Clustering or cluster analysis is a machine learning technique, which groups the unlabelled dataset.
It does it by finding some similar patterns in the unlabelled dataset such as shape, size, color, behavior, etc., and divides them as per the presence and absence of those similar patterns.
It is an unsupervised learning method, hence no supervision is provided to the algorithm, and it deals with the unlabeled dataset.
After applying this clustering technique, each cluster or group is provided with a cluster-ID. ML system can use this id to simplify the processing of large and complex datasets.
The clustering methods are broadly divided into Hard clustering (datapoint belongs to only one group) and Soft Clustering (data points can belong to another group also). But there are also other various approaches of Clustering exist. Below are the main clustering methods used in Machine learning:
- Partitioning Clustering
- Density-Based Clustering
- Distribution Model-Based Clustering
- Hierarchical Clustering
- Fuzzy Clustering
It is a type of clustering that divides the data into non-hierarchical groups. It is also known as the centroid-based method. The most common example of partitioning clustering is the KMeans Clustering algorithm.
In this type, the dataset is divided into a set of k groups, where K is used to define the number of pre-defined groups. The cluster center is created in such a way that the distance between the data points of one cluster is minimum as compared to another cluster centroid.
The density-based clustering method connects the highly-dense areas into clusters, and the arbitrarily shaped distributions are formed as long as the dense region can be connected. This algorithm does it by identifying different clusters in the dataset and connects the areas of high densities into clusters. The dense areas in data space are divided from each other by sparser areas.
These algorithms can face difficulty in clustering the data points if the dataset has varying densities and high dimensions.
In the distribution model-based clustering method, the data is divided based on the probability of how a dataset belongs to a particular distribution. The grouping is done by assuming some distributions commonly Gaussian Distribution.
The example of this type is the Expectation-Maximization Clustering algorithm that uses Gaussian Mixture Models (GMM).
Hierarchical clustering can be used as an alternative for the partitioned clustering as there is no requirement of pre-specifying the number of clusters to be created. In this technique, the dataset is divided into clusters to create a tree-like structure, which is also called a dendrogram. The observations or any number of clusters can be selected by cutting the tree at the correct level. The most common example of this method is the Agglomerative Hierarchical algorithm.
Clustering algorithms that are widely used in machine learning:
1.:heavy_check_mark: K-Means algorithm: The k-means algorithm is one of the most popular clustering algorithms. It classifies the dataset by dividing the samples into different clusters of equal variances. The number of clusters must be specified in this algorithm. It is fast with fewer computations required, with the linear complexity of O(n).
2.:heavy_check_mark: Mean-shift algorithm: Mean-shift algorithm tries to find the dense areas in the smooth density of data points. It is an example of a centroid-based model, that works on updating the candidates for centroid to be the center of the points within a given region
3.:heavy_check_mark: DBSCAN Algorithm: It stands for Density-Based Spatial Clustering of Applications with Noise. It is an example of a density-based model similar to the mean-shift, but with some remarkable advantages. In this algorithm, the areas of high density are separated by the areas of low density. Because of this, the clusters can be found in any arbitrary shape.
4.:heavy_check_mark: Expectation-Maximization Clustering using GMM: This algorithm can be used as an alternative for the k-means algorithm or for those cases where K-means can be failed. In GMM, it is assumed that the data points are Gaussian distributed.
5.:heavy_check_mark: Agglomerative Hierarchical algorithm: The Agglomerative hierarchical algorithm performs the bottom-up hierarchical clustering. In this, each data point is treated as a single cluster at the outset and then successively merged. The cluster hierarchy can be represented as a tree-structure.
6.:heavy_check_mark: Affinity Propagation: It is different from other clustering algorithms as it does not require to specify the number of clusters. In this, each data point sends a message between the pair of data points until convergence. It has O(N2T) time complexity, which is the main drawback of this algorithm.
In Identification of Cancer Cells The clustering algorithms are widely used for the identification of cancerous cells. It divides the cancerous and non-cancerous data sets into different groups.
In Search Engines: Search engines also work on the clustering technique. The search result appears based on the closest object to the search query. It does it by grouping similar data objects in one group that is far from the other dissimilar objects. The accurate result of a query depends on the quality of the clustering algorithm used.
