### Machine Leaning interview questions and answers

#### 1. **What is Data Science?**

Data Science is a combination of algorithms, tools, and machine learning technique which helps you to find common hidden patterns from the given raw data.

#### 2. **What are the differences between supervised and unsupervised learning?**

Supervised Learning | Unsupervised Learning |

Uses known and labeled data as input | Uses unlabeled data as input |

Supervised learning has a feedback mechanism | Unsupervised learning has no feedback mechanism |

The most commonly used supervised learning algorithms are decision trees, logistic regression, and support vector machine | The most commonly used unsupervised learning algorithms are k-means clustering, hierarchical clustering, and apriori algorithm |

| |

#### 3. What do you understand by linear regression?

Linear regression helps in understanding the linear relationship between the dependent and the independent variables. Linear regression is a supervised learning algorithm, which helps in finding the linear relationship between two variables. One is the predictor or the independent variable and the other is the response or the dependent variable. In Linear Regression, we try to understand how the dependent variable changes w.r.t the independent variable. If there is only one independent variable, then it is called simple linear regression, and if there is more than one independent variable then it is known as multiple linear regression.

#### 4. How do you find RMSE and MSE in a linear regression model?

RMSE and MSE are two of the most common measures of accuracy for a linear regression model. RMSE indicates the Root Mean Square Error.

MSE indicates the Mean Square Error.

#### 5. **How is logistic regression done?**

Logistic regression measures the relationship between the dependent variable (our label of what we want to predict) and one or more independent variables (our features) by estimating probability using its underlying logistic function (sigmoid).

The image shown below depicts how logistic regression works:

The formula and graph for the sigmoid function are as shown:

#### 6. What is the Sigmoid Function?

It is a mathematical function having a characteristic that can take any real value and map it to between 0 to 1 shaped like the letter “S”. The sigmoid function also called a logistic function.

So, if the value of z goes to positive infinity then the predicted value of y will become 1 and if it goes to negative infinity then the predicted value of y will become 0. And if the outcome of the sigmoid function is more than 0.5 then we classify that label as class 1 or positive class and if it is less than 0.5 then we can classify it to negative class or label as class 0.

#### 7. Why do we use the Sigmoid Function?

Sigmoid Function acts as an activation function in machine learning which is used to add non-linearity in a machine learning model, in simple words it decides which value to pass as output and what not to pass.

#### 8. How will you explain linear regression to a non-tech person?

Linear Regression is a statistical technique of measuring the linear relationship between the two variables. By linear relationship, we mean that an increase in a variable would lead to increase in the other variable and a decrease in one variable would lead to attenuation in the second variable as well. Based on this linear relationship, we establish a model that predicts the future outcomes based on an increase in one variable.

#### 9. Explain how a ROC curve works?

The ROC curve is a graphical representation of the contrast between true positive rates and false-positive rates at various thresholds. It is often used as a proxy for the trade-off between the sensitivity (true positive rate) and false-positive rate

#### 10. What is Precision, Recall, Accuracy and F1-score?

Once you have built a classification model, you need evaluate how good the predictions made by that model are. So, how do you define ‘good’ predictions?

There are some performance metrics which help us improve our models. Let us explore the differences between them for a binary classification problem:

Consider the following Confusion Matrix for a classification problem which predicts whether a patient has Cancer or not for 100 patients:

Now, the following are the fundamental metrics for the above data:

**Precision:** It is implied as the measure of the correctly identified positive cases from all the predicted positive cases. Thus, it is useful when the costs of False Positives is high.

**Recall:** It is the measure of the correctly identified positive cases from all the actual positive cases. It is important when the cost of False Negatives is high.

**Accuracy:** One of the more obvious metrics, it is the measure of all the correctly identified cases. It is most used when all the classes are equally important.

Now for our above example, suppose that there only 30 patients who actually have cancer. What if our model identifies 25 of those as having cancer?

The accuracy in this case is = 90% which is a high enough number for the model to be considered as ‘accurate’. However, there are 5 patients who actually have cancer and the model predicted that they don’t have it. Obviously, this is too high a cost. Our model should try to minimize these False Negatives. For these cases, we use the F1-score.

**F1-score**: This is the harmonic mean of Precision and Recall and gives a better measure of the incorrectly classified cases than the Accuracy Metric.

We use the Harmonic Mean since it penalizes the extreme values.

