List of packages to deploy:

library(tidyverse)
library(rio)
library(ggfortify)
library(ggforce)
library(GGally)
library(ggsci)
library(RColorBrewer)
library(cowplot)
library(cluster)
library(factoextra)
library(randomForest)
library(randomForestExplainer)

Functions

binwidth_FD <- function(x){
  2*IQR(x, na.rm = T)*sum(!is.na(x))^(-1/3)}
getmode <- function(v){
  d <- density(v, na.rm = T)
  d$x[which.max(d$y)]
}
quantInv <- function(distr, value) ecdf(distr)(value)
df <- import("dataset_preprocessed.csv") %>% 
  mutate_at(vars(c(kg,kb)), funs(log(.,10))) %>% select(-contains("V"))
raw_data <- import("dataset_raw.csv")
moe <- import("moe_descriptors.csv")

1. Cluster analysis

1.1. Model \(G = k_g \Delta C^g\) (mod_1)

  • Standardization of kg and g, and selection of cluster by silhouette.
mod_1 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(growth.rate %in% c("G=kg?Cg"))
kinetic_parameters_1 <- mod_1 %>% select(c(g,kg)) %>% mutate_all(funs(scale(.)))

fviz_nbclust(kinetic_parameters_1, hcut, method = "silhouette")

  • Based on silhouette criterion, the optimal number of clusters is 3 as it maximizes the index. Thus, AHC was carried out using k = 3 and method = “ward.D” with N = 92, corresponding to 35 solutes.
ahc1 <- hcut(kinetic_parameters_1, 3, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc1, geom = "point") +
  geom_text(aes(label = abbreviate(mod_1$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[g]))

  • Samples were assigned a group and the groups were characterized in term of their values of \(k_g\) and g
mod_1 <- mod_1 %>% mutate(cluster = ahc1$cluster)
mod_1 %>% group_by(cluster) %>% summarise(n(),mean(kg), median(kg), min(kg), max(kg), sd(kg), IQR(kg))
mod_1 %>% group_by(cluster) %>% summarise(n(),mean(g), median(g), min(g), max(g), sd(g),IQR(g))

1.2. Model \(G = k_g (S-1)^g\) (mod_2)

  • Standardization of kg and g, and selection of cluster by silhouette.
mod_2 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(growth.rate %in% c("G=kg(S-1)g"))
kinetic_parameters_2 <- mod_2  %>%  select(c(g,kg)) %>% mutate_all(funs(scale(.)))
fviz_nbclust(kinetic_parameters_2, hcut, method = "silhouette")

  • Based on silhoutte criterion, the optimal number of clusters is 2 as it maximizes the index. However, AHC was carried out using k = 3, given it provides better discrimination and silhoutte index is similar to k = 2. Method = “ward.D2” with N = 68, corresponding to 26 solutes
ahc2 <- hcut(kinetic_parameters_2, 3, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc2, geom = "point") +
  geom_text(aes(label = abbreviate(mod_2$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[g]))

mod_2 <- mod_2 %>% mutate(cluster = ahc2$cluster)
mod_2 %>% group_by(cluster) %>% summarise(n(),mean(kg), median(kg), min(kg), max(kg), sd(kg), IQR(kg))
mod_2 %>% group_by(cluster) %>% summarise(n(),mean(g), median(g), min(g), max(g), sd(g),IQR(g))

1.3. Model \(B = k_b \Delta C^b\) (mod_3)

mod_3 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(nucleation.rate %in% c("B=kb?Cb"))
kinetic_parameters_3 <- mod_3  %>%  select(c(b,kb)) %>% mutate_all(funs(scale(.)))
fviz_nbclust(kinetic_parameters_3, hcut, method = "silhouette")

ahc3 <- hcut(kinetic_parameters_3, 5, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc3, geom = "point") +
  geom_text(aes(label = abbreviate(mod_3$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[b]))

mod_3 <- mod_3 %>% mutate(cluster = ahc3$cluster)
mod_3 %>% group_by(cluster) %>% summarise(n(),mean(kb), median(kb), min(kb), max(kb), sd(kb), IQR(kb))
mod_3 %>% group_by(cluster) %>% summarise(n(),mean(b), median(b), min(kb), max(b), sd(b), IQR(b))

2. Random Forest

2.1. Model \(G = k_g \Delta C^g\)

Co-crystallization datum is removed since descriptors are limited to pure substances (agomelatine-citric acid and caffeine-glutaric acid) (6 data point). RF is run using mtry = 10, ntree = 15000, set.seed = 50

system <- raw_data %>% select(solvent, id) %>% 
  mutate_at(vars(solvent), funs(if_else(str_detect(., "water:"), "aqueous", .)))

excluded_vars <- c("id", "solute", "solute.mw", "density", "b", "kb",   "g", "kg",  "En",   "Eg",   "growth.rate",  "nucleation.rate",  "driving.force", "units.driving.force", "comments", "bidimensional")
mod_1.rf <- mod_1 %>% 
  filter(!(id %in% c(18:22,69) | seeding == "both")) %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.)))

