# Category Archives: Time Series Analysis

## Film style and narration in Rashomon

UPDATE: 13 April 2014: The revised version of this article has now been published as Film Style and Narration in

Rashomon,Journal of Japanese and Korean Cinema5 (1-2) 2013: 21-36. DOI: 10.1386/jjkc.5.1-2.21_1.A post-print of the article can be downloaded here: Nick_Redfern – Film style and narration in Rashomon (post print)

And so after a long (and much enjoyed break) I return to the blogosphere with the first draft of paper on film style and narration in *Rashomon*. This paper is different to other statistical analyses of film style I have published on this site and to all other studies of film style and narration because it uses multivariate analysis to look at several different aspects of film style together. The method used is multiple correspondence analysis, and you can find a good introductory chapter on MCA here. The software I used is FactoMineR for R, and the website explaining how to do the analysis can be found here.

Multivariate analysis has been used in the quantitative study of literature for some time (see the links below the abstract), but this is the first time multivariate analysis has been applied to film style and it appears to work very well. I am currently looking at some other applications, particularly in distinguishing between the different parts of portmanteau horror films (which is a proper scholarly endeavour and not simply an excuse to watch lots of portmanteau horror films).

An Excel file contain the data used in the analysis can be accessed here: Nick Redfern – Rashomon. This file contains two worksheets: the first is the shot length data for the film, and the second is that data used in the multiple correspondence analysis.

## Abstract

This article analyses the use of film style in

Rashomon(1950) to determine if the different accounts of the rape and murder provided by the bandit, the wife, the husband, and the woodcutter are formally distinct by comparing shot length data and using multiple correspondence analysis to look for relationships between shot scale, camera movement, camera angle, and the use of point-of-view shots, reverse-angle cuts, and axial cuts. The results show that the four accounts of the rape and the murder inRashomondiffer not only in their content but also in the way they are narrated. The editing pace varies so that although the action of the film is repeated the presentation of events to the viewer is different each time. There is a distinction between presentational (shot scale and camera movement) and perspectival (shot types) aspects of style depending on their function within the film, while other elements (camera angle) fulfil both these functions. Different types of shot are used to create the narrative perspectives of the bandit, the wife, and the husband that marks them out as either active or passive narrators reflecting their level of narrative agency within the film, while the woodcutter’s account exhibits both active and passive aspects to create an ambiguous mode of narration.Rashomonis a deliberately and precisely constructed artwork in which form and content work together to create an epistemological puzzle for the viewer.

On the multivariate analysis of literature see the following:

**Hoover DL** 2003 Multivariate analysis and the study of style variation, *Literary and Linguistic Computing* 18 (4): 341-360.

**Stewart LL** 2003 Charles Brockden Brown: quantitative analysis and literary style, *Literary and Linguistic Computing* 18 (2): 129-138.

**Tabata T** 1995 Narrative style and the frequencies of very common words: a corpus-based approach to Dickens’s first person and third person narratives, *English Corpus Studies* 2: 91-109.

## The mAR index of Hollywood films

UPDATE (March 2015): A revised version of this paper has now been published as Robust estimation of the mAR index of high grossing films at the US box office, 1935 to 2005, *Journal of Data Science* 12 (2) 2014: 277-291. [The pdf of this article can be accessed here: 4.JDS-1181_final-1].

UPDATE: reviewing the methodology of the mAR index in general, Mike Baxter noted an error in the data whereby I had reported the exponent of the negative exponential function instead of the mAR index for films from the 1960s. I have now corrected this and redone the analysis and the graphs (which are still cool). This mainly effects the conclusions regarding differences between genres. Overall, it turns out that, as a result of this error, I had actually underestimated the difference between the classical and rank mAR indices. If anyone finds any other errors then feel free to add a comment to this post and I’ll try to correct it as soon as possible.

And so to finish the month as we started, looking at robust estimates of the mAR index of film style. Below is the first draft of a paper comparing the mAR index based on the methods used by James Cutting, Jordan De Long and Christine Nothelfer to describe the clustering of shots in motion picture with a rank-based alternative that is resistant to outliers. Naturally, it features some pretty cool graphs.

Robust estimation of the modified autoregressive index for high grossing films at the US box office, 1935 to 2005The modified autoregressive (mAR) index describes the clustering of shots of similar duration in a motion picture. In this paper we derive robust estimates of the mAR index for high grossing films at the US box office using a rank-based autocorrelation function resistant to the influence of outliers and compare this to estimates obtained using the classical, moment-based autocorrelation function. The results show that (1) The classical mAR function underestimates both the level of shot clustering and the variation in style among the films in the sample.; (2) there is a decline in shot clustering from 1935 to the 1950s followed by an increase from the 1960s to the 1980s and a levelling off thereafter rather than the monotonic trend indicated by the classical index, and this is mirrored in the trend of the median shot lengths and interquartile range; and (3) the rank mAR index indentifies differences between genres missed by the classical index.

## Robust estimation of the modified autoregressive index of film style

Earlier this I looked at the time series structure ITV news bulletins using robust methods of autocorrelation. This post follows on from that earlier study, this time looking at BBC news bulletins. This paper was written with three goals in mind. First, I wanted to improve on the method used before. Second, I wanted to try the rank based method of estimating the mAR index. Third, I wanted to apply these methods to a different cluster of data sets to see if I would come up with similar results.

