Loading and adjusting database

The dataset was downloaded here and, as dataset comes without column names, I included column names using r colnames function from {r base}. Then, I removed all categorical variables considering since that i intend to reduce the dimensionality of the data using Principal Component Analysis (PCA) which do not appear to be an adequate approach for categorical variables. More details may be checked here

data <- 
  read_csv("processed.cleveland.data", 
    col_names = FALSE)

colnames(data) <- c(
  "age",
  "sex",
  "cp",
  "trestbps",
  "chol",
  "fbs",
  "restecg",
  "thalach",
  "exang",
  "oldpeak",
  "slope",
  "ca",
  "thal",
  "num"
)

data <- 
  data |>
  mutate(ca = as.double(ca)) |> 
  select(-sex,
         -cp,
         -fbs,
         -exang,
         -thal,
         -num)

The filtered dataset can be checked above.

datatable(data = data, rownames = FALSE)

Verifying missing values

DataExplorer::plot_missing(data) +
  theme_bw() + 
  theme(legend.title = element_blank(),
        legend.position = "none")

Looking missing value plot, we observed an low frequency of missing value in the variable ca, and I opted to remove then.

Removing missing data

data <-
  drop_na(data)

Lets see missing data again

DataExplorer::plot_missing(data) +
  theme_bw() + 
  theme(legend.title = element_blank(),
        legend.position = "none")

Yeah, now, we does not have missing values ❗️ Now, let’s to see data summary.

Data summary

skimr::skim(data)

Table 1: Data summary

Name	data
Number of rows	299
Number of columns	8
_______________________
Column type frequency:
numeric	8
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
age	0	1	54.53	9.02	29	48	56.0	61.0	77.0	▁▅▇▇▁
trestbps	0	1	131.67	17.71	94	120	130.0	140.0	200.0	▃▇▅▁▁
chol	0	1	247.10	51.91	126	211	242.0	275.5	564.0	▃▇▂▁▁
restecg	0	1	1.00	0.99	0	0	1.0	2.0	2.0	▇▁▁▁▇
thalach	0	1	149.51	22.95	71	133	153.0	165.5	202.0	▁▂▅▇▂
oldpeak	0	1	1.05	1.16	0	0	0.8	1.6	6.2	▇▂▁▁▁
slope	0	1	1.60	0.62	1	1	2.0	2.0	3.0	▇▁▇▁▁
ca	0	1	0.67	0.94	0	0	0.0	1.0	3.0	▇▃▁▂▁

We may observed a wide range in the units of the variables. So, I opted to scale all variables in order to put then in standardized units, in the case, using z-score. Now, we may observe standardized units for all variables.

Now, let’s to reduce dimentionality ❗️

Scaling data - z-score approach

data_scaled <- scale(data)

skimr::skim(data_scaled)

Table 2: Data summary

Name	data_scaled
Number of rows	299
Number of columns	8
_______________________
Column type frequency:
numeric	8
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
age	0	1	0	1	-2.83	-0.72	0.16	0.72	2.49	▁▅▇▇▁
trestbps	0	1	0	1	-2.13	-0.66	-0.09	0.47	3.86	▃▇▅▁▁
chol	0	1	0	1	-2.33	-0.70	-0.10	0.55	6.10	▃▇▂▁▁
restecg	0	1	0	1	-1.00	-1.00	0.00	1.01	1.01	▇▁▁▁▇
thalach	0	1	0	1	-3.42	-0.72	0.15	0.70	2.29	▁▂▅▇▂
oldpeak	0	1	0	1	-0.90	-0.90	-0.22	0.47	4.42	▇▂▁▁▁
slope	0	1	0	1	-0.97	-0.97	0.64	0.64	2.26	▇▁▇▁▁
ca	0	1	0	1	-0.72	-0.72	-0.72	0.35	2.48	▇▃▁▂▁

Checking optimal number of clustering using Hierarchical Clustering

Hierarchical clustering is an unsupervised machine learning algorithm for identifying groups in the dataset. It does not require us to pre-specify the number of clusters to be generated. Furthermore, hierarchical clustering has an added advantage over other commonly used methods in that it results in an attractive tree-based representation of the observations, called a dendrogram. More details may be checked here

Firstly, let’s to determine optimal number of cluster elbow method. As we can observe above, the “elbow” is not clear. Let-s to see another method, i.e., silhouette method, to indicate optimal number of cluster.

fviz_nbclust(data_scaled, hcut, method = "wss")

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

Despite of elbow and silhouette methods are not equivalent, i will used 4 cluster. Let’s to see dendrogram and

#hierarchichal clustering using k = 4

hc <- hcut(data_scaled, k = 4,
           hc_method = "ward.D2",
           hc_metric = "euclidean")

# Plot the obtained dendrogram
plot(hc, cex = 0.6, hang = -10)

fviz_cluster(hc, data = data_scaled) +
  theme_bw()

After trying distinct approaches using Hierarchical Cluster method the figure below illustrated the 4 clusters as silhouette method suggested. Thus, it is notable that this approach were not able to identify appropriately the cluster.

Let’s to try K-means method ❗️

In brief, K-means clustering is the most commonly used unsupervised machine learning algorithm for partitioning a given data set into a set of k groups (i.e. k clusters), where k represents the number of groups pre-specified by the analyst. It classifies objects in multiple groups (i.e., clusters), such that objects within the same cluster are as similar as possible (i.e., high intra-class similarity), whereas objects from different clusters are as dissimilar as possible (i.e., low inter-class similarity). In k-means clustering, each cluster is represented by its center (i.e, centroid) which corresponds to the mean of points assigned to the cluster. For more details click here

Checking optimal number of clustering using K-Means

fviz_nbclust(data_scaled, kmeans, method = "wss")

fviz_nbclust(data_scaled, kmeans, method = "silhouette")

Differently of the hierarchical clustering, both elbow and silhouette method indicated 2 cluster in the dataset.

Let’s obsverve it ❗️

k2 <- kmeans(data_scaled,
             centers = 2,
             nstart = 25)

fviz_cluster(k2,data = data_scaled) +
  theme_bw()

Wowww, now we are able to see clusters ❗️. Nice, but let’s to try some more cluster for us to see if something is better ❗️

k3 <- kmeans(data_scaled, centers = 3, nstart = 25)
k4 <- kmeans(data_scaled, centers = 4, nstart = 25)
k5 <- kmeans(data_scaled, centers = 5, nstart = 25)

# plots to compare
p1 <- fviz_cluster(k2, geom = "point", data = data_scaled) + ggtitle("k = 2")
p2 <- fviz_cluster(k3, geom = "point",  data = data_scaled) + ggtitle("k = 3")
p3 <- fviz_cluster(k4, geom = "point",  data = data_scaled) + ggtitle("k = 4")
p4 <- fviz_cluster(k5, geom = "point",  data = data_scaled) + ggtitle("k = 5")

grid.arrange(p1, p2, p3, p4,
             nrow = 2) +
  theme_bw()

## NULL

Observing plots above, we can observe that elbow and silhouette methods indicated adequately the number of cluster, since that there are some overlaps when using more cluster.