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_1.rf)))
rf1 <- randomForest(x1~., data = mod_1.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf1

Call:
 randomForest(formula = x1 ~ ., data = mod_1.rf %>% rename_all(renamed_vars),      ntree = 15000, mtry = 10, importance = T, localimp = T) 
               Type of random forest: classification
                     Number of trees: 15000
No. of variables tried at each split: 10

        OOB estimate of  error rate: 25.88%
Confusion matrix:
  1  2  3 class.error
1 7  0  4   0.3636364
2 1 16  6   0.3043478
3 5  6 40   0.2156863
  • Cross-validation
rf1.cv <- data.frame(actual = rep(NA, nrow(mod_1.rf)), predicted = rep(NA, nrow(mod_1.rf)))

for (i in 1:nrow(mod_1.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_1.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf1.cv[i,1] <- mod_1.rf[i,1]
  rf1.cv[i,2] <- predict(rf, (mod_1.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf1.cv)))/nrow(rf1.cv)
[1] 0.7411765
  • Importance by MDA
imp_est_1 <- data.frame(variable = colnames(mod_1.rf)[-1] , MDA = rf1$importance[,4])
imp_est_1 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")

2.2. Model \(G = k_g (S-1)^g\)

  • Bidimentional growth data were removed
mod_2.rf <- mod_2 %>% 
  filter(bidimensional != "yes", seeding != "both") %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.))) %>% 
  na.omit()

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_2.rf)))
rf2 <- randomForest(x1~., data = mod_2.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf2

Call:
 randomForest(formula = x1 ~ ., data = mod_2.rf %>% rename_all(renamed_vars),      ntree = 15000, mtry = 10, importance = T, localimp = T) 
               Type of random forest: classification
                     Number of trees: 15000
No. of variables tried at each split: 10

        OOB estimate of  error rate: 14.55%
Confusion matrix:
   1 2 3 class.error
1 35 4 0   0.1025641
2  3 7 0   0.3000000
3  1 0 5   0.1666667
  • Cross-validation
rf2.cv <- data.frame(actual = rep(NA, nrow(mod_2.rf)), predicted = rep(NA, nrow(mod_2.rf)))

for (i in 1:nrow(mod_2.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_2.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf2.cv[i,1] <- mod_2.rf[i,1]
  rf2.cv[i,2] <- predict(rf, (mod_2.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf2.cv)))/nrow(rf2.cv)
[1] 0.8545455
  • Importance by MDA
imp_est_2 <- data.frame(variable = colnames(mod_2.rf)[-1] , MDA = rf2$importance[,4])
imp_est_2 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")

2.3. Model \(B = k_b \Delta C^g\)

mod_3.rf <- mod_3 %>% 
  filter(!(id %in% c(18,19))) %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.)))

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_3.rf)))
rf3 <- randomForest(x1~., data = mod_3.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf3

Call:
 randomForest(formula = x1 ~ ., data = mod_3.rf %>% rename_all(renamed_vars),      ntree = 15000, mtry = 10, importance = T, localimp = T) 
               Type of random forest: classification
                     Number of trees: 15000
No. of variables tried at each split: 10

        OOB estimate of  error rate: 16.95%
Confusion matrix:
   1 2 4 5 class.error
1 33 1 0 0  0.02941176
2  0 8 0 0  0.00000000
4  7 0 2 0  0.77777778
5  2 0 0 6  0.25000000
  • Cross-validation
rf3.cv <- data.frame(actual = rep(NA, nrow(mod_3.rf)), predicted = rep(NA, nrow(mod_3.rf)))

for (i in 1:nrow(mod_3.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_3.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf3.cv[i,1] <- mod_3.rf[i,1]
  rf3.cv[i,2] <- predict(rf, (mod_3.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf3.cv)))/nrow(rf3.cv)
[1] 0.8305085
  • Importance by MDA
imp_est_3 <- data.frame(variable = colnames(mod_3.rf)[-1] , MDA = rf3$importance[,4])
imp_est_3 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")

---
title: "R Notebook"
output: html_notebook
---

List of packages to deploy:

```{r, warning=FALSE}
library(tidyverse)
library(rio)
library(ggfortify)
library(ggforce)
library(GGally)
library(ggsci)
library(RColorBrewer)
library(cowplot)
library(cluster)
library(factoextra)
library(randomForest)
library(randomForestExplainer)

