September 28, 2023


Make Some Fun

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

4 min read
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 on the market and topic of an inquiry about * the theme * the style * the interval * the fashion * the kind * the fabric * and so on. On this submit a case-study is offered 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 in accordance with their equal theme ‘Venus’, offered within the foregoing submit 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 important Matters) was accomplished (2).

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

 It’s tough to study one thing from this plot. Nonetheless, we are able to scale back the scattering by defining a ‘centroid’ for every Subject because the synthesis of the information factors, by defining a heart yr 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 = (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 entire 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 known as ‘supervised’ clusters. There are a lot of methods to explain the centroid level within the x, y area. The only 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 Subject: F = complete frequency, n = variety of years of manufacturing of the artworks throughout interval p < P = 50 years, complete interval from 1720 to 1770. Notice 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
As an instance the potential of the cluster evaluation, Subject 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 Subject 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 an alternative of 1744 in Desk 1.
Thus the unique scatter diagram of information 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 entire 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, just isn’t included within the graph under.

We observe that each one however three Matters have their heart within the second half of BOUCHER’s profession. In different phrases, his manufacturing of Venusis especially 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 in fact highest for the massive frequencies.


Comparable analyses of ‘supervised’ clusters, on the choice of the investigator, like ‘themes’ or  ‘genres’ (non secular themes, portraits, landscapes, and so on.) would assist to know in a quantitative manner  BOUCHER’s total manufacturing, or as a matter of truth, 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 Put up 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 only one, relevant on this case-study, is : numerical evaluation of a lot of related objects collected and grouped along with the target to simplify the information.  
  4.  The art work of 1767 ‘Vénus appuyée sur son cher Adonis’ is a drawing ready for an illustration of ‘Les Métamorphoses d’Ovide’. It might be a duplicate of an earlier drawing. The art work 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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