Quantifying Creativity in Art Networks Ahmed Elgammal and Babak Saleh Department of Computer Science Rutgers University {elgammal,babaks}@cs.rutgers.edu digihumanlab.rutgers.edu Abstract This paper proposes a computational framework for assessing the creativity of products, such as paintings, sculptures, poetry, etc. The proposed computational framework is based on constructing a network between creative products and using this network to infer about the originality and influence of its nodes. Through a series of transformations, we construct a Creativity Implication Network. We show that inference about creativity in this network reduces to a variant of network centrality problems which can be solved efficiently. We apply the proposed framework to the task of quantifying creativity of paintings (and sculptures). We experimented on two datasets with over 62K paintings to illustrate the behavior of the proposed framework. Introduction The field of computational creativity is focused on giving the machine the ability to generate human-level “creative” products such as computer generated poetry, stories, jokes, music, art, etc., as well as creative problem solving. An important characteristic of a creative agent is its ability to assess its creativity as well as judge other agents’ creativity. In this paper we focus on developing a computational framework for assessing the creativity of products, such as painting, sculpture, etc. We use the most common definition of creativity, which emphasizes the originality of the product and its influential value (Paul and Kaufman 2014a). In the next section we justify the use of this definition in contrast to other definitions. The proposed computational framework is based on constructing a network between products and using it to infer about the originality and influence of its nodes. Through a series of transformations, we show that the problem can reduce to a variant of network centrality problems, which can be solved efficiently. We apply the proposed framework to the task of quantifying creativity of paintings (and sculptures). The reader might question the feasibility, limitation, and usefulness of performing such task by a machine. Artists, art historians and critics use different concepts to describe pantings. In particular, elements of arts such as space, texture, form, shape, color, tone and line. Artists also use principles of art including movement, unity, harmony, variety, balance, contrast, proportion, and pattern; besides brush strokes, subject matter, and other descriptive concepts (Fichner-Rathus 2008). We collectively call these concepts artistic concepts. These artistic concepts can, more or less, be quantified by today’s computer vision technology. With the rapid progress in computer vision, more advanced techniques are introduced, which can be used to measure similarity between paintings with respect to a given artistic concept. Whether the state of the art is already sufficient to measure similarity in meaningful ways, or whether this will happen in the near or far future, the goal of this paper is to design a framework that can use such similarity measures to quantify our chosen definition of creativity in an objective way. Hence, the proposed framework would provide a ready-to-use approach that can utilize any future advances in computer vision that might provide better ways for visual quantification of digitized paintings. In fact, we applied the proposed framework using state-of-the-art computer vision techniques and achieved very reasonable automatic quantification of creativity on two large datasets of paintings. One of the fundamental issues with the problem of quantifying creativity of art is how to validate any results that the algorithm can obtain. Even if art historians would agree on a list of highly original and influential paintings that can be used for validation, any algorithm that aims at assigning creativity scores will encounter three major limitations: I) Closed-world limitation: The algorithm is only limited to the set of paintings it analyzed. It is a closed world for the algorithm where this set is every thing it has seen about art history. The number of images of paintings available in the public domain is just a small fraction of what are in museums and private collections. II) Artistic concept quantification limitation: the algorithm is limited by what it sees, in terms of the ability of the underlying computer vision methods to encode the important elements and principles of art that relates to judging creativity. III) Parameter setting: the results will depend on the setting of the parameters, where each setting would mean a different way to assign creativity scores with different interpretation and different criteria. However, these limitations should not stop us from developing and testing algorithms to quantify creativity. The first two limitations are bound to disappear in the future, with more and more paintings being digitized, as well as with the continuing advances in computer vision and machine learning. The third limitation should be thought of as an advanProceedings of the Sixth International Conference on Computational Creativity June 2015 39 tage, since the different settings