Customer Segmentation: It is used in market research to segment the customers based on their choice and preferences
In Biology: It is used in the biology stream to classify different species of plants and animals using the image recognition technique.
SVM is a powerful supervised algorithm that works best on smaller datasets but on complex ones. Support Vector Machine, abbreviated as SVM can be used for both regression and classification tasks, but generally, they work best in classification problems.
It is a supervised machine learning problem where we try to find a hyperplane that best separates the two classes.
Note: Donโt get confused between SVM and logistic regression. Both the algorithms try to find the best hyperplane, but the main difference is logistic regression is a probabilistic approach whereas support vector machine is based on statistical approaches.
When the data is perfectly linearly separable only then we can use Linear SVM. Perfectly linearly separable means that the data points can be classified into 2 classes by using a single straight line(if 2D).
When the data is not linearly separable then we can use Non-Linear SVM, which means when the data points cannot be separated into 2 classes by using a straight line (if 2D) then we use some advanced techniques like kernel tricks to classify them. In most real-world applications we do not find linearly separable datapoints hence we use kernel trick to solve them.
Support Vectors: These are the points that are closest to the hyperplane. A separating line will be defined with the help of these data points.
Margin: it is the distance between the hyperplane and the observations closest to the hyperplane (support vectors). In SVM large margin is considered a good margin. There are two types of margins hard margin and soft margin.
SVM is defined such that it is defined in terms of the support vectors only, we donโt have to worry about other observations since the margin is made using the points which are closest to the hyperplane (support vectors), whereas in logistic regression the classifier is defined over all the points. Hence SVM enjoys some natural speed-ups.
The best hyperplane is that plane that has the maximum distance from both the classes, and this is the main aim of SVM. This is done by finding different hyperplanes which classify the labels in the best way then it will choose the one which is farthest from the data points or the one which has a maximum margin.
The dot product can be defined as the projection of one vector along with another, multiply by the product of another vector.
Here a and b are 2 vectors, to find the dot product between these 2 vectors we first find the magnitude of both the vectors and to find magnitude we use the Pythagorean theorem or the distance formula.
To find this first we assume this point is a vector (X) and then we make a vector (w) which is perpendicular
to the hyperplane. Letโs say the distance of vector w from origin to decision boundary is โcโ. Now we take
the projection of X vector on w.
We already know that projection of any vector or another vector is called dot-product. Hence, we take the dot product of x and w vectors. If the dot product is greater than โcโ then we can say that the point lies on the right side. If the dot product is less than โcโ then the point is on the left side and if the dot product is equal to โcโ then the point lies on the decision boundary.
The most interesting feature of SVM is that it can even work with a non-linear dataset and for this, we use โKernel Trickโ which makes it easier to classifies the points. Suppose we have a dataset like this:
Here we see we cannot draw a single line or say hyperplane which can classify the points correctly. So
what we do is try converting this lower dimension space to a higher dimension space using some quadratic
functions which will allow us to find a decision boundary that clearly divides the data points. These
functions which help us do this are called Kernels and which kernel to use is purely determined by
hyperparameter tuning.
Some kernel functions which you can use in SVM are given below:
Following is the formula for the polynomial kernel:
Here d is the degree of the polynomial, which we need to specify manually.
Suppose we have two features X1 and X2 and output variable as Y, so using polynomial kernel we can write it as:
We can use it as the proxy for neural networks. Equation is:
It is just taking your input, mapping them to a value of 0 and 1 so that they can be separated by a simple straight line.
What it actually does is to create non-linear combinations of our features to lift your samples onto a higherdimensional feature space where we can use a linear decision boundary to separate your classes It is the most used kernel in SVM classifications, the following formula explains it mathematically:
- โฯโ is the variance and our hyperparameter
- ||Xโ โ Xโ|| is the Euclidean Distance between two points Xโ and Xโ
It is mainly used for eliminating the cross term in mathematical functions. Following is the formula of the Bessel function kernel:
It performs well on multidimensional regression problems. The formula for this kernel function is:
