Practical_b.Rmd: reformat implementing your own kmeans

Practical_b.Rmd

@@ -584,120 +584,44 @@ What can you say about the axes of this plot ?
 
 ## Implementing your own $k$-means clustering algorithm
 
+You are going to implement your own $k$-means algorithm in this section.
 The $k$-means algorithm follow the following steps:
 
 - Assign point to the cluster with the nearest centroid
 - Compute the new cluster centroids
 
+Justify each of your function.
+
 <div class="pencadre">
 Think about the starting state of your algorithm and the stopping condition
 </div>
 
-<details><summary>Solution</summary>
-<p>
-We have no prior information about the centroid, we can randomly draw them.
-We are going to iterate over the two-step of the algorithm until the centroids stay the same.
-</p>
-</details>
-
 <div class="pencadre">
-Start by implementing a `kmeans_initiation(x, k)` function for your algorithm, returning $k$ centroids
+Start by implementing a `kmeans_initiation(x, k)` function, returning $k$ centroids as a starting point.
 </div>
 
-<details><summary>Solution</summary>
-<p>
-```{r}
-kmeans_initiation <- function(x, k) {
-  centroid <- matrix(0, k, ncol(x))
-  for (i in 1:ncol(x)) {
-    centroid[, i] <- runif(k, min = min(x[, i]), max = max(x[, i]))
-  }
-  return(centroid)
-}
-```
-</p>
-</details>
-
 <div class="pencadre">
-Implement a `compute_distance(x, centroid)` function for your algorithm, the distance of each point (row of x) to each centroid, based on the squared Euclidian distance.
+Implement a `compute_distance(x, centroid)` function that compute the distance of each point (row of x) to each centroid
 </div>
 
-<details><summary>Solution</summary>
-<p>
-```{r}
-compute_distance <- function(x, centroid) {
-  distance <- matrix(0, nrow(x), nrow(centroid))
-  for (i in 1:ncol(distance)) {
-      distance[, i] <- rowSums((x - centroid[i, ])^2)
-  }
-  return(distance)
-}
-```
-</p>
-</details>
-
 <div class="pencadre">
-Implement a `cluster_assignment(distance)` function for your algorithm, returning the assignment of each point (row of x), based on the squared Euclidian distance.
+Implement a `cluster_assignment(distance)` function returning the assignment of each point (row of x), based on the results of your `compute_distance(x, centroid)` function.
 </div>
 
-<details><summary>Solution</summary>
-<p>
-```{r}
-cluster_assignment <- function(distance) {
-  cluster <- c()
-  for (i in 1:nrow(distance)) {
-    cluster[i] <- which(distance[i, ] == min(distance[i, ]))[1]
-  }
-  return(cluster)
-}
-```
-</p>
-</details>
-
-
 <div class="pencadre">
-Implement a `centroid_update(x, cluster, k)` function for your algorithm, returning the updated centroid for your clusters.
+Implement a `centroid_update(x, cluster, k)` function returning the updated centroid for your clusters.
 </div>
 
-<details><summary>Solution</summary>
-<p>
-```{r}
-centroid_update <- function(x, cluster, k) {
-  centroid <- matrix(0, k, ncol(x))
-  for (i in 1:k) {
-    centroid[i, ] <- mean(x[cluster[i], ])
-  }
-  return(centroid)
-}
-```
-</p>
-</details>
+<div class="pencadre">
+Implement a `metric_example(x, k)` function to compute a criteria of the goodness st of your clustering.
+</div>
 
 <div class="pencadre">
-Implement a `kmeans_example(x, k)` function for your algorithm, wrapping everything and test it.
+Implement a `kmeans_example(x, k)` function, wrapping everything and test it.
 </div>
 
-<details><summary>Solution</summary>
-<p>
-```{r}
-kmeans_example <- function(x, k) {
-  centroid <- kmeans_initiation(x, k)
-  stop_condition <- T
-  while (stop_condition) {
-    old_centroid <- centroid
-    cluster <- cluster_assignment(compute_distance(x, centroid))
-    centroid <- centroid_update(x, cluster, k)
-    if (max(centroid - old_centroid) < 5) {
-      stop_condition <- F
-    }
-  }
-  return(cluster)
-}
-```
-</p>
-</details>
 
-```{r, echo = F}
+```{r, eval = F}
 data_pca %>%
   fviz_pca_ind(
     geom = "point",