mean a rich ability of the algorithm to assign creativity scores based on different criteria. For the purpose of validation, we propose a methodology for validating the results of the algorithm through what we denote as “time machine experiments”, which provides evidence of the correctness of the algorithm. Having discussed the feasibility and limitations, let us discuss the value of using any computational framework to assess creativity in art. For a detailed discussion about the implications of using computational methods in the domain of aesthetic-judgment-related tasks, we refer the reader to (Spratt and Elgammal 2014). Our goal is not to replace art historians’ or artists’ role in judging creativity of art products. Providing a computational tool that can process millions of artworks to provide objective similarity measures and assessments of creativity, given certain visual criteria can be useful in the age of digital humanities. From a computational creativity point of view, evaluating the framework on digitized art data provides an excellent way to optimize and validate the framework, since art history provides us with suggestions about what is considered creative and what might be less creative. In this work we did not use any such hints in achieving the creativity scores, since the whole process is unsupervised, i.e., the approach does not use any creativity, genre, or style labels. However we can use evidence from art history to judge whether the results make sense or not. Validating the framework on digitized art data makes it possible to be used on other products where no such knowledge is available, for example to validate computergenerated creative products. On the Notion of Creativity There is a historically long and ongoing debate on how to define creativity. In this section we give a brief description of some of these definitions that directly relate to the notion we will use in the proposed computational framework. Therefore, this section is by no means intended to serve as a comprehensive overview of the subject. We refer readers to (Taylor 1988; Paul and Kaufman 2014b) for comprehensive overviews of the different definitions of creativity. We can describe a person (e.g. artist, poet), a product (painting, poem), or the mental process as being creative (Taylor 1988; Paul and Kaufman 2014a). Among the various definitions of creativity it seems that there is a convergence to two main conditions for a product to be called “creative”. That product must be novel, compared to prior work, and also has to be of value or influential (Paul and Kaufman 2014a). These criteria resonate with Kant’s definition of artistic genius, which emphasizes two conditions “originality” and being “exemplary” 1. Psychologists would 1 Among four criteria for artistic genius suggested by Kant, two describe the characteristic of a creative product “That genius 1) is a talent for producing that for which no determinate rule can be given, not a predisposition of skill for that which can be learned in accordance with some rule, consequently that originality must be it’s primary characteristic. 2) that since there can also be original nonsense, its products must at the same time be models, i.e., exemplary, hence, while not themselves the result of imitation, they must not totally agree with this definition since they favor associating creativity with the mental process that generates the product (Taylor 1988; Nanay 2014). However associating creativity with products makes it possible to argue in favor of “Computational Creativity”, since otherwise, any computer product would be an output of an algorithmic process and not a result of a creative process. Hence, in this paper we stick to quantifying the creativity of products instead of the mental process that create the product. Boden suggested a distinction between two notions of creativity: psychological creativity (P-creativity), which assesses novelty of ideas with respect to its creator, and historical creativity (H-creativity), which assesses novelty with respect to the whole human history (Boden 1990). It follows that P-creativity is a necessary but not sufficient condition for H-creativity, while H-creativity implies P-creativity (Boden 1990; Nanay 2014). This distinction is related to the subjective (related to person) vs. objective creativity (related to the product) suggested by Jarvie (Jarvie 1986). In this paper our definition of creativity is aligned with objective/Hcreativity, since we mainly quantify creativity within a historical context. Computational Framework According to the discussion in the previous section, a creative product must be original, compared to prior work, and valuable (influential) moving forward. Let us construct a network of creative products and use it to assign a creativity score to each product in the network according to the aforementioned criteria. In this section, for simplicity and without loss of generality, we describe the approach based on a network of paintings, however the framework is applicable to other art or literature forms. Constructing a Painting Graph Let us denote by P = {pi, i = 1 ··· N} a set of paintings. The goal is to assign a creativity score for each painting, denoted