The paper can be accessed as a pdf file here: Nick Redfern – Robust estimation of the modified autoregressive index of film style

AbstractThe modified autoregressive index (mAR) describes the tendency of shots of similar length to cluster together in a motion picture but is not resistant to the influence of outliers if derived from the classical moment-based partial autocorrelation function. In this paper we calculate robust estimates of the modified autoregressive index based on outlier-resistant partial autocorrelation function based on the ranks of the shot length data and robust measure of scale. The classical, rank, and robust methods of determining mAR are compared for a sample of BBC news bulletins.

## Exploratory data analysis and film form

Following on from my earlier posts on the editing structure of slasher films, this week I have a draft of a paper that combines my early observations (much re-written) along with an analysis of the relationship between editing and the narrative structure of *Friday the Thirteenth* (1980)

Exploratory data analysis and film form: The editing structure of slasher filmsWe analyse the dynamic editing structure of four slasher films released between 1978 and 1983 with simple ordinal time series methods. We show the order structure matrix is a useful exploratory data analytical method for revealing the editing structure of motion pictures without requiring

a prioriassumptions about the objectives of a film. Comparing the order structure matrices of the four films, we find slasher films share a common editing pattern closely comprising multiple editing regimes with change points between editing patterns occur with large changes in mood and localised clusters of shorter and longer takes are associated with specific narrative events. The multiple editing regimes create different types of frightening experiences for the viewer with slower edited passages creating a pervading sense of foreboding and rapid editing linked to the frenzied violence of body horror, while the interaction of these two modes of expression intensifies the emotional experience of watching a slasher film.

The paper can be accessed here: Nick Redfern – The Editing Structure of Slasher Films.

The shot length data for all four films can be accessed as a single Excel file: Nick Redfern – Slasher Films.

Analysing the editing structure of these slasher films is only part of this paper. Another goal was to outline exploratory data analysis as a data-driven approach to understanding film style that avoids a specific problem of existing ways of thinking about film style.

Existing methods of analysing film style make *a priori* assumptions about the functions of style and then provide examples to support this assertion. This runs the risk of begging the question and *circulus in probando*, in which the researcher’s original assumption is used as a basis for selecting the pertinent relations of film style which are then used to justify the basis for making assumptions about the functions of film style. We would like to avoid such logically flawed reasoning whilst also minimising the risk that we will miss pertinent relations that did not initially occur to us. By adopting a data-driven approach we can derive the functions of film style by studying the elements themselves without the need to make any such *a priori* assumptions. Exploratory data analysis (EDA) allows us to do this by forcing us to attend to the data on its own terms.

Although this is a method developed within statistics, EDA can be applied not just to numerical data but to any situation where we need to understand the phenomenon before us. For example, I had not noticed that the number of scenes between hallucinations in *Videodrome* reduces by constant factor until I sat down and wrote out the narrative structure of the film (see here).

Two very useful references are:

**Behrens JT** 1997 Principles and practices of exploratory data analysis, *Psychological Methods* 2 (2): 131-160.

**Ellison AM** 1993 Exploratory data analysis and graphic display, in SM Scheiner and J Gurevitch (eds.) *Design and Analysis of Ecological Experiments*. New York: Chapman & Hall: 14-45.

In this paper I discuss some relations between editing and the emotional experience of watching slasher films, and below are listed some interesting references that follow on from last week’s collection of paper on neuroscience and the cinema:

**Bradley MM, Codispoti M, Cuthbert BN, and Lang PJ** 2001 Emotion and motivation I: defensive and appetitive reactions in picture processing, *Emotion* 1 (3): 276-298.

**Bradley MM, Lang PJ, and Cuthbert BN** 1993 Emotion, novelty, and the startle reflex: habituation in humans, *Behavioural Neuroscience* 107 (6): 970-980.

**Lang PJ, Bradley MM, and Cuthbert BN** 1998 Emotion, motivation, and anxiety: brain mechanisms and psychophysiology, *Biological Psychiatry* 44 (12): 1248-1263.

**Lang PJ, Davis M, and Öhman A** 2000 Fear and anxiety: animal models and human cognitive psychophysiology, *Journal of Affective Disorders* 61 (3): 137-159.

**Willems RM, Clevis K, and Hagoort P** 2011 Add a picture for suspense: neural correlates of the interaction between language and visual information in the perception of fear, *Social Cognition and Affective Neuroscience* 6 (4): 404-416.

## The editing structure of The House on Sorority Row (1983)

Following on from earlier posts on the editing structure of *Halloween* (here) and *Slumber Party Massacre* (here), this week I look at the editing in *The House on Sorority Row* (1983). The shot length data can be accessed here: Nick Redfern – The House on Sorority Row. The shot length data has been corrected by a factor of 1.0416, and includes the opening credits since these are shown over footage of the characters and locations and are therefore relevant to the narrative.

As before I’m using the order structure matrix to visualise the time series of the data for this film, but to make clearer how the matrix relates to observed data values I’ve included two run charts in Figure 1 showing the shot lengths (bottom) and the ranks of the shot lengths (middle).

**Figure 1** Order structure matrix (top), ranks (middle), and shot length data (bottom) for *The House on Sorority Row* (1983)

With a median shot length of 3.0s and interquartile range of 3.7s *The House on Sorority Row* is edited more quickly than *Halloween* (median = 4.2s, IQR = 5.7s) but is similar to *Slumber Party Massacre* (median = 3.2s, IQR = 4.5s). There is no clear trend in shot lengths across the whole film and there are no clear distinctions between different narrative sections similar to the very abrupt shift we see in the final third of *Halloween*. Nonetheless, this film follows the general formal pattern set out in the earliest films of this sub-genre, with a number of clusters of longer and shorter takes associated with the same types of narrative events as in the other films. The replication of narrative events, character types, themes, and actions in the slasher film has been extensively analysed, and looking at their editing structure in detail it becomes very clear just how quickly a single style of editing became established in this type of film. There are only a few years between them, but the only major difference between *Halloween*, *Slumber Party Massacre*, and *The House on Sorority Row* is that the latter two films are cut more quickly.

