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Statistical Patterns in Movie Rating Behavior.

Ramos M, Calvão AM, Anteneodo C - PLoS ONE (2015)

Bottom Line: We find that the distribution of votes presents scale-free behavior over several orders of magnitude, with an exponent very close to 3/2, with exponential cutoff.It is remarkable that this pattern emerges independently of movie attributes such as average rating, age and genre, with the exception of a few genres and of high-budget films.These results point to a very general underlying mechanism for the propagation of adoption across potential audiences that is independent of the intrinsic features of a movie and that can be understood through a simple spreading model with mean-field avalanche dynamics.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, PUC-Rio, Rio de Janeiro, Brazil.

ABSTRACT
Currently, users and consumers can review and rate products through online services, which provide huge databases that can be used to explore people's preferences and unveil behavioral patterns. In this work, we investigate patterns in movie ratings, considering IMDb (the Internet Movie Database), a highly visited site worldwide, as a source. We find that the distribution of votes presents scale-free behavior over several orders of magnitude, with an exponent very close to 3/2, with exponential cutoff. It is remarkable that this pattern emerges independently of movie attributes such as average rating, age and genre, with the exception of a few genres and of high-budget films. These results point to a very general underlying mechanism for the propagation of adoption across potential audiences that is independent of the intrinsic features of a movie and that can be understood through a simple spreading model with mean-field avalanche dynamics.

No MeSH data available.


Pictorial representation of the contagion process and the equivalent branching process.(a) Underlying network of contacts. The contagion starts at an initiator node (largest node). Contagion occurs (green arrows) to some of its neighbors (a number of them that we assume to be a random variable) and so on an avalanche develops. (b) A branching tree is built from the contacts that participate of the contagion process. (c) Branching tree realization of a simple Galton-Watson process. The largest node represents the initiator, the first successive generations of the tree are identified with colors, and the final tree is shown as a result of a cascade that becomes extinct at the 13th generation. (d) Distribution of avalanche sizes from simulations of the contagion process: for a simple (network-free) Galton-Watson (GW) process and for the equivalent contagion process on top of Erdős-Rényi (ER) and Barabási-Albert (BA) networks of size 106 and average connectivity 〈k〉 = 100. In all cases the probability pj of influencing j individuals was arbitrarily chosen to be exponential with mean p ≲ 1.0, and 106 realizations were considered.
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pone.0136083.g011: Pictorial representation of the contagion process and the equivalent branching process.(a) Underlying network of contacts. The contagion starts at an initiator node (largest node). Contagion occurs (green arrows) to some of its neighbors (a number of them that we assume to be a random variable) and so on an avalanche develops. (b) A branching tree is built from the contacts that participate of the contagion process. (c) Branching tree realization of a simple Galton-Watson process. The largest node represents the initiator, the first successive generations of the tree are identified with colors, and the final tree is shown as a result of a cascade that becomes extinct at the 13th generation. (d) Distribution of avalanche sizes from simulations of the contagion process: for a simple (network-free) Galton-Watson (GW) process and for the equivalent contagion process on top of Erdős-Rényi (ER) and Barabási-Albert (BA) networks of size 106 and average connectivity 〈k〉 = 100. In all cases the probability pj of influencing j individuals was arbitrarily chosen to be exponential with mean p ≲ 1.0, and 106 realizations were considered.

Mentions: In our modeling, one or a few active initiators propagate the idea of watching a given movie, convincing (or infecting) some of their contacts who, in turn, can infect others, and so on. That is, amongst the k contacts of an activated node, a random number j of them, chosen with probability distribution {pj, with 0 ≤ j ≤ k < ∞}, becomes activated (see Fig 11a, where we depicted a small connectivity network only for the sake of clearness). The dissemination process stops when, in a given time step, no new nodes become activated. The total number of activated nodes, which we will refer to as an avalanche or cascade, reflects the number of people who decided to watch the movie.


