PCA.Rmd

---
title: "PCA_raisins"
output:  
  html_document:
    keep_md: true
---

```{r}
data = read.csv('datasets/Raisin_Dataset.csv', sep = ';')
```

We exclude the label variable
```{r}
df = data[-c(8, 9)]
head(df)
```


```{r}
options(scipen = 10)
round((apply(df, 2, mean)), digits = 5); round((apply(df, 2, var)), digits = 5)
```
```{r}
summary(df)
```


```{r}
pr.out = prcomp(df, scale = TRUE)
pr.out
```
```{r}
summary(pr.out)
```


Correct dimensions, show clearly the points but it is not readable
```{r}
plot(pr.out$x[, 1], pr.out$x[, 2], type = "n", xlab = "PC1", ylab = "PC2")  
points(pr.out$x[, 1], pr.out$x[, 2], col = rgb(1, 0, 0, alpha = 0.5), pch = 16) 
arrows(0, 0, pr.out$rotation[, 1], pr.out$rotation[, 2], length = 0.1, angle = 30)
```


Shows both the dimension and the arrows' label, but not the points
```{r}
biplot(pr.out)
```


Compromise, arrows length increased
```{r}
plot(pr.out$x[, 1], pr.out$x[, 2], type = "n", xlab = "PC1", ylab = "PC2") 
points(pr.out$x[, 1], pr.out$x[, 2], col = rgb(1, 0, 0, alpha = 0.5), pch = 16)  
arrows(0, 0, pr.out$rotation[, 1]*7, pr.out$rotation[, 2]*7, length = 0.1, angle = 30)
text(pr.out$rotation[, 1]*7, pr.out$rotation[, 2]*7, labels = rownames(pr.out[[2]]), pos = 3)
```

Get the components' value for each observation


```{r}

pcadf <- predict(pr.out, newdata = df)
head(pcadf)

```


Perform 2-means clustering on the components' values for each observation

```{r}
km.out2 = kmeans(pcadf, 2)
km.out2
```

Graphical representation of the clusters. 
Results are slightly better on PC than on initial features


```{r}
plot (pcadf, col = adjustcolor(km.out2$cluster + 1, alpha.f = 0.5),
main = "K- Means Clustering Results with K = 2", pch = 20)
```