Cluster Analysis to Characterize the Patterns of Complementary and Alternative Medicines Usage in Asthma Controls

2.1. Data Description

The data used for the validation of cluster analysis were collected in a prospective population-based, cross-sectional study setting. The population involved the residents of census areas in the province of Canada and British Columbia. 486 patients with self-reported/physician-diagnosed asthma were involved in the data collection. Primary and secondary outcome measures included assessment of CAM usage over the past year, asthma control level as defined by the Global Initiative for Asthma, along with self-reported intake of controller medications. A total of 179 (36.8%) of the sample reported CAM usage in the past 12 months. Breathing exercises (17.7%), herbal medicines (10.1%), and vitamins (9.7%) were the most popular CAMs reported. After adjustment, female sex (OR: 1.66; 95% CI: 1.09-2.52) and uncontrolled asthma (vs. controlled asthma, OR: 2.25, 95% CI: 1.30-3.89) were associated with a higher likelihood of using any CAMs in the past 12 months. Controller medication use was not associated with CAM usage in general and in the subgroups defined by asthma control [6].

The data file, as made available by BMJ (British Medical Journal) Publishing Group from an electronic file supplied by the authors, has been used for the study and has not been edited for content [2].

2.2. Cluster Analysis and Initialization Methods (IMs)

Cluster analysis aims at grouping individual entities into groups such that objects within the group tend to exhibit a high degree of similarity while objects of different groups seem to demonstrate a low similarity. Clustering techniques are widely used in the process of asthma phenotyping [8, 9].

The categorical attributes were treated as numerical attributes while applying the K-Means algorithm and different initialization methods have experimented.

2.3. Random Initialization

The steps involved in the selection of the seeds using random initialization areas follows:

Step 1: Choose ‘K’, representing the number of clusters

Step 2: Randomly choose ‘K’ centroids from the input dataset

Step 3: Allocate each data point to its nearest centroid

Step 4: Place the new centroid for each cluster by re-computing the new centroid

Step 5: Check if any data points in the dataset can be reassigned to a different cluster based on the new centroid

2.4. K-Means++

K-means++ is designed to improve the centroid initialization for k-means. The basic idea is that the initial centroid should be far away from each other. The algorithm starts by randomly selecting a centroid c0 from all data points. For centroid ci, it is interpreted that the probability of a data point, x, been chosen as a centroid is proportional to the squares of the distance of x to its nearest centroid.

K means ++ aims at choosing the initial centroids in such a way that the initial centroids are far as possible from each other.

2.5. Method: Farthest First

The issue of k-center clustering is also called the min-max radius clustering problem, whose goal is to minimize any cluster's peak diameter on some set of points. Gonzales, using a farthest-point clustering heuristic, proposes a straightforward2-approximation algorithm for the k-center clustering issue.

The heuristic of farthest point begins with an arbitrary point s1. Select a point s2 as far as possible from s1. Preference of si is done so as to maximize the distance selected so far to the nearest of all centroids. This means maximizing min {dist (si, s1), dist (si, s2), ...}. The partition of D after all k representatives have been selected, may be defined as: cluster Cj comprises of all points nearer to sj than any other representative. The maximum radius of these k clusters should be π, and then the maximum radius, even in the ideal k-clustering, should be at least π/2. This is most preferred for minimizing any cluster's maximum radius.

2.6. Method: Canopy

To group objects into clusters, Canopy Clustering is a very easy, quick, and amazingly precise technique. All items in the multidimensional feature space are depicted as a point. For processing, the algorithm utilizes a rapid approximate range metric and two range thresholds T1 > T2. The fundamental algorithm is to start with a set of points and randomly remove one. As the algorithm utilizes distance features and needs distance threshold specification, the curse of dimensionality limits its applicability to high-dimensional information. The produced canopies will only maintain the clusters generated by K-means when an inexpensive and approximate-low-dimensional-distance function is accessible.

Type: Kmeans++

Number of iterations: 5

Within cluster sum of squared errors: 470.27

Type: Random

Number of iterations: 7

Within cluster sum of squared errors: 470.27

Type: Farthest first

Number of iterations: 11

Within cluster sum of squared errors: 504.86

Type: Canopy

Number of iterations: 8

Within cluster sum of squared errors: 496.60