by C(pi) for painting pi . Every painting comes with a time label indicating the date it was created, denoted by t(pi). We create a directed graph where each vertex corresponds to a painting. A directed edge (arc) connects painting pi to pj if pi was created before pj . Each directed edge is assigned a positive weight (we will discuss later where the weights come from), we denote the weight of edge (pi, pj ) by wij . We denote by Wij the adjacency matrix of the painting graph, where Wij = wij if there is an edge from pi to pj and 0 otherwise. Note that according to this definition, a painting is not connected to itself, i.e., wii = 0, i = 1 ··· N. By construction, wij > 0 ! wji = 0, i.e., the graph is anti-symmetric. To assign the weights we assume that there is a similarity function that takes two paintings and produces a positive scalar measure of affinity between them (higher value indicates higher similarity). We denote such a function by S(·, ·) yet serve others in that way, i.e., as a standard or rule for judging.” (Guyer and Wood 2000)-p186 Proceedings of the Sixth International Conference on Computational Creativity June 2015 40 Figure 1: Illustration of the construction of the Creativity Implication Network: blue arrows indicate temporal relation and orange arrows indicate reverse creativity implication (converse). and, therefore, wij = ⇢ S(pi, pj ) if t(pi) < t(pj ). 0 otherwise. Since there are multiple possible visual aspects that can be used to measure similarity, we denote such a function by Sa(·, ·) where the superscript a indicates the visual aspect that is used to measure the similarity (color, subject matter, brush stroke, etc.) This implies that we can construct multiple graphs, one for each similarity function. We denote the corresponding adjacency matrix by Wa, and the induced creativity score by Ca, which measure the creativity along the dimension of visual aspect a. In the rest of this section, for the sake of simplicity, we will assume one similarity function and drop the superscript. Details about the similarity function will be explained in the next section. Creativity Propagation Giving the constructed painting graph, how can we propagate the creativity in such a network? To answer this question we need to understand the implication of the weight of the directed edge connecting two nodes on their creativity scores. Let us assume that initially we assign equal creativity indices to all nodes. Consider painting pi and consider an incoming edge from a prior painting pk. A high weight on that edge (wki) indicates a high similarity between pi and pk, which indicates that pi is not novel, implying that we should lower the creativity score of pi (since pi is subsequent to pk and similar to it) and increase the creativity score of pk. In contrast, a low weight implies that pi is novel and hence creative compared to pk, therefore we need to increase the creativity score of pi and decreases that of pk. Let us now consider the outgoing edges from pi. According to our notion of creativity, for pi to be creative it is not enough to be novel, it has to be influential as well (some others have to imitate it). This indicates that a high weight, wij , between pi and a subsequent painting pj implies that we should increase the creativity score of pi and decrease that of pj . In contrast, a lower weight implies that pi is not influential on pj , and hence we should decrease the score for pi and increase it for pj . These four cases are illustrated in Figure 1. A careful look reveals that the two cases for the incoming edges and those for the outgoing edges are in fact the same. A higher weight implies the prior node is more influential and the subsequent node is less creative, and a lower weight implies the prior node is less influential and the subsequent node is more creative. Creativity Implication Network Before converting this intuition to a computational approach, we need to define what is considered high and low for weights. We introduce a balancing function on the graph. Let m(i) denote a balancing value for node i, where for the edges connected to that node a weight above m(i) is considered high and below that value is considered low. We define a balancing function as a linear function on the weights connecting to each node in the form Bi(w) = ⇢ w " m(i) if w > 0. 0 otherwise. We can think of different forms of balancing functions that can be used. Also there are different ways to set the parameter m(i) with different implications, which we will discuss in the next section. This form of balancing function basically converts weights lower than m(i) to negative values. The more negative the weight of an edge the more creative the subsequent node and the less influential the prior node. The more positive the weight of an edge the less creative the subsequent node and the more influential the prior node. The introduction of the negative weights in the graph, despite providing a solution to represent low weights, is problematic when propagating the creativity scores. The intuition is, a negative edge between pi and pj is equivalent to a positive edge between pj and pi. This directly suggests that we should reverse all negative edges and negate their values. Notice