the influence propagation score, the higher is its mind-viral immunity — that is, such network will be more resilient and adaptive than a less diverse one.

In case of a discourse network, high mind-viral immunity means that the text proposes multiple points of view and propagates its influence using both highly influential concepts and smaller, secondary topics.

We recommend to try to increase mind-viral immunity for texts that have a low score and to decrease it for texts that have a high score. This ensures that your discourse will be open, but not dispersed.

The higher is the diversity, the more distinct communities (topics) there are in this network, the more likely it will be pluralist.

Modularity	0	Influence Distribution	0 %

Topics	Nodes in Top Topic	Components	Nodes in Top Comp
0	0 %	0	0 %
Nodes	Av Degree	Density	Weighed Betweenness
0	0	0	0

Discourse Advice:

N/A

Narrative Influence Propagation:

The chart above shows how influence propagates through the network. X-axis: lemma to lemma step (narrative chronology). Y-axis: change of influence.

The more even and rhythmical this propagation is, the stronger is the central idea or agenda (see alpha exponent below ~ 0.5 or less).

The more variability can be seen in the propagation profile, the less is the reliance on the main concepts (agenda), the stronger is the role of secondary topical clusters in the narrative.

propagation dynamics: | alpha exponent: (based on Detrended Fluctuation Analysis of influence)

We plot the narrative as a time series of influence (using the words' betweenness score). We then apply detrended fluctuation analysis to identify fractality of this time series, plotting the log2 scales (x) to the log2 of accumulated fluctuations (y). If the resulting loglog relation can be approximated on a linear polyfit, there may be a power-law relation in how the influence propagates in this narrative over time (e.g. most of the time non-influential words, occasionally words with a high influence).

Using the alpha exponent of the fit (which is closely related to Hurst exponent)), we can better understand the nature of this relation: uniform (pulsating | alpha <= 0.65), variable (stationary, has long-term correlations | 0.65 < alpha <= 0.85), fractal (adaptive | 0.85 < alpha < 1.15), and complex (non-stationary | alpha >= 1.15).

For maximal diversity, adaptivity, and plurality, the narrative should be close to "fractal" (near-critical state). For fiction, essays, and some forms of poetry — "uniform". Informative texts will often have "variable + stationary" score. The "complex" state is an indicator that the text is always shifting its state.

Degree Distribution:

(based on kolmogorov-smirnov test)

Using this information, you can identify whether the network has scale-free / small-world (long-tail power law distribution) or random (normal, bell-shaped distribution) network properties.

This may be important for understanding the level of resilience and the dynamics of propagation in this network. E.g. scale-free networks with long degree tails are more resilient against random attacks and will propagate information across the whole structure better.

If a power-law is identified, the nodes have preferential attachment (e.g. 20% of nodes tend to get 80% of connections), and the network may be scale-free, which may indicate that it's more resilient and adaptive. Absence of power law may indicate a more equalized distribution of influence.

Kolmogorov-Smirnov test compares the distribution above to the "ideal" power-law ones (^1, ^1.5, ^2) and looks for the best fit. If the value d is below the critical value cr it is a sign that the both distributions are similar.