90/ From chaos to synthesis in artwork historical past with a bit of 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 accessible and topic of an inquiry about * the theme * the style * the interval * the fashion * the sort * the fabric * and so forth. On this put up a case-study is introduced the place a typical fuzzy scatter diagram of information factors is transformed right into a ‘artificial’ graph which may be simply understood.

Desk of Matters

The pattern consists of 295 artworks by François BOUCHER, chosen based on their equal theme ‘Venus’, introduced within the foregoing put up 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 predominant Matters) was accomplished (2).

The mix of each ranges of research yields a typical scatter graph of information factors proven within the determine under.

 It’s troublesome to study one thing from this plot. Nevertheless, we will scale back the scattering by defining a ‘centroid’ for every Subject because the synthesis of the info factors, by defining a heart yr of manufacturing YEARc(determine above proper facet).

Firstly, the metrics of the info should be harmonized. The horizontal axis xis normalized as follows:
x = (yr – yrmin ) / (yrmax – yrmin)  or  yr = 1720 + 50 * x
with yrmin= 1720 and yrmax = 1770 and the horizontal axis runs now from 0 to 1 .


  The metrics of the vertical axis y is unchanged and associated to the overall frequency F of every Subject.
The idea of a centroid of information factors is utilized in ‘cluster evaluation’ of so-called unsupervised classification of information (3). On this case-study Matters may be referred to as ‘supervised’ clusters. There are lots of methods to explain the centroid level within the x, y area. The best is the calculation of xav, yav because the averages of all x, y knowledge 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 Subject: F = whole frequency, n = variety of years of manufacturing of the artworks throughout interval p < P = 50 years, whole interval from 1720 to 1770. Word that by definition yav = F / n .

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

                                                                YEARc = 1720 + 50 * xav.

Instance of two outliers in a cluster
For example the potential of the cluster evaluation, Subject 6 (Venus & Adonis)acquired 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 moderately small and comparable, e.g. to Subject 11 (Venus & Mars) with F = 12 and n = 5.
The graph of the info factors exhibits 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 an alternative of 1744 in Desk 1.
Thus the unique scatter diagram of knowledge factors may be simplified right into a x , y graph of 18 centroids with the important data as labels.

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

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


Related analyses of ‘supervised’ clusters, on the choice of the investigator, like ‘themes’ or  ‘genres’ (non secular themes, portraits, landscapes, and so forth.) would assist to know in a quantitative method  BOUCHER’s total 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 question, the French expression ‘Humanités numériques’ is extra significant than ‘Digital Humanities’: evaluation of numbers is the true function of ‘digital’ humanities.

  2. See Submit of February 24, 2020 “François BOUCHER: the Rococo Famous person of the 18th century and his Imitators” 
  3. Cluster evaluation is an enormous approach in knowledge exploration and subsequently has no normal accepted definition. The best one, relevant on this case-study, is : numerical evaluation of numerous comparable objects collected and grouped along with the target to simplify the info.  
  4.  The paintings of 1767 ‘Vénus appuyée sur son cher Adonis’ is a drawing ready for an illustration of ‘Les Métamorphoses d’Ovide’. It may very well 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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