The main feature in Figure 1 is the confrontation between and the girls that begins at shot 302 and runs until shot 440. This sequence is edited very quickly (Σ = 362.2s, median = 2.0s, IQR = 2.1s), but it is clear from Figure 1 that from shot 302 to shot 366 the length of the shots actually get shorter as the scene reaches its peak: the girls force Mrs. Slater into the swimming pool at gun point and the moment of greatest tension – as one of the girls fires a shot into the pool – is the point at which editing is fastest. From shot 367 the sequence slows down using longer shots, and this can be clearly seen in the order structure matrix and the run chart of the ranks. Of course, longer is a relative term, and the ‘slowing down’ of the editing in the second part of this scene means a shift from shots less than 0.5 seconds to shots between 1.5 and 5 seconds (though there are few longer than 10 seconds). (The editing in this sequence is related to the cluster of short shots that can be seen as the white column at shots 89 – 102, and which features Vicki practising with the gun). There is clearly a relationship between the way in which this scene is edited and the way in which the emotional impact of the scene is generated; and, while it is clear from watching the film that it is edited very quickly, it is easier to appreciate how this scene is structured by looking at the time series given the difference between shorter and longer shots may only be a couple of seconds.

The other clusters of shorter takes serve a different function but are also related to moments of intense emotion. The cluster beginning 165 is part of a sequence of photographs of Mrs. Slater’s old sorority classes that begins quite slowly as the camera pans across the photos; but from shot 165 there is a change to rapid editing (accompanied by a change in the music and the use of whip pans) as Mrs. Slater tears up the pictures and burns them. Again, the change in editing style is associated with a change in the mood of the scene. The cluster of short shots from shot 855 to shot 874 is typical of the rapid editing in the latter stages of a slasher film, and is associated with the killing of Vicki and Liz as they dispose of a body. The intensity of the violence is reflected in the intensity of the editing.

This last cluster sits between two sequences edited much more slowly. The dark column in the matrix between shots 797 and shot 854 focuses on Katherine’s attempt to raise help by calling Dr. Beck, and his subsequent arrival and explanation of the night’s events. It also includes the scenes in the graveyard and the attempts to dispose of a body that we know results in disaster. This sequence is heavy on plot since it explains much if the background about Mrs. Slater and her son, Eric (i.e. the killer). The sequence that follows on from the deaths of in the graveyard (shots 875-897) shifts us back to Katherine and Dr. Beck, and is again lacking action while setting up the film’s finale.

The earlier clusters of longer takes slow down the pace of the film in order to create a pervasive sense of foreboding that de-accentuates the violence of the killings and which seek to put the viewer on edge. Shots 480-540 focus on the girls at the party and their anxiety that the body of Mrs. Slater might be discovered. This is framed as a series of long takes as Katherine meets Peter and resists his attempts to make her enjoy the party; and is notable for an elaborate tracking shot as the girls exchange glances across the dance floor. This cluster also includes the scene in which makes the rookie mistake of going down to a darkened cellar by herself to check the fuse box, and again uses a slow editing pattern to build tension before she is finally dispatched. Similarly, shots 655-692 follow Katherine as she tries to find the girls who have gone missing from the party and explores the attic room of the Mrs. Slater’s murderous son. These scenes are again important for establishing plot points and Katherine finds important symbolic objects (e.g. the jack-in-the-box), but their main purpose is to build up a state of nervous apprehension in the viewer. Interestingly, this is achieved by using slow panning shots from Katherine’s point-of-view whereas such shots in slasher films are typically used to represent the killer’s stalking of his victims. This sequence also includes the other members of the sorority trying to dispose of Mrs. Slater’s body only to run into a policeman. These sequences and the various narrative threads they present serve to create an emotionally tense atmosphere for the viewer but unlike the aggressive tensity of the rapidly cut sections this mood is one of foreboding.

This use of two different editing patterns to create two different moods for the viewer is characteristic of the slasher film and can also be seen in the time series of *Halloween* and *Slumber Party Massacre*. We tend to speak of the style of a film in singular terms as though it definitely has one – and only one – mode of expression; but since the slasher film uses different editing patterns to create different effects it would make more sense to talk of the *styles* of these films. This can also be seen in the time series of RKO musicals (see here, here, and here).

The ‘final girl’ sequence begins at shot 985 (Σ = 434.4s, median = 2.7s, IQR = 2.1s). Here *The House on Sorority Row* does show some (minor) differences to *Halloween* and *Slumber Party Massacre*. In this film we have a progressive increase in the cutting rate, and the shift to shorter shots is particularly marked in the run chart of the shot ranks. The first part of this sequence is edited relatively slowly as Katherine makes her way through the sorority house to the attic, and this can be seen in the dark column at this point in the matrix in Figure 1. This is different to the other films in which this corresponding sequence begins when the killer attacks the final girl (as can clearly be seen at shot 437 in the matrix for *Halloween*). In *The House on Sorority Row* the final girl goes looking for the killer. Once the struggle between Katherine and the killer begins (shot 1063) we see the same rapid editing observed in the *Halloween* and *Slumber Party Massacre*, but we do not see the same fast-slow-fast pattern noted in the other films as the struggle between the killer and the final girl is temporarily suspended. This is due to the postponement of the killer’s return once we think he has been killed. The last shot of the film is a close-up of the eye as we discover Katherine has not defeated him and assume their struggle to the death will continue. *The House on Sorority Row* presents the same final girl sequence as the other slasher films I have looked at but cuts the narrative (and therefore the editing pattern) off before it reaches its ‘natural’ conclusion.

