# the method / metric which is not useful to determine the optimal number of clusters in unsupervised clustering algorithms is

### Mohammed

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get the method / metric which is not useful to determine the optimal number of clusters in unsupervised clustering algorithms is from screen.

## Answer in Python for deepak #306862

## Answer to Question #306862 in Python for deepak

Answers>Programming & Computer Science>Python

Question #306862

**1.**The method / metric which is NOT useful to determine the optimal number of clusters in unsupervised clustering algorithms is

a)Dendogram b)Elbow method c) Scatter plot

**d) None of the above**

Expert's answer

The scatter plot cannot be used to determine the optimal number of clusters in unsupervised clustering algorithms

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## 40 Questions (with solution) to test Data Scientist on Clustering Techniques

Test your knowledge on Unsupervised Learning. 40 Questions and solutions on K-means, hierarchical clustering & other related concepts.

Sauravkaushik8 Kaushik — Published On February 5, 2017 and Last Modified On August 26th, 2021

Business Analytics Career Intermediate Machine Learning R Skilltest

## Introduction

The idea of creating machines which learn by themselves has been driving humans for decades now. For fulfilling that dream, unsupervised learning and clustering is the key. Unsupervised learning provides more flexibility, but is more challenging as well.

Clustering plays an important role to draw insights from unlabeled data. It classifies the data in similar groups which improves various business decisions by providing a meta understanding.

In this skill test, we tested our community on clustering techniques. A total of 1566 people registered in this skill test. If you missed taking the test, here is your opportunity for you to find out how many questions you could have answered correctly.

If you are just getting started with Unsupervised Learning, here are some comprehensive resources to assist you in your journey:

Machine Learning Certification Course for Beginners

The Most Comprehensive Guide to K-Means Clustering You’ll Ever Need

Certified AI & ML Blackbelt+ Program

## Overall Results

Below is the distribution of scores, this will help you evaluate your performance:

You can access your performance here. More than 390 people participated in the skill test and the highest score was 33. Here are a few statistics about the distribution.

**Overall distribution**

Mean Score: 15.11 Median Score: 15 Mode Score: 16

## Helpful Resources

An Introduction to Clustering and different methods of clustering

Getting your clustering right (Part I)

Getting your clustering right (Part II)

## Questions & Answers

**Q1. Movie Recommendation systems are an example of:**

**Classification**

**Clustering**

**Reinforcement Learning**

**Regression**

Options: B. A. 2 Only C. 1 and 2 D. 1 and 3 E. 2 and 3 F. 1, 2 and 3 H. 1, 2, 3 and 4

**Solution: (E)**

Generally, movie recommendation systems cluster the users in a finite number of similar groups based on their previous activities and profile. Then, at a fundamental level, people in the same cluster are made similar recommendations.

In some scenarios, this can also be approached as a classification problem for assigning the most appropriate movie class to the user of a specific group of users. Also, a movie recommendation system can be viewed as a reinforcement learning problem where it learns by its previous recommendations and improves the future recommendations.

**Q2. Sentiment Analysis is an example of:**

**Regression**

**Classification**

**Clustering**

**Reinforcement Learning**

Options: A. 1 Only B. 1 and 2 C. 1 and 3 D. 1, 2 and 3 E. 1, 2 and 4 F. 1, 2, 3 and 4

**Solution: (E)**

Sentiment analysis at the fundamental level is the task of classifying the sentiments represented in an image, text or speech into a set of defined sentiment classes like happy, sad, excited, positive, negative, etc. It can also be viewed as a regression problem for assigning a sentiment score of say 1 to 10 for a corresponding image, text or speech.

Another way of looking at sentiment analysis is to consider it using a reinforcement learning perspective where the algorithm constantly learns from the accuracy of past sentiment analysis performed to improve the future performance.

**Q3. Can decision trees be used for performing clustering?**

A. True B. False

**Solution: (A)**

Decision trees can also be used to for clusters in the data but clustering often generates natural clusters and is not dependent on any objective function.

**Q4. Which of the following is the most appropriate strategy for data cleaning before performing clustering analysis, given less than desirable number of data points:**

**Capping and flouring of variables**

**Removal of outliers**

Options: A. 1 only B. 2 only C. 1 and 2

D. None of the above

**Solution: (A)**

Removal of outliers is not recommended if the data points are few in number. In this scenario, capping and flouring of variables is the most appropriate strategy.

**Q5. What is the minimum no. of variables/ features required to perform clustering?**

A. 0 B. 1 C. 2 D. 3

**Solution: (B)**

At least a single variable is required to perform clustering analysis. Clustering analysis with a single variable can be visualized with the help of a histogram.

