List the different techniques used for clustering the big data. Explain k-means clustering
Types of Clustering
Broadly speaking, clustering can be divided into two subgroups :
- Hard Clustering: In hard clustering, each data point either belongs to a cluster completely or not. For example, in the above example, each customer is put into one group out of the 10 groups.
- Soft Clustering: In soft clustering, instead of putting each data point into a separate cluster, a probability or likelihood of that data point being in those clusters is assigned. For example, from the above scenario, each costumer is assigned a probability to be in either of 10 clusters of the retail store.
Types of clustering algorithms
Since the task of clustering is subjective, the means that can be used for achieving this goal are plenty. Every methodology follows a different set of rules for defining the ‘similarity’ among data points. In fact, there are more than 100 clustering algorithms known. But few of the algorithms are used popularly, let’s look at them in detail:
- Connectivity models: As the name suggests, these models are based on the notion that the data points closer in data space exhibit more similarity to each other than the data points lying farther away. These models can follow two approaches. In the first approach, they start by classifying all data points into separate clusters & then aggregating them as the distance decreases. In the second approach, all data points are classified as a single cluster and then partitioned as the distance increases. Also, the choice of distance function is subjective. These models are very easy to interpret but lack scalability for handling big datasets. Examples of these models are the hierarchical clustering algorithm and its variants.
- Centroid models: These are iterative clustering algorithms in which the notion of similarity is derived by the closeness of a data point to the centroid of the clusters. K- Means clustering algorithm is a popular algorithm that falls into this category. In these models, the no. of clusters required at the end has to be mentioned beforehand, which makes it important to have prior knowledge of the dataset. These models run iteratively to find the local optima.
- Distribution models: These clustering models are based on the notion of how probable is it that all data points in the cluster belong to the same distribution (For example: Normal, Gaussian). These models often suffer from overfitting. A popular example of these models is the Expectation-maximization algorithm which uses multivariate normal distributions.
- Density Models: These models search the data space for areas of the varied density of data points in the data space. It isolates various different-density regions and assigns the data points within these regions in the same cluster. Popular examples of density models are DBSCAN and OPTICS.
Now I will be taking you through two of the most popular clustering algorithms in detail – K Means clustering and Hierarchical clustering. Let’s begin.
K Means Clustering
K means is an iterative clustering algorithm that aims to find local maxima in each iteration. This algorithm works in these 5 steps :
1. Specify the desired number of clusters K : Let us choose k=2 for these 5 data points in 2-D space.
2. Randomly assign each data point to a cluster: Let’s assign three points in cluster 1 shown using red color and two points in cluster 2 shown using grey color.
3. Compute cluster centroids: The centroid of data points in the red cluster is shown using red cross and those in grey cluster using grey cross.
4. Re-assign each point to the closest cluster centroid : Note that only the data point at the bottom is assigned to the red cluster even though its closer to the centroid of grey Thus, we assign that data point into grey cluster
5. Re-compute cluster centroids: Now, re-computing the centroids for both clusters.
6. Repeat steps 4 and 5 until no improvements are possible: Similarly, we’ll repeat the 4th and 5th steps until we’ll reach global When there will be no further switching of data points between two clusters for two successive repeats. It will mark the termination of the algorithm if not explicitly mentioned.
Hierarchical Clustering
Hierarchical clustering, as the name suggests is an algorithm that builds a hierarchy of clusters. This algorithm starts with all the data points assigned to a cluster of their own. Then two nearest clusters are merged into the same cluster. In the end, this algorithm terminates when there is only a single cluster left.
The results of hierarchical clustering can be shown using a dendrogram. The dendrogram can be interpreted as:
At the bottom, we start with 25 data points, each assigned to separate clusters. The two closest clusters are then merged till we have just one cluster at the top. The height in the dendrogram at which two clusters are merged represents the distance between two clusters in the data space.
The decision of the no. of clusters that can best depict different groups can be chosen by observing the dendrogram. The best choice of the no. of clusters is the no. of vertical lines in the dendrogram cut by a horizontal line that can transverse the maximum distance vertically without intersecting a cluster.
In the above example, the best choice of no. of clusters will be as the red horizontal line in the dendrogram below covers the maximum vertical distance AB.
Two important things that you should know about hierarchical clustering are:
- This algorithm has been implemented above using bottom up approach. It is also possible to follow top-down approach starting with all data points assigned in the same cluster and recursively performing splits till each data point is assigned a separate cluster.
- The decision of merging two clusters is taken on the basis of closeness of these There are multiple metrics for deciding the closeness of two clusters :
- Euclidean distance: ||a-b||2 = √(Σ(ai-bi))
- Squared Euclidean distance: ||a-b||22 = Σ((ai-bi)2)
- Manhattan distance: ||a-b||1 = Σ|ai-bi|
- Maximum distance:||a-b||INFINITY = maxi|ai-bi|
- Mahalanobis distance: √((a-b)T S-1 (-b)) {where, s : covariance matrix}
Difference between K Means and Hierarchical clustering
- Hierarchical clustering can’t handle big data well but K Means clustering can. This is because the time complexity of K Means is linear i.e. O(n) while that of hierarchical clustering is quadratic e. O(n2).
- In K Means clustering, since we start with random choice of clusters, the results produced by running the algorithm multiple times might differ. While results are reproducible in Hierarchical clustering.
- K Means is found to work well when the shape of the clusters is hyper spherical (like circle in 2D, sphere in 3D).
- K Means clustering requires prior knowledge of K i.e. no. of clusters you want to divide your data into. But, you can stop at whatever number of clusters you find appropriate in hierarchical clustering by interpreting the dendrogram
Applications of Clustering
Clustering has a large no. of applications spread across various domains. Some of the most popular applications of clustering are:
- Recommendation engines
- Market segmentation
- Social network analysis
- Search result grouping
- Medical imaging
- Image segmentation
- Anomaly detection
Improving Supervised Learning Algorithms with Clustering
Clustering is an unsupervised machine learning approach, but can it be used to improve the accuracy of supervised machine learning algorithms as well by clustering the data points into similar groups and using these cluster labels as independent variables in the supervised machine learning algorithm? Let’s find out.
Let’s check out the impact of clustering on the accuracy of our model for the classification problem using 3000 observations with 100 predictors of stock data to predict whether the stock will go up or down using R. This dataset contains 100 independent variables from X1 to X100 representing the profile of a stock and one outcome variable Y with two levels: 1 for a rise in stock price and -1 for drop in stock price
