# A Neural-Network-Based Landscape Search Engine:
## 3 Case Studies  
### Observations of General Patterns  
In order to better understand how similarity scores are distributed and what the results mean, the authors aggregated the similarity scores of each location pair for every model. Then, the distributions and correlations between measures were investigated. In general,  
Figure 2: Similarity calculation flowchart.  
the aggregated similarity scores produced by ResNet-50 and NasNet are highly left-skewed, with NasNet scores being more leptokurtic (Figure 3). This means that these scores are generally closer to a value of 1, or deemed more similar on average. The VGG16 similarity scores, on the other hand, are far more mesokurtic and slightly right-skewed. This means that, for any given pair of landscapes, the ResNet-50 and NasNet scores are more likely to be scored as more similar, though it should be kept in mind that this is simply a function of how the models produce and compare feature vectors. Min-max normalization helps in compensating for non-normality, but, in the end, such transformations do not alter the ordering of similar images, only the way in which they are represented. The vegetation similarity scores are also left-skewed (Figure 4).  
A correlogram of all variable pairs helps determine how similar model metrics are in terms of what they fundamentally measure (Figure 5). Pairs with stronger correlations exhibit a higher degree of overlap, while those with weaker correlations manifest distinctive measurements. The inclusion of distance in correlation computations also provides insights into spatial dependence. Spearman's \(\rho\) is used due to the non-normal nature of the distributions. Correlations among the variables are generally weak with the exception of the terrain variable pairs:  
The strongest relationship is between resnet50_sim and nasnet_sim (\(\rho\) = 0.72), meaning that these variables capture similar things. In turn, this means that vgg16_sim is capturing something relatively unique. Despite the high correlations between ResNet-50 and NasNet, we keep both due to the exploratory nature of the web application. Indeed, in practice, the two do seem to function differently.  
There is virtually no correlation between the individual vegetation metrics with any of the terrain metrics. On the surface, this appears counterintuitive as the amount of vegetation in a location is, to a certain degree, dependent on characteristics closely tied to the terrain: lithology, topography, and soil. However, while Wisconsin is far from isotropic, its terrain admittedly does not vary nearly as much as a state like Colorado, which straddles the Rocky Mountains. Following this, very flat locations in the state can have wildly different NDVI values--consider, for example, a location of mostly water and one of flat farmland. Further, given the right skew of most model metrics, yet the low amount of correlation between the terrain and vegetation similarity scores, using these two in tandem to produce the total similarity score is wise, as, importantly, the two combined help separate individual observations.  
In general, there is a surprisingly low amount of spatial dependence in the data as evidenced by the small Spearman's \(\rho\) correlations of the variable dist with others. In fact, the relationship between dist and veg_mean_sim along with the relationship between dist  
Figure 5: Correlogram of similarity results.  
and veg_sd_sim are both negative, meaning that nearby locations are likely to be dissimilar in terms of NDVI. While this is a little surprising given the apparent regional differences in Wisconsin with respect to vegetation, the scale of analysis is such that adjacent locations can indeed vary greatly.