**To summaries the differences between the F1-score and the accuracy**,

- Accuracy is used when the True Positives and True negatives are more important while F1-score is used when the False Negatives and False Positives are crucial
- Accuracy can be used when the class distribution is similar while F1-score is a better metric when there are imbalanced classes as in the above case.
- In most real-life classification problems, imbalanced class distribution exists and thus F1-score is a better metric to evaluate our model on.

#### 11. **How is AUC different from ROC?**

AUC curve is a measurement of precision against the recall. Precision = TP/(TP + FP) and TP/(TP + FN). This is in contrast with ROC that measures and plots True Positive against False positive rate.

#### 12. **What is Selection Bias?**

Selection bias is a kind of error that occurs when the researcher decides who is going to be studied. It is usually associated with research where the selection of participants isn’t random. It is sometimes referred to as the selection effect. It is the distortion of statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may not be accurate.

The types of selection bias include:

**Sampling bias**: It is a systematic error due to a non-random sample of a population causing some members of the population to be less likely to be included than others resulting in a biased sample.**Time interval**: A trial may be terminated early at an extreme value (often for ethical reasons), but the extreme value is likely to be reached by the variable with the largest variance, even if all variables have a similar mean.**Data**: When specific subsets of data are chosen to support a conclusion or rejection of bad data on arbitrary grounds, instead of according to previously stated or generally agreed criteria.**Attrition**: Attrition bias is a kind of selection bias caused by attrition (loss of participants) discounting trial subjects/tests that did not run to completion

**13. Differentiate between uni-variate, bi-variate, and multivariate analysis**

**Univariate:**

Univariate data contains only one variable. The purpose of the univariate analysis is to describe the data and find patterns that exist within it.

Example: height of students.

The patterns can be studied by drawing conclusions using mean, median, mode, dispersion or range, minimum, maximum, etc.

**Bivariate:**

Bivariate data involves two different variables. The analysis of this type of data deals with causes and relationships and the analysis is done to determine the relationship between the two variables.

Example: temperature and ice cream sales in the summer season. Here, the relationship is visible from the table that temperature and sales are directly proportional to each other. The hotter the temperature, the better the sales.

**Multivariate:**

Multivariate data involves three or more variables, it is categorized under multivariate. It is similar to a bivariate but contains more than one dependent variable. Example: data for house price prediction. The patterns can be studied by drawing conclusions using mean, median, and mode, dispersion or range, minimum, maximum, etc. You can start describing the data and using it to guess what the price of the house will be.

#### 14. Explain the steps in making a decision tree.

###### Following are the steps:

**Step-1:**Begin the tree with the root node, says S, which contains the complete dataset.**Step-2:**Find the best attribute in the dataset using**Attribute Selection Measure (ASM).****Step-3:**Divide the S into subsets that contains possible values for the best attributes.**Step-4:**Generate the decision tree node, which contains the best attribute.**Step-5:**Recursively make new decision trees using the subsets of the dataset created in step -3. Continue this process until a stage is reached where you cannot further classify the nodes and called the final node as a leaf node.

For example, let’s say you want to build a decision tree to decide whether you should accept or decline a job offer. The decision tree for this case is as shown:

It is clear from the decision tree that an offer is accepted if:

- Salary is greater than $50,000
- The commute is less than an hour
- Incentives are offered

**Attribute Selection Measures**:

While implementing a Decision tree, the main issue arises that how to select the best attribute for the root node and for sub-nodes. So, to solve such problems there is a technique which is called as **Attribute selection measure or ASM. **By this measurement, we can easily select the best attribute for the nodes of the tree. There are two popular techniques for ASM, which are:

**Information Gain****Gini Index**

**Information Gain:**

- Information gain is the measurement of changes in entropy after the segmentation of a dataset based on an attribute.
- It calculates how much information a feature provides us about a class.
- According to the value of information gain, we split the node and build the decision tree.
- A decision tree algorithm always tries to maximize the value of information gain, and a node/attribute having the highest information gain is split first. It can be calculated using the below formula:

Information Gain= Entropy(S)- [(Weighted Avg) *Entropy(each feature)

**Entropy:** Entropy is a metric to measure the impurity in a given attribute. It specifies randomness in data. Entropy can be calculated as:

Entropy(s)= -P(yes)log2 P(yes)- P(no) log2 P(no)

**Where,**

**S= Total number of samples****P(yes)= probability of yes****P(no)= probability of no**

**2. Gini Index:**

- Gini index is a measure of impurity or purity used while creating a decision tree in the CART(Classification and Regression Tree) algorithm.
- An attribute with the low Gini index should be preferred as compared to the high Gini index.
- It only creates binary splits, and the CART algorithm uses the Gini index to create binary splits.
- Gini index can be calculated using the below formula:

Gini Index= 1- ∑_{j}P_{j}^{2}

#### 15. How do you build a random forest model?

A random forest is built up of a number of decision trees. If you split the data into different packages and make a decision tree in each of the different groups of data, the random forest brings all those trees together.