**Q6. For two runs of K-Mean clustering is it expected to get same clustering results?**

A. Yes B. No

**Solution: (B)**

K-Means clustering algorithm instead converses on local minima which might also correspond to the global minima in some cases but not always. Therefore, it’s advised to run the K-Means algorithm multiple times before drawing inferences about the clusters.

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## Determining The Optimal Number Of Clusters: 3 Must Know Methods

In this article, we'll describe different methods for determining the optimal number of clusters for k-means, k-medoids (PAM) and hierarchical clustering.

## Determining The Optimal Number Of Clusters: 3 Must Know Methods

30 mins

Cluster Validation Essentials

Determining the **optimal number of clusters** in a data set is a fundamental issue in partitioning clustering, such as k-means clustering, which requires the user to specify the number of clusters k to be generated.

Unfortunately, there is no definitive answer to this question. The optimal number of clusters is somehow subjective and depends on the method used for measuring similarities and the parameters used for partitioning.

A simple and popular solution consists of inspecting the dendrogram produced using hierarchical clustering to see if it suggests a particular number of clusters. Unfortunately, this approach is also subjective.

In this chapter, we’ll describe different methods for determining the optimal number of clusters for k-means, k-medoids (PAM) and hierarchical clustering.

These methods include direct methods and statistical testing methods:

Direct methods: consists of optimizing a criterion, such as the within cluster sums of squares or the average silhouette. The corresponding methods are named elbow and silhouette methods, respectively.

Statistical testing methods: consists of comparing evidence against null hypothesis. An example is the gap statistic.

In addition to elbow, silhouette and gap statistic methods, there are more than thirty other indices and methods that have been published for identifying the optimal number of clusters. We’ll provide R codes for computing all these 30 indices in order to decide the best number of clusters using the “majority rule”.

For each of these methods:

We’ll describe the basic idea and the algorithm

We’ll provide easy-o-use R codes with many examples for determining the optimal number of clusters and visualizing the output.

Contents: Elbow method

Average silhouette method

Gap statistic method

Computing the number of clusters using R

Required R packages Data preparation

fviz_nbclust() function: Elbow, Silhouhette and Gap statistic methods

NbClust() function: 30 indices for choosing the best number of clusters

Summary References

### Related Book

Practical Guide to Cluster Analysis in R

## Elbow method

Recall that, the basic idea behind partitioning methods, such as k-means clustering, is to define clusters such that the total intra-cluster variation [or total within-cluster sum of square (WSS)] is minimized. The total WSS measures the compactness of the clustering and we want it to be as small as possible.

The Elbow method looks at the total WSS as a function of the number of clusters: One should choose a number of clusters so that adding another cluster doesn’t improve much better the total WSS.

The optimal number of clusters can be defined as follow:

Compute clustering algorithm (e.g., k-means clustering) for different values of k. For instance, by varying k from 1 to 10 clusters.

For each k, calculate the total within-cluster sum of square (wss).

Plot the curve of wss according to the number of clusters k.

The location of a bend (knee) in the plot is generally considered as an indicator of the appropriate number of clusters.

Note that, the elbow method is sometimes ambiguous. An alternative is the average silhouette method (Kaufman and Rousseeuw [1990]) which can be also used with any clustering approach.

## Average silhouette method

The average silhouette approach we’ll be described comprehensively in the chapter cluster validation statistics. Briefly, it measures the quality of a clustering. That is, it determines how well each object lies within its cluster. A high average silhouette width indicates a good clustering.

Average silhouette method computes the average silhouette of observations for different values of k. The optimal number of clusters k is the one that maximize the average silhouette over a range of possible values for k (Kaufman and Rousseeuw 1990).

The algorithm is similar to the elbow method and can be computed as follow:

Compute clustering algorithm (e.g., k-means clustering) for different values of k. For instance, by varying k from 1 to 10 clusters.

For each k, calculate the average silhouette of observations (avg.sil).

Plot the curve of avg.sil according to the number of clusters k.

The location of the maximum is considered as the appropriate number of clusters.

## Gap statistic method

The gap statistic has been published by R. Tibshirani, G. Walther, and T. Hastie (Standford University, 2001). The approach can be applied to any clustering method.

The gap statistic compares the total within intra-cluster variation for different values of k with their expected values under null reference distribution of the data. The estimate of the optimal clusters will be value that maximize the gap statistic (i.e, that yields the largest gap statistic). This means that the clustering structure is far away from the random uniform distribution of points.

The algorithm works as follow:

Cluster the observed data, varying the number of clusters from k = 1, …, kmax, and compute the corresponding total within intra-cluster variation Wk.

Generate B reference data sets with a random uniform distribution. Cluster each of these reference data sets with varying number of clusters k = 1, …, kmax, and compute the corresponding total within intra-cluster variation Wkb.

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