that the original graph construction guarantees that an edge between pi and pj implies no edge between pj and pi, therefore there is no problem with edge reversal. This process results in what we call “Creativity Implication Network”. We denote the weights of that graph by w˜ij and its adjacency matrix by W f. This process can be described Proceedings of the Sixth International Conference on Computational Creativity June 2015 41 mathematically as B(wij ) > 0 ! w˜ij = B(wij ) B(wij )=0 ! w˜ij = 0 B(wij ) < 0 ! w˜ji = "B(wij ) The Creativity Implication Network has one simple rule that relates its weights to creativity propagation: the higher the weight of an edge between two nodes, the less creative the subsequent node and the more creative the prior node. Note that the direction of the edges in this graph is no longer related to the temporal relation between its nodes, instead it is directly inverse to the way creativity scores should propagate from one painting to another. Notice that the weights of this graph are non-negative. Computing Creativity Scores Given the construction of the Creativity Implication Network, we are now ready to define a recursive formula for assigning creativity scores. We will show that the construction of the Creativity Implication Network reduces the problem of computing the creativity scores to a traditional network centrality problem. The algorithm will maintain creativity scores that sum up to one, i.e., the creativity scores form a probability distribution over all the paintings in our set. Given an initial equal creativity scores, the creativity score of node pi should be updated as C(pi) = (1 " ↵) N + ↵ X j w˜ij C(pj ) N(pj ) , (1) where 0  ↵  1 and N(pj ) = P k w˜kj . In this formula, the creativity of node pi is computed from aggregating a fraction ↵ of the creativity scores from its outgoing edges weighted by the adjusted weights w˜ij . The constant term (1 " ↵)/N reflects the chance that similarity between two paintings might not necessarily indicate that the subsequent one is influenced by the prior one. For example, two paintings might be similar simply because they follow a certain style or art movement. The factor 1 " ↵ reflects the probability of this chance. The normalization term N(pj ) for node j is the sum of its incoming weights, which means that the contribution of node pj is split among all its incoming nodes based on the weights, and hence, pi will collect only a fraction w˜ij/ P k w˜kj of the creativity score of pj . The recursive formula in Eq 1 can be written in a matrix form as C = (1 " ↵) N 1 + ↵W C, ff (2) where W ff is a column stochastic matrix defined as W ffij = w˜ij/ P k w˜kj , and 1 is a vector of ones of the same size as C. It is easy to see that since W ff, C, and 1 N 1 are all column stochastic, the resulting scores will always sum up to one. The creativity scores can be obtained by iterating over Eq 2 until conversion. Also a closed-form solution for the case where ↵ 6= 1 can be obtained as C⇤ = (1 " ↵) N (I " ↵W ff) "11. (3) A reader who is familiar with social network analysis literature might directly see the relation between this formulation and some traditional network centrality algorithms. Eq 2 represents a random walk in a Markov chain. Setting ↵ = 1, the formula in Eq 2 becomes a weighted variant to eigenvector centrality (Borgatti and Everett 2006), where a solution can be obtained by the right eigenvector corresponding to the largest eigenvalue of W ff. The formulation in Eq 2 is also a weighted variant of Hubbell’s centrality (Hubbell 1965). Finally the formulation can be seen as an inverted weighted variant of the Page Rank algorithm (Brin and Page 1998). Notice that this reduction to traditional network centrality formulations was only possible because of the way the Creativity Implication Network was constructed. Originality vs. Influence The formulation above sums up the two criteria of creativity, being original and being influential. We can modify the formulation to make it possible to give more emphasis to either of these two aspects when computing the creativity scores. For example it might be desirable to emphasize novel works even though they are not influential, or the other way around. Recall that the direction of the edges in Creativity Implication Network are no longer related to the temporal relation between the nodes. We can label (color) the edges in the network such that each outgoing edge e(pi, pj ) from a given node pi is either labeled as a subsequent edge or a prior edge depending on the temporal relation between pi and pj . This can be achieved by defining two disjoint subsets of the edges in the networks Eprior = {e(pi, pj ) : t(pj ) < t(pi)} Esubseq = {e(pi, pj ) : t(pj ) % t(pi)} This results in two adjacency matrices, denoted by W fp and W fs such that W f = W fp + W fs, where the superscripts p and s denote the prior and subsequent edges respectively. Now Eq 1 can be rewritten as C(pi) = (1 ! ↵) N + (4) ↵[" X j w˜p ij C(pj ) Np(pj ) + (1 ! ") X j w˜s ij C(pj ) Ns(pj ) ], where Np(pj ) = P k w˜p kj and Ns(pj ) = P k w˜s kj . The first summation collects the creativity scores stemming from prior nodes, i.e., encodes the originality part of the score, while the