```
Functions
```{r}
binwidth_FD <- function(x){
  2*IQR(x, na.rm = T)*sum(!is.na(x))^(-1/3)}
getmode <- function(v){
  d <- density(v, na.rm = T)
  d$x[which.max(d$y)]
}
quantInv <- function(distr, value) ecdf(distr)(value)
```

* Loading data and molecular descriptors
* Change of scale of kb and kg

```{r, warning=FALSE}
df <- import("dataset_preprocessed.csv") %>% 
  mutate_at(vars(c(kg,kb)), funs(log(.,10))) %>% select(-contains("V"))
raw_data <- import("dataset_raw.csv")
moe <- import("moe_descriptors.csv")
```

# 1. Cluster analysis

## 1.1. Model $G = k_g \Delta C^g$ (mod_1)

* Standardization of kg and g, and selection of cluster by silhouette.

```{r}
mod_1 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(growth.rate %in% c("G=kg?Cg"))
kinetic_parameters_1 <- mod_1 %>% select(c(g,kg)) %>% mutate_all(funs(scale(.)))

fviz_nbclust(kinetic_parameters_1, hcut, method = "silhouette")
```
* Based on silhouette criterion, the optimal number of clusters is 3 as it maximizes the index. Thus, AHC was carried out using k = 3 and method = “ward.D” with N = 92, corresponding to 35 solutes.

```{r, warning=FALSE}
ahc1 <- hcut(kinetic_parameters_1, 3, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc1, geom = "point") +
  geom_text(aes(label = abbreviate(mod_1$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[g]))

```
* Samples were assigned a group and the groups were characterized in term of their values of $k_g$ and g

```{r}
mod_1 <- mod_1 %>% mutate(cluster = ahc1$cluster)
mod_1 %>% group_by(cluster) %>% summarise(n(),mean(kg), median(kg), min(kg), max(kg), sd(kg), IQR(kg))
mod_1 %>% group_by(cluster) %>% summarise(n(),mean(g), median(g), min(g), max(g), sd(g),IQR(g))
```

## 1.2. Model $G = k_g (S-1)^g$ (mod_2)

* Standardization of kg and g, and selection of cluster by silhouette.

```{r}
mod_2 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(growth.rate %in% c("G=kg(S-1)g"))
kinetic_parameters_2 <- mod_2  %>%  select(c(g,kg)) %>% mutate_all(funs(scale(.)))
fviz_nbclust(kinetic_parameters_2, hcut, method = "silhouette")
```
* Based on silhoutte criterion, the optimal number of clusters is 2 as it maximizes the index. However, AHC was carried out using k = 3, given it provides better discrimination and silhoutte index is similar to k = 2. Method = “ward.D2” with N = 68, corresponding to 26 solutes

```{r, warning=FALSE}
ahc2 <- hcut(kinetic_parameters_2, 3, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc2, geom = "point") +
  geom_text(aes(label = abbreviate(mod_2$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[g]))
```
```{r}
mod_2 <- mod_2 %>% mutate(cluster = ahc2$cluster)
mod_2 %>% group_by(cluster) %>% summarise(n(),mean(kg), median(kg), min(kg), max(kg), sd(kg), IQR(kg))
mod_2 %>% group_by(cluster) %>% summarise(n(),mean(g), median(g), min(g), max(g), sd(g),IQR(g))
```
# 1.3. Model $B = k_b \Delta C^b$ (mod_3)

* Standardization of kb and b, and selection of cluster by silhouette.

```{r}
mod_3 <- left_join(df, moe, by = c("solute"="compound")) %>% filter(nucleation.rate %in% c("B=kb?Cb"))
kinetic_parameters_3 <- mod_3  %>%  select(c(b,kb)) %>% mutate_all(funs(scale(.)))
fviz_nbclust(kinetic_parameters_3, hcut, method = "silhouette")
```

* Based on silhouette criterion, the optimal number of clusters is 2 as it maximizes the index; but, k = 5 is also good since the index is just slightly lower than k = 2 and provide a better separation. Thus, AHC was carried out using k = 5 and method = “ward.D” with N = 61, corresponding to 21 solutes.

```{r, warning=FALSE}
ahc3 <- hcut(kinetic_parameters_3, 5, hc_method = "ward.D", graph = T) 
fviz_cluster(ahc3, geom = "point") +
  geom_text(aes(label = abbreviate(mod_3$solute, 3, strict = TRUE))) + 
  scale_fill_jco() + scale_color_jco() + theme_classic() + theme(legend.position = "top") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(y = expression(log~k[b]))
```

