Attempt to build color prediction model based on the Pantone data
According to the article http://onlinelibrary.wiley.com/doi/10.1002/col.22057/abstract color prediction for industry is possible.
The method suggested in the article is clustering the colors from previous years and applying prediction model.
The same approaches are used in the following source:
Clustering ==> choosing parameter in the cluster (Hue for Yellow) ==> prediction using ANN:
http://www.cmnt.lv/upload-files/ns_39art95.pdf
The dataset spring-Pantone_TPX_RGB_Colours.csv contains Pantone palettes for spring season for years 2003-2016. Year 2003 contains 9 values, other years contain 10 values. For year 2015 Pantone released two color sets for Men and Women, the Women data is used.
The dataset Full_Pantone_TPX_RGB_Colours.csv contains all Pantone color reports in RGB, 2003-2016
gray.R contains the actual implementation in R that loops through all the data (28-4 rows) with 5-row moving window and constructs predictions using manual euctidean clustering for HUE coordinate ang GM(1,1) model for prediction.
It seems that they did not use Fuzzy C-Means for their main result, just show the picture (or I need to read more carefully). They think of Pantone 10 colors as clusters, and propose FCM to aggregate real-world data (from images,etc.) into similar n-color sequences. The clusternig was performed manually using euclidean metric.
I failed to exactly reproduce their vertical clusters, it seems that we have a little bit different RGB values (mine are taken generally from pantone.com). My clustering vs theirs (vertical sequences): 
The following prediction was obtained (0-360 degrees, i.e. 328 and 4 are quite nearby):
> real
205 218 6 104 31 53 4 1 181 249
> pred
203 222 2 117 25 58 328 1 119 225
I attempted pure RGB clustering using euclidean metric as well (RGB_ordering.R), however the results are not as good, maybe because I'm still using Hue as covariate (regression over RGB values is worth to try): 
> real
181 249 104 1 6 53 31 218 4 205
> pred
179 9 92 357 9 14 5 209 1 179
Also the general program tries to test all the 5-sequences in the data through a loop. The results are totally not that impressive (notice that prediction often resembles the shifted data):
RGB_ordering.R Prediction for other two parameters (sat, val) wasn't successful. In order to construct some colors, prediction based on R,G,B components was used (R component shows good fit) and Hue is ther replaced with previous successful prediction. Residual correction proposed in the original article was also used:
hue:
> real
X4 X3 X2 X10 X9 X5 X8 X1 X6 X7
h 205 218 6 104 31 53 4 1 181 249
> pred
[1] 203 222 3 117 25 58 328 1 122 225
red:
> real_r
X10 X6 X8 X7 X9 X4 X3 X1 X2 X5
1 113 152 220 152 177 3 145 247 247 251
> pred_r
[1] 127 146 225 165 212 0 138 255 109 41
green:
> real_g
X6 X9 X3 X7 X1 X8 X5 X10 X2 X4
1 152 177 145 152 247 220 251 113 247 3
> pred_g
[1] 113 255 61 217 249 83 99 138 58 203
blue:
> real_b
X5 X1 X3 X7 X4 X10 X6 X8 X9 X2
1 251 247 145 152 3 113 152 220 177 247
> pred_b
[1] 255 107 178 255 2 203 159 49 147 205
Result (upper - real, lower - predicted):
The accuracy arcieved is somewhat ~50%. No idea how authors obtained their precise results. For example, the results for H-S-V prediction (hsv_color_predict.R) are:
convert_to_16.R contains the the first attempt that rounds the values to 16-color palette. For the missing value simple imputation was used.
The Yellow colour code was set afterwards to Pantone 13-0858 Yellow (255,220,1).
The Yellow_hue_predict.R does some reverse-engineering of the second article. The colors were clustered to the 4-bit palette, the code for Yellow (8) is present from the year 2007 (exactly as in the source article, where the palettes were taken beginning from 2007). After that, mean Hue for all the colors in the Yellow group was calculated and glm model (x[n] ~ x[n-1]+x[n-2]+x[n-3]) applied (if they found a precise relationship with ANN, then simple models should detect something as well). The result shows that indeed some link exists within Yellow cluster:
Two last states can be indeed predicted (i.e. the data for them can be not included during the training of the model), however the amount of data is insufficient to derive any conclusions.
All the data from the entire history (i.e. all the colors ) were merged and K-means++ used to obtain 6 clusters. Then the values from each year are assigned to the corresponding clusters using euclidean metric:
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
X2003s 4 4 1 6 2 5 5 3 5 5
X2003f 3 1 6 1 1 5 1 1 5 1
X2004s 2 2 2 3 4 5 4 5 5 6
X2004f 5 4 2 1 1 3 1 2 6 2
X2005s 3 6 2 3 5 6 4 5 5 5
X2005f 3 1 1 2 2 1 6 3 1 5
X2006s 4 4 4 4 4 4 5 3 1 6
X2006f 5 5 3 2 2 5 1 6 1 1
X2007s 4 5 5 3 1 3 5 3 3 5
X2007f 1 2 1 6 5 5 1 3 5 1
X2008s 3 5 2 4 3 3 3 3 6 4
X2008f 6 1 6 6 2 1 2 6 2 3
X2009s 2 3 6 5 3 3 4 6 5 4
X2009f 2 1 3 1 2 5 2 3 6 4
X2010s 5 2 3 5 5 3 6 4 1 5
X2010f 3 3 2 2 2 1 6 1 4 4
X2011s 2 2 5 3 4 1 6 6 4 4
X2011f 3 2 2 1 5 6 1 5 4 5
X2012s 2 3 2 5 6 4 4 5 5 5
X2012f 1 3 2 2 6 3 6 5 5 4
X2013s 6 5 5 3 3 5 4 6 2 3
X2013f 3 6 6 1 2 2 1 2 1 1
X2014s 5 5 5 5 3 3 2 2 5 6
X2014f 4 1 2 3 1 1 6 6 5 5
X2015s 4 6 5 6 4 3 3 4 1 4
X2015f 1 5 1 6 5 5 3 3 1 1
X2016s 4 3 5 6 3 4 5 2 3 5
X2016f 5 5 6 5 6 3 5 2 2 1
The target cluster is 6. If it is not present for a certain year, the previous value is used.
The glm model was trained on the first 20 values (out of 28), the Hue dynamics for the last 8 (4 years) was approximately predicted. The result shows that prediction can be possible, but K-Means result is very unstable for different seed, so it fails.