**Steps to build a random forest model:**

- Randomly select ‘k’ features from a total of ‘m’ features where k << m
- Among the ‘k’ features, calculate the node D using the best split point
- Split the node into daughter nodes using the best split
- Repeat steps two and three until leaf nodes are finalized
- Build forest by repeating steps one to four for ‘n’ times to create ‘n’ number of trees

#### 16. What is bias-variance trade-off?

**Bias:** Bias is an error introduced in your model due to oversimplification of the machine learning algorithm. It can lead to underfitting. When you train your model at that time model makes simplified assumptions to make the target function easier to understand.

Low bias machine learning algorithms — Decision Trees, k-NN and SVM High bias machine learning algorithms — Linear Regression, Logistic Regression

**Variance:** Variance is how much your model changes based on the changes in the input. It is an error introduced in your model due to complex machine learning algorithm, your model learns noise also from the training data set and performs badly on test data set. It can lead to high sensitivity and overfitting.

**Bias-Variance trade-off:** The goal of any supervised machine learning algorithm is to have low bias and low variance to achieve good prediction performance.

**Example:**

- The k-nearest neighbour algorithm has low bias and high variance, but the trade-off can be changed by increasing the value of k which increases the number of neighbours that contribute to the prediction and in turn increases the bias of the model.
- The support vector machine algorithm has low bias and high variance, but the trade-off can be changed by increasing the C parameter that influences the number of violations of the margin allowed in the training data which increases the bias but decreases the variance.

#### 17. How can you avoid the overfitting your model?

Overfitting refers to a model that is only set for a very small amount of data and ignores the bigger picture. There are three main methods to avoid overfitting:

- Keep the model simple – Take fewer variables into account, thereby removing some of the noise in the training data
- Use cross-validation techniques, such as k folds cross-validation
- Use regularization techniques, such as LASSO, that penalize certain model parameters if they’re likely to cause overfitting.

#### 18. What is a confusion matrix?

The confusion matrix is a 2X2 table that contains 4 outputs provided by the binary classifier. Various measures, such as error-rate, accuracy, specificity, sensitivity, precision and recall are derived from it. *Confusion Matrix.*

A data set used for performance evaluation is called a test data set. It should contain the correct labels and predicted labels.

The predicted labels will exactly the same if the performance of a binary classifier is perfect.

The predicted labels usually match with part of the observed labels in real-world scenarios.

A binary classifier predicts all data instances of a test data set as either positive or negative. This produces four outcomes-

- True-positive(TP) — Correct positive prediction
- False-positive(FP) — Incorrect positive prediction
- True-negative(TN) — Correct negative prediction
- False-negative(FN) — Incorrect negative prediction

**Basic measures derived from the confusion matrix**

**Error Rate**= (FP+FN)/(P+N)**Accuracy**= (TP+TN)/(P+N)**Sensitivity(Recall or True positive rate)**= TP/P**Specificity(True negative rate)**= TN/N**Precision(Positive predicted value)**= TP/(TP+FP)**F-Score**(Harmonic mean of precision and recall) = (1+b)(PREC.REC)/(b²PREC+REC) where b is commonly 0.5, 1, 2.

#### 19. What is the difference between classification and regression?

Classification is used to produce discrete results, classification is used to classify data into some specific categories. For example, classifying emails into spam and non-spam categories.

Whereas, We use regression analysis when we are dealing with continuous data, for example predicting stock prices at a certain point in time.

#### 20. What is meant by ‘Training set’ and ‘Test Set’?

We split the given data set into two different sections namely,’Training set’ and ‘Test Set’. ‘Training set’ is the portion of the dataset used to train the model.

‘Testing set’ is the portion of the dataset used to test the trained model.

#### 21. How Do You Handle Missing or Corrupted Data in a Dataset?

One of the easiest ways to handle missing or corrupted data is to drop those rows or columns or replace them entirely with some other value.

