Visual entropy norms and psychological measures of complexity

  1. REAL OBJECTS

Entropy measures

Below are histograms of the Shannon entropy measures for the four measures (CNN_features, wavelet, color, and gist) for each of the 60 objects. Entropy was calculated using the wentropy function in matlab. I’m not sure whether the feature weights should be normalized within each object, and I get somewhat different results depending on whether or not I do this (the correlation between color and effect size below is not reliable when not normalizing). Below are the results WITH normalizing. plot of chunk unnamed-chunk-2

Here are the images sorted by the CNN feature entropy:
[none of these look very intuitive to me]


Here are the images sorted by the wavelet feature entropy:


Here are the images sorted by the color feature entropy:


Here are the images sorted by the gist feature entropy:


Here are the correlations between all measures.
plot of chunk unnamed-chunk-3

Conceptual complexity ratings are weakly correlated with wavelet and color, though these are only mariginal. Gist and color are highly correlated.

Object mapping task

Next we look at whether the ratios of these measures predict the linguistic complexity bias. In particular, whether the ratio of the two alternatives in the mapping task predicts the bias to map the long word onto the more complex object.

Below are histograms of the complexity ratios (simple/complex) for each trial for all 6 complexity metrics. plot of chunk unnamed-chunk-5 Visual features look skewed, so we try taking the log. Here are the logged ratios: plot of chunk unnamed-chunk-6

These ratios are somewhat correlated (bottom is in log space), though this isn’t entirely fair because a lot of these points are non-independent (need to aggergate). plot of chunk unnamed-chunk-7

plot of chunk unnamed-chunk-8

Below are plots of the effect sizes as a function of the complexity ratios. plot of chunk unnamed-chunk-10

Below are the same plots in log space (not really any different). plot of chunk unnamed-chunk-11

The correlation between the effect size and color ratio is reliable. Gist is marginal.

cor.test(de$effect_size, de$color.Mratio)
## 
##  Pearson's product-moment correlation
## 
## data:  de$effect_size and de$color.Mratio
## t = -2.783, df = 13, p-value = 0.01554
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8555 -0.1437
## sample estimates:
##    cor 
## -0.611
cor.test(de$effect_size, de$l.color.Mratio)
## 
##  Pearson's product-moment correlation
## 
## data:  de$effect_size and de$l.color.Mratio
## t = -2.403, df = 13, p-value = 0.03191
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.83082 -0.05912
## sample estimates:
##     cor 
## -0.5546
cor.test(de$effect_size, de$l.gist.Mratio)
## 
##  Pearson's product-moment correlation
## 
## data:  de$effect_size and de$l.gist.Mratio
## t = 2.093, df = 13, p-value = 0.05652
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.01374  0.80682
## sample estimates:
##    cor 
## 0.5021

  1. GEONS

Entropy measures

Below are histograms of the Shannon entropy measures for three measures (CNN_features, wavelet, and gist). Color was not evaluated for the geons because they are monochromatic. plot of chunk unnamed-chunk-13

Gist is correlated with conceptual and RT measures of complexity. CNN is marginal for both. plot of chunk unnamed-chunk-14

Here are the ratio histograms. plot of chunk unnamed-chunk-17

And, here are the ratio histograms in log space plot of chunk unnamed-chunk-18

Here are the ratio plots. plot of chunk unnamed-chunk-19

Below are the same plots in log space. plot of chunk unnamed-chunk-20

The correlation is reliable for both wavelet and CNN.

cor.test(de$effect_size, de$l.wavelet.Mratio)
## 
##  Pearson's product-moment correlation
## 
## data:  de$effect_size and de$l.wavelet.Mratio
## t = 2.683, df = 13, p-value = 0.01878
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1221 0.8495
## sample estimates:
##   cor 
## 0.597
cor.test(de$effect_size, de$l.CNN.Mratio)
## 
##  Pearson's product-moment correlation
## 
## data:  de$effect_size and de$l.CNN.Mratio
## t = 2.436, df = 13, p-value = 0.03001
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.06662 0.83314
## sample estimates:
##    cor 
## 0.5598