Complexity measures

For a series, defined as ranks of words at consecutive positions in a text, following measures are used (formatted as Quantity: ML features):

Power spectrum: psLen, psExp

Power spectrum S(f) of a series at a frequency f can be interpreted as the strength of correlation of the series with itself at word-to-word distances 1/f. As Fig. 2 illustrates, it is described well by two parameters: the length psLen of the high-correlation plateau and the slope of its decay psExp.

Predictability: pred

As the name suggests, it measures how well can the next step in a series be predicted given previous steps (see definition: Stone, 1996).

Fano factor exponent: fanoF

Fano factor measures signal autocorrelation, especially in fractal processes (Thurner et al., 1997), as one takes increasingly bigger chunks of text – similarly to the slope of power spectrum or detrended fluctuation analysis (Grabska-Gradzińska et al., 2013).

Entropy rate of word variation: entExp, entConst

The entropy is maximal for equiprobable word occurences, and minimal when a single word is always used. As one reads a text, new words appear and the entropy grows, and saturates. entExp and entConst are characteristic time and a multiplicative constant of such a growth.

Static entropy: entLocM, entLocSD

For a window of a constant length moving across the whole text, the entropy fluctuates. Parameters entLocM and entLocSD are its mean and standard deviation.

Figure 2 Power spectrum S(f) of the time-series as a function of word-to-word distance 1/f

Algorithm and parameters

AA was performed with the R package stylo (Eder et al., 2013) with settings: delta distance (Burrows, 2002), 1000-fold cross-validation, one book of each author in the training set. (None of the other ML methods (Stamatatos, 2009; Jockers and Witten, 2010) implemented in stylo did significantly better than Burrows’s delta.)

Since on this corpus about 90 most frequent words (MFW) are needed for 100% accuracy, only the first ten were used as features, which left room for improvement. Having precomputed all the eight measures, they were appended to the feature list.

Authorship attribution

AA algorithms at best use 6-grams (Eder, 2011), whereas the correlations may reach hundreds of words, as demonstrated in Fig. 2. The results in Tables 1-2 show that the measures from Sec. 2.1 can aid ML. As a proof of concept, Fig. 3 shows a cluster analysis based exclusively on these complexity measures; although imperfect, it strongly indicates that the temporal characteristics contain traces of authorial style.

Figure 3 Cluster analysis of the corpus based only on the eight complexity measures

Informativeness of complexity measures

Surprisingly, psLen is not correlated with paragraph lengths (cf. Kosmidis et al., 2006). Its smallest values 280-300 come, intriguingly, from Austen and Anne and Emily Brontë, while the largest 370-390 from Dickens, Thackeray and Trollope.

Note that correlated features (see Tab. 3 for a summary) worsen performance and should be eliminated. Remaining parameters are expected to contain non-overlapping information. Further, PCA analysis showed that psLen and entLocM contain the most distinctive information. Tables 1-2 show that indeed these parameters most significantly aid ML.