There are two useful methods in Pandas:

- IsNull() and dropna() will help to find the columns/rows with missing data and drop them
- Fillna() will replace the wrong values with a placeholder value

#### 22. What are the feature selection methods used to select the right variables?

Following are the technique to select features:

**Principle component analysis(PCA)****t-Sne**- Random forest
**Forward Selection**: We test one feature at a time and keep adding them until we get a good fit.**Backward Selection**: We test all the features and start removing them to see what works better

#### 23.You are given a data set consisting of variables with more than 30 percent missing values. How will you deal with them?

The following are ways to handle missing data values:

If the data set is large, we can just simply remove the rows with missing data values. It is the quickest way; we use the rest of the data to predict the values.

For smaller data sets, we can substitute missing values with the mean or average of the rest of the data using the pandas’ data frame in python. There are different ways to do so, such as df.mean(), df.fillna(mean).

#### 24. What do you understand by the term Normal Distribution?

Data is usually distributed in different ways with a bias to the left or to the right or it can all be jumbled up.

However, there are chances that data is distributed around a central value without any bias to the left or right and reaches normal distribution in the form of a bell-shaped curve.

The random variables are distributed in the form of a symmetrical, bell-shaped curve.

Properties of Normal Distribution are as follows;

- Unimodal -one mode
- Symmetrical -left and right halves are mirror images
- Bell-shaped -maximum height (mode) at the mean
- Mean, Mode, and Median are all located in the centre

#### 25. What is the goal of A/B Testing?

It is a hypothesis testing for a randomized experiment with two variables A and B.

The goal of A/B Testing is to identify any changes to the web page to maximize or increase the outcome of interest. A/B testing is a fantastic method for figuring out the best online promotional and marketing strategies for your business. It can be used to test everything from website copy to sales emails to search ads

An example of this could be identifying the click-through rate for a banner ad.

#### 26. What is p-value?

When you perform a hypothesis test in statistics, a p-value can help you determine the strength of your results. p-value is a number between 0 and 1. Based on the value it will denote the strength of the results. The claim which is on trial is called the Null Hypothesis.

Low p-value (≤ 0.05) indicates strength against the null hypothesis which means we can reject the null Hypothesis. High p-value (≥ 0.05) indicates strength for the null hypothesis which means we can accept the null Hypothesis p-value of 0.05 indicates the Hypothesis could go either way. To put it in another way, High P values: your data are likely with a true null. Low P values: your data are unlikely with a true null.

#### 27. What are the differences between over-fitting and under-fitting?

In statistics and machine learning, one of the most common tasks is to fit a *model* to a set of training data, so as to be able to make reliable predictions on general untrained data.

**In overfitting**, a statistical model describes random error or noise instead of the underlying relationship. Overfitting occurs when a model is excessively complex, such as having too many parameters relative to the number of observations. A model that has been overfitted, has poor predictive performance, as it overreacts to minor fluctuations in the training data.

**Underfitting** occurs when a statistical model or machine learning algorithm cannot capture the underlying trend of the data. Underfitting would occur, for example, when fitting a linear model to non-linear data. Such a model too would have poor predictive performance.

#### 28. How to combat Overfitting and Underfitting?

To combat overfitting and underfitting, you can resample the data to estimate the model accuracy (k-fold cross-validation) and by having a validation dataset to evaluate the model.

#### 29. Explain cross-validation.

Cross-validation is a model validation technique for evaluating how the outcomes of a statistical analysis will generalize to an independent data set. It is mainly used in backgrounds where the objective is to forecast and one wants to estimate how accurately a model will accomplish in practice.

The goal of cross-validation is to term a data set to test the model in the training phase (i.e. validation data set) to limit problems like overfitting and gain insight into how the model will generalize to an independent data set.

#### 30. What is k-fold cross-validation?

In k-fold cross-validation, we divide the dataset into *k* equal parts. After this, we loop over the entire dataset k times. In each iteration of the loop, one of the k parts is used for testing, and the other k − 1 parts are used for training. Using k-fold cross-validation, each one of the k parts of the dataset ends up being used for training and testing purposes.

#### 31. How should you maintain a deployed model?

The steps to maintain a deployed model are:

**Monitor:**

Constant monitoring of all models is needed to determine their performance accuracy. When you change something, you want to figure out how your changes are going to affect things. This needs to be monitored to ensure it’s doing what it’s supposed to do.

**Evaluate:**

Evaluation metrics of the current model are calculated to determine if a new algorithm is needed.