second summation collects creativity scores stemming from subsequent nodes, i.e, encodes influence. We introduced a parameter 0  "  1 to control the effect of the two criteria on the result. The modified formulation above can be written as C = (1 " ↵) N 1 + ↵["W ggpC + (1 " ")W ggsC], (5) where W ggp and W ggs are the column stochastic adjacency matrices resulting from normalizing the columns of W fp and W fs respectively. It is obvious that the closed-form solution Proceedings of the Sixth International Conference on Computational Creativity June 2015 42 in Eq 3 is applicable to this modified formulation where W ff is defined as W ff = "W ggp + (1 " ")W ggs. Creativity Network for Art In this section we explain how the framework can be realized for the particular case of visual art. Visual Likelihood: For each painting we can use computer vision techniques to obtain different feature representations for its image, each encoding a specific visual aspect(s) related to the elements and principles of arts. We denote such features by fa i for painting pi, where a denotes the visual aspect that the feature quantifies. We define the similarity between painting pi and pj , as the likelihood that painting pj is coming from a probability model defined by painting pi. In particular, we assume a Gaussian probability density model for painting pi, i.e., Sa(pj , pi) = P r(pj |pi, a) = N (·; fa i , #aI). It is important to limit the connections coming to a given painting. By construction, any painting will be connected to all prior paintings in the graph. This makes the graph highly biased since modern paintings will have extensive incoming connections and early paintings will have extensive outgoing connections. Therefore we limit the incoming connections to any node to at most the top K edges (the K most similar prior paintings). Temporal Prior: It might be desirable to add a temporal prior on the connections. If a painting in the nineteenth century resembles a painting from the fourteenth century, we shouldn’t necessarily penalize that as low creativity. This is because certain styles are always reinventions of older styles, for example neoclassicism and renaissance. Therefore, these similarities between styles across distant time periods should not be considered as low creativity. Therefore, we can add a temporal prior to the likelihood as Sa(pj , pi) = P rv(pj |pi, a) · P rt (pj |pi), where the second probability is a temporal likelihood (what is the likelihood that pj is influenced pi given their dates) and the first is the visual likelihood. There are different ways to define such a temporal likelihood. The simplest way is a temporal window function, i.e., P rt (pj |pi)=1 if pi is within K temporal neighbors prior to pj and 0 otherwise2. Balancing Function: There are different choices for the balancing function B(w), as well as the parameter for that function. We mainly used a linear function for that purpose. The parameter m can be set globally over the whole graph, or locally for each time period. A global m can be set as the p-percentile of the weights of the graph, which is p-percentile of all the pairwise likelihoods. This directly means that p% of the edges of the graph will be reversed when constructing the Creativity Implication Graph. 2 Alternatively, a Gaussian density can be use, P rt (pj |pi) = exp(![t(pi)!t(pj )]2/#2 t ). However, adding such temporal Gaussian would complicate the algorithm since it will not be easy to estimate a suitable #t, specially the graph can have non-uniform density over the time line. One disadvantage of a global balancing function is that different time periods have different distributions of weights. This suggests using a local-in-time balancing function. To achieve that we compute mi for each node as p% of the weight distribution based on its temporal neighborhood. Experiments and Results Datasets and Visual Features Artchive: This dataset was previously used for style classification and influence discovery (Saleh et al. 2014). It contains a total of 1710 images of art works (paintings and sculptures) by 66 artists, from 13 different styles from 1412- 1996, chosen from Mark Harden’s Artchive database of fineart (Harden ). The majority of the images are of the full work, while a few are details of the work. Wikiart.org: We used the publicly available dataset of “Wikiart paintings”3; which, to the best of our knowledge, is the largest online public collection of artworks. This collection has images of 81,449 fine-art paintings and sculptures from 1,119 artist spanning from 1400-2000+. These paintings are from 27 different styles (Abstract, Byzantine, Baroque, etc.) and 45 different genres (Interior, Landscape, Portrait, etc.). We pruned the dataset to 62,254 western paintings by removing genres and mediums that are not suitable for the analysis such as sculpture, graffiti, mosaic, installation, performance, photos, etc. For both datasets the time annotation is mainly the year. Therefore, it is not possible to tell which is prior between any pair of paintings with the same year of creation. Therefore no edge is added between their corresponding nodes. We experimented with different state-of-the-art feature representations. In particular, the