NOTE: This write-up picks up where the previous one left off. All of the session data is carried over.

Color Similarity

Now, I’d like to evaluate color similarity more closely. To help verify any quantitative deductions with some intuition, I’ll consider only a single league for this–the NBA, the league that I know the best.

Because I’ll end up plotting team names at some point and some of the full names are relatively lengthy, I want to get the official abbreviations for each team. Unfortunately, these don’t come with the teamcolor package, but I can use Alex Bresler’s nbastatR package to get them.

# Assign `df_dict_nba_teams` to Global environment.
nbastatR::assign_nba_teams()
nms_nba <-
  teamcolors::teamcolors %>% 
  filter(league == "nba") %>% 
  inner_join(
    df_dict_nba_teams %>%
      setNames(snakecase::to_snake_case(names(.))) %>%
      filter(!is_non_nba_team) %>% 
      select(name = name_team, slug = slug_team),
    by = c("name")
  )

colors_tidy_ord2_nba <-
  nms_nba %>% 
  select(name, league, slug) %>% 
  inner_join(colors_tidy_ord2, by = c("name", "league"))

To give the unfamiliar reader a better understanding of what exactly this subset of the teamcolors data incorporate, here’s a visualization of the primary and secondary colors of all NBA teams

After grabbing the abbreviations (or slugs), I can move on to breaking up the hex values into their RGB components. ¹ I’ll be looking at only the primary and secondary colors again.

colors_ord2_nba_rgb_tidy <-
  colors_tidy_ord2_nba %>%
  add_rgb_cols() %>% 
  select(-hex) %>%
  tidyr::gather(rgb, value, red, green, blue)

colors_ord2_nba_rgb_tidy %>% 
  create_kable()

With the RGB values extracted, I can use the widyr::pairwise_dist() function to compute the relative distance among teams in terms of RGB values for each color ordinality.I think the default method–“Euclidean” distance–is reasonable.

do_pairwise_dist <- function(data, method) {
  data %>% 
    group_by(ord) %>% 
    widyr::pairwise_dist(name, rgb, value, upper = TRUE, method = method) %>% 
    rename(name1 = item1, name2 = item2) %>% 
    select(everything(), value = ncol(.)) %>% 
    arrange(value, .by_group = TRUE) %>% 
    ungroup()
}

As one might expect, there’s not much difference between these two distance methods (if correlation is deemed a valid metric for quantifying similarity).

How exactly do all of the individual distances compare?

I think that the above plot does a good job of highlighting the average distance values (in terms of RGB) of each team. Additionally, by sorting the teams by value, it illustrates exactly which teams are the most “generic” (i.e. most similar to all other teams) and the most “unique” (i.e. least similar to all other teams.)

I can also use a heat map to visualize the same data (Who doesn’t like a good heat map?)

Like with the previous plot, I order the teams on each axis by total distance from all other teams–teams with the highest cumulative similarity to all other teams appear towards the bottom and left, while teams that contrast most with all others appear towards the top and right. And, to add some nuance, I emphasize the individual pairs that have the highest and lowest similarity with different colors.

Exactly which teams match most and least closely with one another (in terms of color similarity)? Here’s a list of the top and bottom matches for each team.

These results don’t really agree with what I–and maybe other NBA fans–would have guessed. The Sacramento Kings (SAC) have purple as their primary color, which is relatively unusual. I would think that they would be in the lower half of these rankings. Whats going on? …

Color Theory

When doing this color-based analysis, several questions came to mind:

1. Is the RGB model really the best framework to use for comparing colors? What about the HSL (Hue, Saturation, Lightness) model? Additionally, a quick Google search for “What is the best method for identifying similarity between colors?” indicates the YUV representation–a model I hadn’t heard of before–is best, (if human perception is the main concern).

2. Is Euclidean distance the best “distance” method to use? But, because I’m curious, I’ll look at how different the results would be if the “Manhattan” distance is used instead.

3. Is “distance” even the best method for determining color similarity. Why not a “similarity” metric (such as cosine similarity)?

Since I’m not expert in color models, and because I there is no definitive/conclusive research with which I can cross-check my findings for color similarity among NBA teams, I think its worthwhile to explore these questions in more detail. First, I’ll need to create HSL and YUV variations of the color data that I can compare to the RGB version that I’ve used up to this point. (This will help me answer the first question.) ² Then, with each of these data sets in hand, I’ll tackle the latter two questions directly. In the end, by comparing the different models with different methods, I hope to come to some stronger conclusions and/or justifications of my findings about NBA team colors.

class=“section level3”>

Euclidean Distance vs. Manhattan Distance

I’ll look at two distance methods–Euclidean and Manhattan–to justify my choice of Euclidean distance before. To do this, I want to verify that the similarity determined by the two methods is nearly identical. (I would be surprised if they aren’t.)

Indeed, it looks like there is high correlation found between the Euclidean and Manhattan distances calculated when the hex color values are broken down into color components, regardless of whether the RGB, HSL, or YUV representation is used.

Now, when keeping the distance method constant (Euclidean), how do the color models compare?

rowname rgb_dist hsl_dist yuv_dist rgb_dist NA 62.53 97.88 hsl_dist 62.53 NA 68.12 yuv_dist 97.88 68.12 NA

The numbers indicate that there is some strong positive correlation, especially between the RGB and YUV color schemas. This indicates that the conclusions that I came to regarding most similar and dissimilar NBA team colors would not be much different if using the HSL or YUV models instead of the RGB model.

Distance vs. Similarity

To compare distance (Euclidean) with cosine similarity, I can create and use a similar set of functions to those used for comparing distance methods. To visualize the results in an interpretable manner, I can use the network_plot() function from Dr. Simon’s corrr package`. This function is cool for visualizing correlation data in a way other than with a traditional correlation matrix. ³

It’s clear that the RGB and YUV schemas are fairly similar “within” both metrics–Euclidean distance and cosine similarity–and both are relatively dissimilar to HSL. However, all three color models show negative correlations “within” themselves when comparing the two metrics against one another. (i.e. The RGB schema has a negative correlation when comparing its distance values to its similarity values, and likewise for the HSL and YUV models.)

So, which color model and which metric should be used? In my opinion, the RGB model seems like a good choice, both because it is relatively similar to at least one other method (YUV) and because it is (probably) the most relatable scheme to people who don’t know much about color theory. For metric, I think that the choice of Euclidean distance is valid. My Google search (which makes the case for YUV) makes the assumption that Euclidean distance is being used. Additionally, a separate Google search for “euclidean distance vs. cosine similarity” turns up an easy-to-follow technical write-up that implies that cosine similarity is probably not really appropriate for this kind of color analysis.

Conclusion

That’s all I got for this topic. I hope that the techniques shown here are general enough that they can be applied to any set of color to extract some fun (and meaningful) insight.