**Compare:**

The new models are compared to each other to determine which model performs the best.

**Rebuild:**

The best performing model is re-built on the current state of data.

#### 32. What is ‘Naive’ in a Naive Bayes?

The **Naive Bayes Algorithm** is based on the Bayes Theorem. Bayes’ theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

The Algorithm is ‘naive’ because it makes assumptions that may or may not turn out to be correct.

#### 33. Explain SVM algorithm in detail.

*SVM* stands for support vector machine, it is a supervised machine learning algorithm which can be used for both *Regression*** and Classification**. If you have n features in your training data set, SVM tries to plot it in n-dimensional space with the value of each feature being the value of a particular coordinate. SVM uses hyperplanes to separate out different classes based on the provided kernel function.

#### 34. What are the support vectors in SVM?

In the diagram, we see that the thinner lines mark the distance from the classifier to the closest data points called the support vectors (darkened data points). The distance between the two thin lines is called the margin.

#### 35. What are the different kernels in SVM?

There are four types of kernels in SVM:

- Linear Kernel
- Polynomial kernel
- Radial basis kernel
- Sigmoid kernel

#### 36. What is pruning in Decision Tree?

As the name implies, pruning involves cutting back the tree. Pruning is one of the techniques that is used to overcome our problem of Overfitting.

Pruning, in its literal sense, is a practice which involves the selective removal of certain parts of a tree(or plant), such as branches, buds, or roots, to improve the tree’s structure, and promote healthy growth. This is exactly what Pruning does to our Decision Trees as well. It makes it versatile so that it can adapt if we feed any new kind of data to it, thereby fixing the problem of overfitting. It reduces the size of a Decision Tree which might slightly increase your training error but drastically decrease your testing error, hence making it more adaptable.

#### 37. What are Recommender Systems?

**Recommender Systems** are a subclass of information filtering systems that are meant to predict the preferences or ratings that a user would give to a product.

Recommender systems are widely used in movies, news, research articles, products, social tags, music, etc.*Examples include movie recommenders in IMDB, Netflix & BookMyShow, product recommenders in e-commerce sites like Amazon, eBay & Flipkart, YouTube video recommendations and game recommendations in Xbox*

#### 38. What is Collaborative filtering?

The process of filtering used by most of the recommender systems to find patterns or information by collaborating viewpoints, various data sources and multiple agents.

An example of collaborative filtering can be to predict the rating of a particular user based on his/her ratings for other movies and others’ ratings for all movies. This concept is widely used in recommending movies in IMDB, Netflix & BookMyShow, product recommenders in e-commerce sites like Amazon, eBay & Flipkart, YouTube video recommendations and game recommendations in Xbox

#### 39. How will you define the number of clusters in a clustering algorithm?

Though the Clustering Algorithm is not specified, this question is mostly in reference to K-**Means clustering** where “K” defines the number of clusters. The objective of clustering is to group similar entities in a way that the entities within a group are similar to each other but the groups are different from each other.

For example, the following image shows three different groups.

Within Sum of squares is generally used to explain the homogeneity within a cluster. If you plot WSS for a range of number of clusters, you will get the plot shown below.

- The Graph is generally known as
.*Elbow Curve* - Red circled a point in above graph i.e.
is the point after which you don’t see any decrement in WSS.*Number of Cluster =6* - This point is known as the
**bending**point and taken as K in K – Means.

This is the widely used approach but few data scientists also use Hierarchical clustering first to create dendrograms and identify the distinct groups from there.

#### 40. Describe in brief any type of Ensemble Learning?

Ensemble learning has many types but two more popular ensemble learning techniques are mentioned below.

**Bagging**

Bagging tries to implement similar learners on small sample populations and then takes a mean of all the predictions. In generalised bagging, you can use different learners on different population. As you expect this helps us to reduce the variance error.

**Boosting**

**Boosting** is an iterative technique which adjusts the weight of an observation based on the last classification. If an observation was classified incorrectly, it tries to increase the weight of this observation and vice versa. Boosting in general decreases the bias error and builds strong predictive models. However, they may over fit on the training data.

#### 41. What is a Box-Cox Transformation?

A Box cox transformation is a statistical technique to transform non-normal dependent variables into a normal shape. If the given data is not normal then most of the statistical techniques assume normality. Applying a box cox transformation means that you can run a broader number of tests.