results shown here are using Classeme features (Torresani, Szummer, and Fitzgibbon 2010). These features were shown to outperform other stateof-the-art features for the task of style classification (Saleh et al. 2014). These features (2659 dimensions) provide semantic-level representation of images, by encoding the presence of a set of basic-level object categories (e.g. horse, cross, etc.), which captures the subject matter of the painting. Some of the low-level features used to learn the Classeme features also capture the composition of the scene. Example Results We show qualitative and quantitative experimental results of the framework applied to the aforementioned datasets. As mentioned in the introduction, any result has to be evaluated given the set of paintings available to the algorithm and the capabilities of the visual features used. Given that the visual features used are mainly capturing subject matter and composition, sensible creativity scores are expected to re- flect these concept. A low creativity score does not mean that the work is not creative in general, it just means that the algorithm does not see it creative with respect to its encoding of subject matter and composition. Figures 2-top and 3 show the creativity scores obtained on the Artchive and Wikiart datasets respectively. Figure 2- bottom shows a zoom in to the period between 1850-1950 in 3 http://www.wikiart.org/ Proceedings of the Sixth International Conference on Computational Creativity June 2015 43 the Artchive dataset, which is very dense in the graph4. In all figures we plot the scores vs. the year of the painting. The figures visualize some of the paintings that obtained high scores, as well as some with low scores (the scores in the plots are scaled). We randomly sampled points with low scores for visualization. A close look at the paintings that scored low (bottom) reveals the presence of typical subject matter that is common in the dataset, or in some cases the image presents an unclear view of a sculpture (e.g. Rodin 1889 sculpture in the bottom right). The general trend shows peaks in creativity around the time of High Renaissance (late 15th , early 16th century) and the late 19th and early 20th centuries, and a significant increase in the second half of the 20th century. One of the interesting findings is the algorithm’s ability to point out wrong annotations in the dataset. For example, one of the highest scoring paintings around 1910 was a painting by Piet Mondrain called “ Composition en blanc, rouge et jaune,” (see Figure 2). By examining this painting, we found that the correct date for it is around 1936 and it was mistakenly annotated in the Artchive dataset as 1910 5. Modrain did not start to paint in this grid-based (Tableau) style untill around 1920. So it is no surprise that wrongly dating one of Mondrain’s tableau paintings to 1910 caused it to obtain high creativity score, even above the cubism paintings from that time. On the Wikiart dataset, one of the highest-scored painting was “tornado” by contemporary artist Joe Goode, which was found to be mistakenly dated 1911 in Wikiart 6. A closer look at the artist biography revealed that he was born in 1937 and this painting was created in 19917. It is not surprising for a painting that was created in 1991 to score very high in creativity if it was wrongly dated to 1911. These two examples, besides indicating that the algorithm works, show the potential of proposed algorithm in in spotting wrong annotations in large datasets, which otherwise would require tremendous human effort. Time Machine Experiment Given the absence of ground truth for creativity, the aforementioned wrong annotations inspired us with a methodology to quantitatively evaluate the framework. We designed what we call “time machine” experiment, where we change the date of an artwork to some point in the past or some point in the future, relative to its correct time of creation. Then we compute the creativity scores using the wrong date, by running the algorithm on the whole data. We then compute the gain (or loss) in the creativity score of that artwork compared to its score using correct dating. What should we expect 4 For Figure 2 a temporal window historical prior is uses. For Figure 3 no historical prior was used. For both, we set K=500,↵=0.15 5 The wrong annotation is in the Artchive CD obtained in 2010. The current online version of Artchive has corrected annotation for this painting 6 http://www.wikiart.org/en/search/tornado/ 1#supersized-search-318512 - accessed on Feb 28th, 20157 http://www.artnet.com/artists/joe-goode/ tornado-9-2Y7erPME95YlkhFp7DRWlA2 Table 1: Time Machine Experiment Art movement avg % gain/loss % increase Moving backward to AD 1600 Neoclassicism 5.78%±1.28 97%±4.8 Romanticism 7.52%± 2.04 98%± 4.2 Impressionism 14.66%± 2.78 99%±3.2 Post-Impressionism 16.82%±2.22 99%±3.1 Symbolism 15.2%±2.94 97%±4.8 Expressionism 16.83%±2.43 98%±4.2 Cubism 13.36%±2.43 89%±9.9 Surrealism 12.66%±1.82 95%±7.1 American Modernism 11.75%±2.99 84%±8.4 Wandering around to AD 1600 Renaissance 0.68 %± 2.05 39%±5.7 Baroque 2.85%± 1.09 71%±19.7 Moving forward to AD 1900 Renaissance -8.13%± 2.02 20%±10.5 Baroque -10.2%±2.03 0%±0 from an algorithm that