Like *Halloween*, *The House on Sorority Row* was remade in 2009 and a future post will look at the similarities and the differences between the original version of these films and their later reinvention.

## Robust time series analysis of ITV news bulletins

I have mentioned numerous times on this blog the importance of using robust statistics to describe film style. This week I continue in this vein, albeit in a different context – time series analysis. In a much publicised piece of work James Cutting, Jordan De Long, and Christine Nothelfer (2010) calculated partial autocorrelation functions and a modified autoregressive index for a sample of Hollywood films. While I have no problems with the basis of this research, I do think the results are dubious due to the use of non-robust methods to determine the autocovariance between shot lengths in these films. The paper attached below analyses the editing structure of the set of ITV news bulletins I discussed in a paper last year, comparing the results produced using classical and robust autocovariance functions.

Robust time series analysis of ITV news bulletinsIn this paper we analyse the editing of ITV news bulletins using robust statistics to describe the distribution of shot lengths and its editing structure. Commonly cited statistics of film style such as the mean and variance do not accurately describe the style of a motion picture and reflect the influence of a small number of extreme values. Analysis based on such statistics will inevitably lead to flawed conclusions. The median and are superior measures of location and dispersion for shot lengths since they are resistant to outliers and unaffected by the asymmetry of the data. The classical autocovariance and its related functions based on the mean and the variance is also non-robust in the presence of outliers, and leads to a substantially different interpretation of editing patterns when compared to robust time statistics that are outlier resistant. In general, the classical methods underestimate the persistence in the time series of these bulletins indicating a random editing process whereas the robust time series statistics suggest an AR(1) or AR(2) model may be appropriate.

The pdf file is here: Nick Redfern – Robust Time Series Analysis of ITV News Bulletins

My original post on the time series analysis of ITV news bulletins can be accessed here, along with the datasets for each of the fifteen bulletins.

My new results indicate the conclusions of Cutting, De Long, and Nothelfer are flawed, and that it is very likely they have underestimated the autocovariance present in the editing of Hollywood films. The discrete and modified autoregressive indexes they present are likely to be too low, though there may be some instances when they are actually too high. This is not enough to reject their conclusion that Hollywood films have become increasingly clustered in packets of shots of similar length, and I have not yet applied this method to their sample of films. It is, however, enough to recognise there are some problems with the methodology and the results of this research.

### References

**Cutting JE, Delong JE, and Nothelfer CE** 2010 Attention and the evolution of Hollywood film, *Psychological Science* 21 (3): 432-439.

## Using kernel densities to analyse film style

### 1. Introduction

Since a film typically comprises several hundred (if not thousands) of shots describing its style clearly and concisely can be challenging. This is further complicated by the fact that editing patterns change over the course of a film. Numerical summaries are useful but limited in the amount of information they can convey about the style of a film, and while two films may have the same median shot length or interquartile range they may have very different editing patterns. Numerical summaries are useful for describing the whole of a data set but are less effective when it comes to accounting for changes in style over time. These problems may be overcome by using graphical as well as numerical summaries to communicate large amounts of information quickly and simply. Graphs also fulfil an analytical role, providing insights into a data set and revealing its structure. A good graph not only allows the reader to see what is important about a data set the writer wishes to convey, but also enables the researcher to discover what is important in the first place.

It should be common practice in the statistical analysis of film style to include graphical summaries of film style (though this is rarely the case), and there are several different types of simple graphs that can be used. These include cumulative distribution functions, box-plots, vioplots, and time-ordered displays such as run charts and order structure matrices. In this post I describe two different uses of kernel density estimation as graphical methods for analysing film style. The next section introduces the basics of kernel density estimation. Section three discusses the use of kernel densities to describe and compare shot length distributions, while section four applies kernel densities to the point process of two RKO musicals to describe and compare how cutting rates change over time.

### 2. Kernel Density Estimation

The kernel density is a nonparametric estimate of the probability density function of a data set, and shows us the range of the data, the presence of any outliers, the symmetry of the distribution (or lack thereof), the shape of the peak, and the modality of the data (Silverman 1986; Sheather 2004). A kernel density thus performs the same functions as histogram but is able to overcome some of the limitations of the latter. Since no assumptions are required about the functional form of the data kernel densities are a useful graphical method for exploratory data analysis (Behrens & Yu 2003). The purpose of exploratory data analysis is to reveal interesting and potentially inexplicable patterns in data so that we can answer the general question ‘what is going on here?’ Kernel densities allows us to this by describing the relative likelihood a shot in a film will take on a particular value, or by allowing us to see how the density of shots in a film changes over time.

The kernel density is estimated by summing the kernel functions superimposed on the data at every value on the 𝑥*x*-axis. This means that we fit a symmetrical function (the kernel) over each individual data point and then add together the values of the kernels so that the contribution of some data point *x*_{i} to the density at *x* depends on how far it lies from *x*. The kernel density estimator is

where *n* is the sample size, *h* is a smoothing parameter called the *bandwidth*, and *K* is the kernel function. There are several choices for *K* (Gaussian, Epanechnikov, triangular, etc.) though the choice of kernel is relatively unimportant, and it is the choice of the bandwidth that determines the shape of the density since this value controls the width of the kernel. If the bandwidth is too narrow the estimate will contain lots of spikes and the noise of the data will obscure its structure. Conversely, if the bandwidth is too wide the estimate will be over-smoothed and this will again obscure the structure of the data. The kernel density estimate is an improvement on the use of histograms to represent the density of a data set since the estimate is smooth and does not depend on the end-points of the bins, although a shared limitation is the dependence on the choice of the bandwidth. Another advantage of the kernel density is that two or more densities can be overlaid on the same chart for ease of comparison whereas this is not possible with a histogram.