* Samples were assigned a group and the groups were characterized in term of their values of $k_b$ and b

```{r, warning=FALSE}
mod_3 <- mod_3 %>% mutate(cluster = ahc3$cluster)
mod_3 %>% group_by(cluster) %>% summarise(n(),mean(kb), median(kb), min(kb), max(kb), sd(kb), IQR(kb))
mod_3 %>% group_by(cluster) %>% summarise(n(),mean(b), median(b), min(kb), max(b), sd(b), IQR(b))
```
# 2. Random Forest

## 2.1. Model $G = k_g \Delta C^g$

Co-crystallization datum is removed since descriptors are limited to pure substances (agomelatine-citric acid and caffeine-glutaric acid) (6 data point). RF is run using mtry = 10, ntree = 15000, set.seed = 50

```{r}
system <- raw_data %>% select(solvent, id) %>% 
  mutate_at(vars(solvent), funs(if_else(str_detect(., "water:"), "aqueous", .)))

excluded_vars <- c("id", "solute", "solute.mw", "density", "b",	"kb",	"g", "kg",	"En",	"Eg",	"growth.rate",	"nucleation.rate",	"driving.force", "units.driving.force",	"comments",	"bidimensional")
```

```{r, warning=FALSE}
mod_1.rf <- mod_1 %>% 
  filter(!(id %in% c(18:22,69) | seeding == "both")) %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.)))

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_1.rf)))
rf1 <- randomForest(x1~., data = mod_1.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf1

```
* Cross-validation

```{r}
rf1.cv <- data.frame(actual = rep(NA, nrow(mod_1.rf)), predicted = rep(NA, nrow(mod_1.rf)))

for (i in 1:nrow(mod_1.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_1.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf1.cv[i,1] <- mod_1.rf[i,1]
  rf1.cv[i,2] <- predict(rf, (mod_1.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf1.cv)))/nrow(rf1.cv)
```
* Importance by MDA

```{r}
imp_est_1 <- data.frame(variable = colnames(mod_1.rf)[-1] , MDA = rf1$importance[,4])
imp_est_1 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")

```

## 2.2. Model $G = k_g (S-1)^g$

* Bidimentional growth data were removed

```{r}
mod_2.rf <- mod_2 %>% 
  filter(bidimensional != "yes", seeding != "both") %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.))) %>% 
  na.omit()

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_2.rf)))
rf2 <- randomForest(x1~., data = mod_2.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf2

```
* Cross-validation

```{r}
rf2.cv <- data.frame(actual = rep(NA, nrow(mod_2.rf)), predicted = rep(NA, nrow(mod_2.rf)))

for (i in 1:nrow(mod_2.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_2.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf2.cv[i,1] <- mod_2.rf[i,1]
  rf2.cv[i,2] <- predict(rf, (mod_2.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf2.cv)))/nrow(rf2.cv)
```
* Importance by MDA

```{r}
imp_est_2 <- data.frame(variable = colnames(mod_2.rf)[-1] , MDA = rf2$importance[,4])
imp_est_2 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")

```

## 2.3. Model $B = k_b \Delta C^g$

```{r}
mod_3.rf <- mod_3 %>% 
  filter(!(id %in% c(18,19))) %>% 
  left_join(., system, by = "id") %>% 
  select(-any_of(excluded_vars)) %>% select(c(cluster, solvent, everything())) %>%  
  mutate_at(vars(cluster, solvent, class, method, seeding), funs(as.factor(.)))

set.seed(50)
renamed_vars <- quo(paste0("x", 1:length(mod_3.rf)))
rf3 <- randomForest(x1~., data = mod_3.rf %>% rename_all(renamed_vars), ntree = 15000, mtry = 10, importance = T, localimp = T)
rf3
```
* Cross-validation
```{r}
rf3.cv <- data.frame(actual = rep(NA, nrow(mod_3.rf)), predicted = rep(NA, nrow(mod_3.rf)))

for (i in 1:nrow(mod_3.rf)) {
  set.seed(50)
  rf <- randomForest(x1~., data = (mod_3.rf %>% rename_all(renamed_vars))[-i,], ntree = 15000, mtry = 10)

  rf3.cv[i,1] <- mod_3.rf[i,1]
  rf3.cv[i,2] <- predict(rf, (mod_3.rf %>% rename_all(renamed_vars))[i,])

}
sum(diag(table(rf3.cv)))/nrow(rf3.cv)
```

* Importance by MDA
```{r}
imp_est_3 <- data.frame(variable = colnames(mod_3.rf)[-1] , MDA = rf3$importance[,4])
imp_est_3 %>% 
  arrange(desc(MDA)) %>% filter(row_number() < 16) %>% ggplot(aes(reorder(variable, MDA), MDA)) + 
  geom_col() + coord_flip() + labs(y = "MDA", x = "Variable")
```