assigns creativity in a sensible way? Moving a creative painting back in history would increase its creativity score, while moving a painting forward would decrease its creativity. Therefore, we tested three settings: I) Moving back to AD 1600: For styles that date after 1750, we set the test paintings back to a random date around 1600 using Normal distribution with mean 1600 and std 50 years, i.e. N(1600, 502) . II) Moving forward to AD 1900: For the Renaissance and Baroque styles, we set the test paintings to random dates around 1900 sampled from N(1900, 502). III) Wandering about AD 1600 (baseline): In this experiment, for the Renaissance and Baroque styles, we set the test paintings to random dates around 1600 sampled from N(1600, 502). Table 1 shows the results of these experiments. We ran this experiment on the Artchive dataset with no temporal prior. In each run we randomly selected 10 test paintings of a given style and applied the corresponding move. We used 10 as a small percentage of the data set (less than 1%), not to disturb the global distribution of creativity. We repeated each experiment 10 times and reported the mean and standard deviations of the runs. For each style we computed the average gain/loss of creativity scores by the time move. We also computed the percentage of the test paintings whose scores have increased. From the table we clearly see that paintings from Impressionist, Post-Impressionist, Expressionist, and Cubism movements have significant gain in their creativity scores when moved back to 1600. In contrast, Neoclassicism paintings have the least gain, which makes sense, because Neoclassicism can be considered as revival to Renaissance. Romanticism paintings also have a low gain when moved back to 1600, which is justified because of the connection between Romanticism and Gothicism and Medievalism. On the other hand, paintings from Renaissance and Baroque styles have loss in their scores when moved forward to 1900, while they did not change much in the wandering-around-1600 setting. Proceedings of the Sixth International Conference on Computational Creativity June 2015 44 1400 1500 1600 1700 1800 1900 2000 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 Mantegna; 1454 Leonardo; 1469 Mantegna 1474 Velazquez 1632 Vermeer 1661 Michelangelo 1564 Durer; 1503 Durer; 1514 Goya 1780 Vermeer 1664 Ingres; 1806 Ingres; 1851 Ingres; 1852 Monet 1865 Rodin; 1889 Munch 1893 Rousseau; 1898 Mondrian 1910 Lichtenstein; 1972 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Cezanne; 1887 Van Gogh 1889 Rousseau 1897 Klimt 1898 Picasso 1903 Picasso; 1907 Mondrian 1910 Picasso; 1912 Picasso; 1912 Braque 1913 Malevich 1916 Malevich; 1915 Okeeffe 1919 Mondrian 1918 Malevich; 1929 Degas; 1870 Pissarro; 1885 Rodin; 1889 Cezanne; 1906 Figure 2: Top: Creativity scores for 1710 paintings from Artchive dataset. Bottom: zoom in to the period 1850-1950. Each point represents a painting. The thumbnails illustrate some of the paintings that scored relatively high or low compared to their neighbors. Only artist names and dates of the paintings are shown on the graph because of limited space. The red-dotted-framed painting by Piet Mondrain scored very high because it was wrongly dated to 1910 instead of 1936 in the dataset. Proceedings of the Sixth International Conference on Computational Creativity June 2015 45 1400 1500 1600 1700 1800 1900 2000 2100 1 2 3 4 5 6 7 8 9 10 Rubens 1635 Gozzoli 1461 Da Vinci; 1480 Signorelli 1482 Carracci 1605 Dorazio 1998 Calhau 1998 Dorazio; 1990 Lefranc 1929 Gilliam; 1965 Mantegna;1502 Veronese;1558 Winterhalter Kittelsen; 1911 Reni, 1625 Canaletto; 1725 Fragonard; 1778 ; 1860 Berkowitz 1978 Landfield 1968 Pissarro; 1897 Spilliaert 1908 Mattis; 1916 Bruegel 1568 Durer 1497 Cranach; 1536 Figure 3: Creativity scores for 62K paintings from the wikiart.org dataset Conclusion and Discusion The paper presented a computational framework to assess creativity among a set of products. We showed that, by constructing a creativity implication network, the problem reduces to a traditional network centrality problem. We realized the framework for the domain of visual art, where we used computer vision to quantify similarity between artworks. We validated the approach qualitatively and quantitively on two large datasets. In this paper we focused on “creative” as an attribute of a product, in particular artistic products such as painting, where creativity of a painting is defined as the level of its originality and influence. However, the computational framework can be applied to other forms such as sculpture, literature, science etc. Quantifying creativity as an attribute of a product facilitates quantifying the creativity of the person who made that product, as a function over the creator’s set of products. Hence, our proposed framework also serves as a way to quantify creativity as an attribute for people. References Boden, M. A. 1990. The creative mind: Myths and mechanisms. Basic Books. Borgatti, S. P., and Everett, M. G. 2006. A graph-theoretic perspective on centrality. Social networks 28(4):466–484. Brin, S., and Page, L. 1998. The anatomy of a large-scale hypertextual web search engine. 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