Figure 1 illustrates this process for *Deduce, You Say* (Chuck Jones, 1956), in which the density shows how the shot lengths of this film are distributed. Beneath the density we see a 1-D scatter plot in which each line indicates the length of a shot in this film (*x*_{i}), with several shots having identical values. The Gaussian kernels fitted over each data point are shown in red and the density at any point on the *x*-axis is equal to the sum of the kernel functions at that point. The closer the data points are to one another the more the individual kernels overlap and the greater the sum of the kernels – and therefore the greater the density – at that point.

All widely available statistical software packages produce kernel density estimates for a data set. An online module for calculating kernel densities can be found here.

### 3. Describing and comparing shot length distributions

A shot length distribution is a description of the data set created for a film by recording the length of each shot in seconds. Analysing the distribution of shot lengths in a motion picture allows us to answer questions such as ‘is this film edited quickly or slowly?’ and ‘does this film use a narrow or a broad range of different shot lengths?’ Comparing the shot length distributions of two or more films allows us to determine if they have similar styles: is film A edited more quickly than film B and does it exhibits more or less variation in its use of shot lengths? A kernel density estimate provides a simple method for answering these questions.

From the kernel density of *Deduce, You Say* in Figure 1 we see the distribution of shot lengths is asymmetrical with the majority of shots less than 10 seconds long. There is a small cluster of shots around 15 seconds in length, and there are three outliers greater than 20 seconds. From just a cursory glance at Figure 1 we can thus obtain a lot of information very quickly that can then guide our subsequent analysis. for example, we might ask what events are associated with the longer takes in this film?

**Figure 1** The kernel density estimate of shot lengths in *Deduce, You Say* (Chuck Jones, 1956) showing the kernel functions fitted to each data point (N = 58, Bandwidth = 1.356)

Suppose we wanted to compare the shot length distributions of two films. Figure 2 shows the kernel density estimates of the Laurel and Hardy shorts *Early to Bed* (1928) and *Perfect Day* (1929). It is immediately that clear though both distributions are positively skewed, the shot length distributions of these two films are very different. The density of shot lengths for *Early to Bed* covers a narrow range of shot lengths while that for *Perfect Day* is spread out over a wide range of shot lengths. The high density at ~2 seconds for *Early to Bed* shows that the majority of shots in this film are concentrated at lower end of the distribution with few shots longer than 10 seconds, while the lower peak for *Perfect Day* shows there is no similar concentration of shots of shorter duration and the shot lengths are spread out across a wide range (from 20 to 50.2 seconds) in the upper tail of the distribution. We can conclude that *Early to Bed* is edited more quickly than *Perfect Day* and that it shot lengths exhibit less variation; and though we could have come to these same conclusions using numerical summaries alone the comparison is clearer and more intuitive when represented visually.

**Figure 2** Kernel density estimates shot lengths in *Early to Bed* (1928) and *Perfect Day* (1929)

### 4. Time series analysis using kernel densities

Film form evolves over time and we can use kernel density estimation to describe the *cutting rate* of a film. Rather than focussing on the length of a shot (*L*) as the time elapsed between two cuts, we are interested in the timing of the cuts (*C*) themselves. There is a one-to-one correspondence between cuts and shot lengths, and the time at which the *j*th cut occurs is equal to the sum of the lengths of the prior shots:

Figure 3 shows the one-to-one nature of this relationship clearly.

**Figure 3** The one-to-one relationship between shot lengths (*L _{i}*) and the timing of a cut (

*C*)

_{j}Analysis of the cutting rate requires us to think of the editing of a film as a *simple point process* (Jacobsen 2006). A point process is a stochastic process whose realizations comprise a set of point events in time, which for a motion picture is simply the set of times at which the cuts occur. We apply the same method used above to the point process to produce a density estimate of the time series. Just as the density in the above examples is greatest when shot lengths are closer together, the density is greatest when one shot quickly follows another and, therefore, the shorter the shot lengths are at that point in the film. Conversely, low densities indicate shots of longer duration as consecutive shots will be distant from one another on the *x*-axis. This is similar to the use of peri-stimulus time histograms and kernel methods in neurophysiology to visualize the firing rate and timing of neuronal spike discharges (see Shimazaki & Shinamoto 2010).

Using kernel density estimation to understand the cutting rate of a film as a point process is advantageous since it requires no assumptions about the nature of the process. Salt (1974) suggested using Poisson distributions as a model of editing as a point process described by the rate parameter λ, but this method is unrealistic since homogenous Poisson point processes are useful only for applications involving temporal uniformity (Streit 2010: 1). For a motion picture the probability distribution of a cut occurring at any point in time is not independent of previous cuts, and the time series will often be non-stationary over the course of a film while also demonstrating acceleration and deceleration of the cutting rate because different types of sequences characterised by different editing regimes. We expect to see clusters of long and short takes in a motion picture and so the assumption of a Poisson process will not be appropriate, while the presence of any trends will mean that the process does not satisfy stationarity. Modelling the cutting rate as an inhomogeneous Poisson point process by allowing λ to vary as function of time may solve some – though not necessarily all – of these problems.