Statistical Patterns in Movie Rating Behavior.

Ramos M, Calvão AM, Anteneodo C - PLoS ONE (2015)

Pictorial representation of the contagion process and the equivalent branching process.(a) Underlying network of contacts. The contagion starts at an initiator node (largest node). Contagion occurs (green arrows) to some of its neighbors (a number of them that we assume to be a random variable) and so on an avalanche develops. (b) A branching tree is built from the contacts that participate of the contagion process. (c) Branching tree realization of a simple Galton-Watson process. The largest node represents the initiator, the first successive generations of the tree are identified with colors, and the final tree is shown as a result of a cascade that becomes extinct at the 13th generation. (d) Distribution of avalanche sizes from simulations of the contagion process: for a simple (network-free) Galton-Watson (GW) process and for the equivalent contagion process on top of Erdős-Rényi (ER) and Barabási-Albert (BA) networks of size 106 and average connectivity 〈k〉 = 100. In all cases the probability pj of influencing j individuals was arbitrarily chosen to be exponential with mean p ≲ 1.0, and 106 realizations were considered.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4555649&req=5

pone.0136083.g011: Pictorial representation of the contagion process and the equivalent branching process.(a) Underlying network of contacts. The contagion starts at an initiator node (largest node). Contagion occurs (green arrows) to some of its neighbors (a number of them that we assume to be a random variable) and so on an avalanche develops. (b) A branching tree is built from the contacts that participate of the contagion process. (c) Branching tree realization of a simple Galton-Watson process. The largest node represents the initiator, the first successive generations of the tree are identified with colors, and the final tree is shown as a result of a cascade that becomes extinct at the 13th generation. (d) Distribution of avalanche sizes from simulations of the contagion process: for a simple (network-free) Galton-Watson (GW) process and for the equivalent contagion process on top of Erdős-Rényi (ER) and Barabási-Albert (BA) networks of size 106 and average connectivity 〈k〉 = 100. In all cases the probability pj of influencing j individuals was arbitrarily chosen to be exponential with mean p ≲ 1.0, and 106 realizations were considered.
Mentions: In our modeling, one or a few active initiators propagate the idea of watching a given movie, convincing (or infecting) some of their contacts who, in turn, can infect others, and so on. That is, amongst the k contacts of an activated node, a random number j of them, chosen with probability distribution {pj, with 0 ≤ j ≤ k < ∞}, becomes activated (see Fig 11a, where we depicted a small connectivity network only for the sake of clearness). The dissemination process stops when, in a given time step, no new nodes become activated. The total number of activated nodes, which we will refer to as an avalanche or cascade, reflects the number of people who decided to watch the movie.

Bottom Line: We find that the distribution of votes presents scale-free behavior over several orders of magnitude, with an exponent very close to 3/2, with exponential cutoff.It is remarkable that this pattern emerges independently of movie attributes such as average rating, age and genre, with the exception of a few genres and of high-budget films.These results point to a very general underlying mechanism for the propagation of adoption across potential audiences that is independent of the intrinsic features of a movie and that can be understood through a simple spreading model with mean-field avalanche dynamics.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, PUC-Rio, Rio de Janeiro, Brazil.

ABSTRACT
Currently, users and consumers can review and rate products through online services, which provide huge databases that can be used to explore people's preferences and unveil behavioral patterns. In this work, we investigate patterns in movie ratings, considering IMDb (the Internet Movie Database), a highly visited site worldwide, as a source. We find that the distribution of votes presents scale-free behavior over several orders of magnitude, with an exponent very close to 3/2, with exponential cutoff. It is remarkable that this pattern emerges independently of movie attributes such as average rating, age and genre, with the exception of a few genres and of high-budget films. These results point to a very general underlying mechanism for the propagation of adoption across potential audiences that is independent of the intrinsic features of a movie and that can be understood through a simple spreading model with mean-field avalanche dynamics.

No MeSH data available.