90/ From chaos to synthesis in artwork historical past with a little bit little bit of numerical evaluation

Les Humanités numériques : une révolution symbolique ?
Béatrice Joyeux-Prunel (1)

There may be loads of alternative, without having for synthetic intelligence, to implement ‘numerical evaluation’ in artwork historical past if a consultant pattern of chosen equal artworks is out there and topic of an inquiry about * the theme * the style * the interval * the type * the kind * the fabric * and many others. On this publish a case-study is introduced the place a typical fuzzy scatter diagram of knowledge factors is transformed right into a ‘artificial’ graph which will be simply understood.

Desk of Subjects

The pattern consists of 295 artworks by François BOUCHER, chosen in keeping with their equal theme ‘Venus’, introduced within the foregoing publish and the place the evaluation on the interval degree (time-frequency distribution of artworks) and on the nominal degree (frequency of artworks categorized into 18 major Subjects) was accomplished (2).

The mix of each ranges of study yields a typical scatter graph of knowledge factors proven within the determine beneath.

 It’s tough to be taught one thing from this plot. Nevertheless, we are able to cut back the scattering by defining a ‘centroid’ for every Matter because the synthesis of the information factors, by defining a heart 12 months of manufacturing YEARc(determine above proper aspect).

Firstly, the metrics of the information have to be harmonized. The horizontal axis xis normalized as follows:
x = (12 months – 12 monthsmin ) / (12 monthsmax – 12 monthsmin)  or  12 months = 1720 + 50 * x
with 12 monthsmin= 1720 and 12 monthsmax = 1770 and the horizontal axis runs now from 0 to 1 .


  The metrics of the vertical axis y is unchanged and associated to the entire frequency F of every Matter.
The idea of a centroid of knowledge factors is utilized in ‘cluster evaluation’ of so-called unsupervised classification of knowledge (3). On this case-study Subjects will be known as ‘supervised’ clusters. There are numerous methods to explain the centroid level within the x, y house. The best is the calculation of xav, yav because the averages of all x, y information factors within the cluster. 

An instance of a cluster with its centroid

Desk 1 summarizes the outcomes of the evaluation with the next notations for every Matter: F = complete frequency, n = variety of years of manufacturing of the artworks throughout interval p < P = 50 years, complete interval from 1720 to 1770. Observe that by definition yav = F / n .

We outline a diploma of scattering:  S = p/P < 1 and a heart 12 months of manufacturing: 

                                                                YEARc = 1720 + 50 * xav.

Instance of two outliers in a cluster
As an example the potential of the cluster evaluation, Matter 6 (Venus & Adonis)bought particular consideration as a result of its diploma of scattering S = 0,98 is the very best in Desk 1.

After all, that is because of the excessive worth of p = 49, whereas values F = 11 and n = 7 are fairly small and comparable, e.g. to Matter 11 (Venus & Mars) with F = 12 and n = 5.
The graph of the information factors reveals two outliers on the very finish (in 1767 and 1769) (4).
If we disregard these outliers, the re-calculated centroid C 6* has now labels F*, n* and p* respectively 9/5/26,  S* = 0,52YEARc* = 1732as a substitute of 1744 in Desk 1.
Thus the authentic scatter diagram of information factors will be simplified right into a x , y graph of 18 centroids with the important info as labels.

The tangible significance of this evaluation is demonstrated within the subsequent graph the place the values y are remodeled into the entire frequency F of every Matter and the values x into years. The centroid worth xavis now outlined because the heart YEAR of manufacturing of every Matter, as defined above and calculated in Desk 1. Matter 17, with a frequency of solely F = 1, is just not included within the graph beneath.

We observe that each one however three Subjects have their heart within the second half of BOUCHER’s profession. In different phrases, his manufacturing of Venusis especially after 1746, his 12 months of mid-career. Fascinating is also the truth that his depiction of ‘Venus & Adonis’(Matter 6) is an early curiosity, along with ‘Venus & Others (Mercury, Pygmalion)’ (Matter 12) and ‘Venus & Psyche’ (Matter 13).  The diploma of scattering S signifies the spreading of manufacturing which is after all highest for the big frequencies.


Comparable analyses of ‘supervised’ clusters, on the desire of the investigator, like ‘themes’ or  ‘genres’ (non secular themes, portraits, landscapes, and many others.) would assist to know in a quantitative manner  BOUCHER’s general manufacturing, or as a matter of reality, the manufacturing categorized at nominal and interval  ranges of any artist of curiosity.


  1. Inaugural lecture on 4 décembre 2019, Chair Humanités numérique,  Université de Genève.
    Little doubt, the French expression ‘Humanités numériques’ is extra significant than ‘Digital Humanities’: evaluation of numbers is the true function of ‘digital’ humanities.

  2. See Publish of February 24, 2020 “François BOUCHER: the Rococo Famous person of the 18th century and his Imitators” 
  3. Cluster evaluation is an enormous method in information exploration and subsequently has no common accepted definition. The best one, relevant on this case-study, is : numerical evaluation of plenty of related objects collected and grouped along with the target to simplify the information.  
  4.  The paintings of 1767 ‘Vénus appuyée sur son cher Adonis’ is a drawing ready for an illustration of ‘Les Métamorphoses d’Ovide’. It might be a replica of an earlier drawing. The paintings dated 1769 is a big portray ‘Venus und der schlafende Bogenschütze’, solely described within the database of the previous Hermann Göring collection.

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