To illustrate the use of kernel densities in time series analysis we compare the editing of two films tow feature Fred Astaire and Ginger Rogers: *Top Hat* (1935) and *Shall We Dance* (1937). In order to make a direct comparison between the evolution of the cutting rates the running time of each film was normalised to a unit length by dividing each shot length by the total running time. In this case we treat slow transitions (e.g. fades, dissolves, etc) as cuts, with the cut between two shots marked at the approximate midpoint of the transition. Figure 4 shows the resulting densities.

From the plot in Figure 4 for *Top Hat* we see the density for this film comprises a series of peaks and troughs, but that there is no overall trend . The low densities in this graph are associated with the musical numbers, while the high densities occur with scenes based around the rapid dialogue between Astaire and Rogers. (See here for alternative time series analyses of *Top Hat* that use different methods but arrive at the same conclusions as those below).

The first musical number is ‘No Strings (I’m Fancy Free)’, which begins at ~0.07. Astaire is then interrupted when Rogers storms upstairs to complain about the racket, and we have a scene between the two in which both the dialogue and the editing are rapid. This occurs at the peak at ~0.11 to ~0.13, and is then followed by a reprise of ‘No Strings,’ which is again shot as a long takes. The next section of the film follows on the next day as Astaire takes on the role of a London cabby and drives Rogers across town and as before this dialogue scene is quickly edited resulting in a high density of shots at ~0.19. This sequence finishes with ‘Isn’t This a Lovely Day (to be Caught in the Rain),’ which accounts for the low density of shots at ~0.21 to ~0.27 since this number again comprises long takes. The rapid cutting rate during dialogue scenes is repeated when Rogers mistakes Astaire for a married man at the hotel, and is again followed by the low density of a slow cutting rate for the scenes between Astaire and Edward Everett Horton at the theatre and the number ‘Top Hat, White Tie and Tails’ at ~0.4. After this number the action moves to Italy and there is much less variation in the density of shots in the first part of these scenes, which are focussed on dialogue and narrative. There is no big musical number until ‘Cheek to Cheek’ and this sequence accounts for the low density seen at ~0.66, being made up of just 13 shots that run to 435.7 seconds. The density increases again as we move back to narrative and dialogue until we get to the sequence between in which Horton explains the mix-up over who is married and who is not to the policeman and ‘The Piccolino’ which begins at ~0.89 and runs until ~0.96.

The density plot of the point process for *Shall We Dance* differs from that of *Top Hat* showing a trend over the running time of the film from higher to lower densities of shots, indicating the cutting rate in this film slows over the course of the film. Nonetheless we see the same pattern of troughs and peaks, and as in *Top Hat* these are associated with musicals and comedy scenes, respectively.

This film features numerous short dancing excerpts in its early scenes, but there is no large scale musical number until well into the picture. In fact, these early scenes are mostly about stopping Astaire dancing (e.g. when Horton keeps turning off the record), and the dialogue scenes that establish the confusion over Astaire’s married status as the ship departs France. These scenes are based around a similar narrative device to that used in *Top Hat* and are again edited quickly. The first big number in the film is ‘Slap that Bass’ and coincides with the low density section of the film beginning at ~0.17, indicating that this part of the film is edited more slowly that the first section. The cutting rate slowly increases until ~0.37, and this section includes the ‘Walking the Dog’ and ‘I’ve Got Beginner’s Luck’ numbers but is mostly made up of dialogue scenes between Astaire and Rogers. After this point the film exhibits a trend from higher to lower densities and there are a number of smaller cycles present between 0.37 and 0.64. This section includes the numbers and ‘They All Laughed (at Christopher Columbus)’ and the subsequent dance routine, which begins at ~0.48 and includes the trough at ~0.54. The low density section beginning at 0.64 is the scene between Astaire and Rogers in which they try to avoid reporters in the park, and comprises a number of lengthy dialogue shots and the film’s most famous number, ‘Let’s Call the Whole Thing Off.’ The editing then picks up during the dialogue scenes until we reach the next drop in the density at ~0.74 which coincides with the scenes on the ferry to Manhattan as Astaire sings ‘They Can’t Take That Away From Me.’ The next low density section begins at ~0.9, and is the big production at the end of the film with the distant framing and static camera completing the long takes in showing off the ‘Hoctor’s Ballet’ sequence, which then gives way to a more rapidly cut section featuring numerous cut-ways from the dancers to Rogers’ arriving at the theatre with the court order for Astaire only to discover him on stage with dancers wearing masks of her face. The cutting rate then slows once more as Rogers insinuates herself into the ‘Shall We Dance’ routine and the film reaches its finale.

**Figure 4** Kernel density estimates of the point processes for two RKO musicals with normalised running times

Comparing the two plots we note some of the low density periods coincide with one another. This is most clearly the case at around 0.2 and 0.64 in both films. The major numbers that end the films also occur at similar points in the narratives. This indicates that a musical number occurs at approximately the same points in both films even though the two films have different running times (*Top Hat*: 5819.9s, *Shall We Dance*: 6371.4s). This raises some interesting questions regarding the structure of other musicals featuring Astaire and Rogers. Is there always a musical number about a fifth of the way into an RKO musical featuring this pair? Is there always a major number about two-thirds the way through picture? And does the finale always occupy the last 10 per cent of the picture? Answers to these questions will have to wait until I finish transcribing all the films Astaire and Rogers made for RKO in the 1930s.

### 5. Conclusion

Kernel density estimation is a simple method for analysing the style of motion pictures, and the wide availability of statistical packages makes the use of kernel densities easy to incorporate into empirical research. Since it requires no prior assumptions about the distribution of the data this method is appropriate for exploratory data analysis. In this paper we demonstrated the how this method may be used to describe and compare the shot length distributions of motion pictures and for the time series analysis of film style.

### References

**Behrens JT and Yu C-H** 2003 Exploratory data analysis, in JA Schinka and WF Velicer (eds.) *Handbook of Psychology: Volume 2 – Research methods in Psychology*. Hoboken, NJ: John Wiley & Sons: 33-64.

**Jacobsen M** 2006 *Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes*. New York: Birkhauser.

**Salt B** 1974 Statistical style analysis of motion pictures, *Film Quarterly* 28 (1): 13-22.

**Sheather SJ** 2004 Density estimation, *Statistical Science* 19 (4): 588-597.

**Shimazaki H and Shinamoto S** 2010 Kernel bandwidth optimization in spike train estimation, *Journal of Computational Neuroscience* 29 (1-2): 171-182.

**Silverman B** 1986 *Density Estimation for Statistics and Data Analysis*. London: Chapman & Hall.

**Streit RL **2010 *Poisson Point Processes: Imaging, Tracking, and Sensing*. Dordrecht: Springer.

## The editing structure of Follow the Fleet (1936)

This I look at the editing structure of the Fred Astaire-Ginger Rogers musical *Follow the Fleet* (1936). I looked at the structure of *Top Hat* in an earlier post, which you can find here. Figure 1 presents the order structure matrix of *Follow the Fleet*, in which white columns indicate shorter shots and darker patches represent clusters of longer takes. A spreadsheet with the raw data (from a PAL DVD and corrected by 1.4016) can be accessed here: Nick Redfern – Follow the Fleet. The opening and closing credits have not been included.

**Figure 1** Order structure matrix of *Follow the Fleet* (1936)

The editing of this film doesn’t show the same clear pattern of alternating between quicker and slower cut segments we see in *Top Hat*. *Follow the Fleet* is certainly cut much more slowly, with a median shot length of 7.5 seconds and an interquartile range of 10.4 seconds compared to Top Hat’s median of 5.5s and IQR of 7.2s. In the earlier film the different editing patterns were associated with musical numbers and comedy sequences, but *Follow the Fleet* lacks the comedy element. Randolph Scott is, I’m afraid to say, terribly dull in this film (and calling his character ‘Bilge’ doesn’t help). The spark between Astaire and Rogers that drives *Top Hat*, especially in the first section set in London, is missing here to and at nearly two hours long this film doesn’t hold the same interest. It somehow achieves the stunning feat of being both lacking in plot and predictable. There does not appear to be any particular trend over time in the editing structure, and this may be due to the high variability of shot lengths. The IQR noted above is much greater than appears to be typical for Hollywood films of the 1930s (or indeed any period), and so the time series in the order structure matrix looks relatively featureless.

Those features that do stand out in the matrix are those sequences comprising several longer takes and these are typically associated with the musical numbers. However, not all musical numbers are associated with such clusters. For example, ‘We saw the sea’ (shots 1-8) and Harriet Hillard singing ‘Get thee behind me Satan’ (shots 124-128) do not immediately jump out at you; while the dark column between shots 270 and 286 is ‘I’d rather lead a band,’ running to 351.1 seconds with its extended dance sequence on-board ship, is instantly recognisable.

‘Let yourself go’ appears several times throughout the film, making its bow with Rogers singing between shots 59 and 67, with the comic dance competition to this tune running from shots 132-150. These numbers are not associated with the sort of clusters of longer shots we see in the second half of the matrix, though they are generally slower than other sequences in the first 35 minutes of the film. Rogers’ solo tap dance audition is shot 317, and is followed by a cluster of short shots (319-325) when Astaire overhears how successful she is and decides to sabotage her singing audition. The subsequent disastrous reprise of ‘Let yourself go’ after Rogers’ drink has been spiked occurs at shots 333 to 338. Hillard singing ‘But where are you?’ begins and ends at shots 356 and 359, respectively, but this does not show up in the matrix as distinguishable from the shots around it.

The musical sequence featuring ‘I’m putting all my eggs in one basket’ begins at shot 416, with Astaire playing piano, and the number itself starts at shot 421 and runs until shot 428 for a total of 334.2 seconds. The most famous sequence from this film accounts for the cluster of long shots from 506 to 534, and includes ‘Let’s face the music and dance.’ The number itself only accounts for the last 2 shots running to 286.0 seconds.

Both *Top Hat* and *Follow the Fleet* were directed by Mark Sandrich, and David Abel was the cinematographer for both films. *Top Hat* was edited by William Hamilton, whereas *Follow the Fleet* was edited by Henry Berman. We do not know enough about RKO’s mode of production to determine how the working relationship between these and other filmmakers was structured, and so we will have to wait and see what the editing structure of other musicals in the Fred Astaire and Ginger Rogers series for the studio will tell us about the authorship of these films (if, indeed, there is any such person).

## Time series analysis of ITV news bulletins

Back in the summer I wrote a post looking at the relationship between the discourse structure and the formal structure of BBC news bulletins (see here). This week I have the first draft of a similar paper looking at news bulletins from ITV.

The pdf file can be accessed here: Nick Redfern – Time series analysis of ITV news bulletins

## Abstract

We analyze shot length data from the three main daily news bulletins broadcast on ITV 1 from 8 August 2011 to 12 August 2011, inclusive. In particular, we are interested to compare the distribution of shot lengths of bulletins broadcast on different days and at different times across this time period, and to examine the time series structure by identifying clusters of shots of shorter and longer duration in order to understand the relationship between this aspect of the formal structure to the discourse structure of these broadcasts. The discourse structure of the bulletins in this sample is fixed, and remains constant irrespective of the subject of news items themselves suggesting that content is adapted to meet the needs of this structure. The statistical results show that neither the day nor the time of broadcast has any impact on the distribution of shot lengths, and the editing style is consistent across the whole sample. There is no common pattern to the time series of these bulletins, but there are some consistent features in the time series for these bulletins: clusters of longer takes are associated with static shots of people talking on-screen, while clusters of shorter takes occur with montage sequences, sports reports, series of news items, and footage from non-ITN sources. Consequently, the presence and order of discourse elements in a bulletin shapes its formal structure.

The data for the bulletins used in this study can be accessed as an Excel 2007 file here: Nick Redfern – ITV News Bulletins

I’m a little wary of making direct comparisons between this data and that of the BBC news bulletins as they are separated by three months and deal with news presentation in very different circumstances. The data used in the ITV study covers the week of the riots in the UK this August, and this presents a very different news cycle to that seen in the BBC data from April. However, some general points can be made:

- In both samples clusters of longer shots are associated with people speaking at length on camera, and these shots are framed in the same way.
- In both samples clusters of shorter shots are often associated with montage sequences accompanied by a description from an off-screen reporter or with footage that is derived from other sources (e.g. library footage, other broadcasters).
- In both samples, there is no evidence of any trends or cycles in the time series.
- There is no significant difference in the median shot lengths and dispersion of shot lengths in the two samples of bulletins (BUT remember these are from different times of the year, so this information is only of limited use).
- Day and time of broadcast have no impact on news bulletins for either broadcaster (but again the comparison is not as direct as I would like).

Overall, there is some evidence that news bulletins are stylistically homogenous across these broadcasters. I will do another study looking at the comparing the bulletins from the both the BBC and ITV from a single week, but this will have to wait for another day.

## Editing in Slumber Party Massacre (1982)

A few weeks ago I posted the order structure matrix of *Halloween* (1978), which can be accessed here. The overall editing structure of this film showed that the last portion when Michael attacks Laurie – the final girl – was edited in a different fashion to the rest of the film. There was also some evidence of clustering of shorter shots when michael is stabbing people to death and of longer takes when adult male characters are on screen.

To see of these features are common across the genre of slasher films, this week we have the editing structure of *Slumber Party Massacre* (1982), directed by Amy Ryan. The data include the opening credits as these are presented over narratively important scenes, but the closing credits are not included. The data can be accessed as an Excel file here: Redfern – Slumber Party. The order structure matrix is presented below.

**Figure 1** The order structure matrix of Slumber Party Massacre

We can immediately see from Figure 1 that a similar pattern to *Halloween* is evident, with the ‘final girl’ sequence that begins at shot 706, when the killer – Russ Thorn – chases the girls outside and they battle to the death next to the swimming pool. The black column that can be seen just after shot 750 occurs when the supposedly dead Thorn rises from the pool to attack for the last time. This moment comprises only a few shots, but they are much longer than those in the action that surrounds them (4-10 seconds),

Generally, the editing is slower in the first half of the film and becomes quicker as the killing spree becomes more intense, but we can see some clusters of short shots in the early part of the film. At shot 165, we have a ‘false killing:’ Thorn is using a drill to murder his victims, so when we see a drill coming through a door towards the head of the basketball coach we assume that she is the next in line, but it turns out that it is just someone installing a peephole in the door (below).

Although there have been a couple of early murders in the film, the killing really begins in earnest from shot 392, when the head of Brenda’s boyfriend comes off, and it is from this point that we start to white spaces in the matrix indicating that these shots tend to be shorter than those that precede them. The virtuoso piece of filmmaking in *Slumber Party Massacre* is the cross-cutting between the murder of one of the boys at the party and Valerie watching a slasher movie on television. This sequence lasts only ~104 seconds but comprises 42 shots (from shot 462), and is edited much more quickly than the scenes that precede and follow it. It is typical of this film that fast editing is associated with scenes of intense violence.

Clusters of long takes are also evident at various points in the film. Notably, there is a solid black column at shot 72 which begins a sequence featuring the main female characters in the shower after a basketball game (which is the cluster of short shots from shot 46 to shot 70). A similar concentration of longer shots can be seen at from shot 267, which is the sequence where the girls get undressed at the beginning of the slumber party. Nudity is thus edited more slowly than other scenes in the film.

Although the killing at the party is well under way by this point, we can see that things are edited more slowly in shots 503 to 565. This sequence lasts for just 10 minutes and focusses on Valerie and her worries that something strange is happening next door, the girls at the party trying to make themselves safe, and Thorn hiding the bodies of those who have so far been unfortunate. We have numerous shots of Valerie searching the grounds and the house, trying to find out what is happening; while the girls inside the house are preparing for Thorn’s next attack. These scenes include many tracking shots that tend not to be evident at other more ‘stabby’ points in the film (pun intended). Like the example mentioned above, when Thorn rises slowly from the swimming pool, this slow sequence is associated with the creation of a sense of dread prior to the big finale. This can be interpreted as evidence that two different types of horror are present in such films: the ‘body horror’ of the violence and the creeping dread of what might be in the darkness, and that these are associated with two different editing regimes. It will of course require a larger sample of films to establish this, but the order structure matrix appears to be quite capable of picking out these different types of sequences.

Overall, the editing structure of *Slumber Party Massacre* is comprised of clusters of shorter shots associated with the violence of the penetrative killings and longer shots used for nudity and to create atmosphere, and is generally similar to *Halloween*.