A Box-Cox transformation is a way to transform non-normal dependent variables into a normal shape. Normality is an important assumption for many statistical techniques, if your data isn’t normal, applying a Box-Cox means that you are able to run a broader number of tests.

#### 42. Explain Principle Component Analysis (PCA).

PCA is a method for transforming features in a dataset by combining them into uncorrelated linear combinations.

These new features, or principal components, sequentially maximize the variance represented (i.e. the first principal component has the most variance, the second principal component has the second most, and so on).

As a result, PCA is useful for dimensionality reduction because you can set an arbitrary variance cutoff.

#### 43. How is KNN different from k-means clustering?

K-Nearest Neighbors is a supervised classification algorithm, while k-means clustering is an unsupervised clustering algorithm. While the mechanisms may seem similar at first, what this really means is that in order for K-Nearest Neighbors to work, you need labeled data you want to classify an unlabeled point into (thus the nearest neighbor part). K-means clustering requires only a set of unlabeled points and a threshold: the algorithm will take unlabeled points and gradually learn how to cluster them into groups by computing the mean of the distance between different points.

#### 44. You’ve built a random forest model with 10000 trees. You got delighted after getting training error as 0.00. But, the validation error is 34.23. What is going on? Haven’t you trained your model perfectly?

The model has overfitted. Training error 0.00 means the classifier has mimicked the training data patterns to an extent, that they are not available in the unseen data. Hence, when this classifier was run on an unseen sample, it couldn’t find those patterns and returned predictions with higher error. In a random forest, it happens when we use a larger number of trees than necessary. Hence, to avoid this situation, we should tune the number of trees using cross-validation.

#### 45. In k-means or kNN, we use euclidean distance to calculate the distance between nearest neighbors. Why not manhattan distance?

We don’t use manhattan distance because it calculates distance horizontally or vertically only. It has dimension restrictions. On the other hand, the euclidean metric can be used in any space to calculate distance. Since the data points can be present in any dimension, euclidean distance is a more viable option.

Example: Think of a chessboard, the movement made by a bishop or a rook is calculated by manhattan distance because of their respective vertical & horizontal movements.

#### 46. When does regularization becomes necessary in Machine Learning?

Regularization becomes necessary when the model begins to overfit/underfit. This technique introduces a cost term for bringing in more features with the objective function. Hence, it tries to push the coefficients for many variables to zero and hence reduce the cost term. This helps to reduce model complexity so that the model can become better at predicting (generalizing).

#### 47. When would you use random forests Vs SVM and why?

There are a couple of reasons why a random forest is a better choice of the model than a support vector machine:

- Random forests allow you to determine the feature importance. SVM’s can’t do this.
- Random forests are much quicker and simpler to build than an SVM.

For multi-class classification problems, SVMs require a one-vs-rest method, which is less scalable and more memory intensive.

#### 48. Do you think 50 small decision trees are better than a large one? Why?

Another way of asking this question is “Is a random forest a better model than a decision tree?” And the answer is yes because a random forest is an ensemble method that takes many weak decision trees to make a strong learner. Random forests are more accurate, more robust, and less prone to overfitting.

#### 49. What’s the Relationship between True Positive Rate and Recall?

The True positive rate in machine learning is the percentage of the positives that have been properly acknowledged, and recall is just the count of the results that have been correctly identified and are relevant. Therefore, they are the same things, just having different names. It is also known as sensitivity.

#### 50. What are Eigenvectors and Eigenvalues?

*Eigenvectors* are used for understanding linear transformations. In data analysis, we usually calculate the eigenvectors for a correlation or covariance matrix. Eigenvectors are the directions along which a particular linear transformation acts by flipping, compressing or stretching.

*Eigenvalue* can be referred to as the strength of the transformation in the direction of eigenvector or the factor by which the compression occurs.

#### 51. What is pickle module in Python?

For serializing and de-serializing an object in Python, we make use of pickle module. In order to save this object on drive, we make use of pickle. It converts an object structure into character stream.

#### 52. How K-means clustering works? explain in details.

The first property of clusters – it states that the points within a cluster should be similar to each other. So,** our aim here is to minimize the distance between the points within a cluster.**

There is an algorithm that tries to minimize the distance of the points in a cluster with their centroid – the k-means clustering technique.

**Let’s now take an example to understand how K-Means actually works:**

We have these 8 points and we want to apply k-means to create clusters for these points. Here’s how we can do it.

**Step 1: Choose the number of clusters k.**

**Step 2: Select k random points from the data as centroids**:

Next, we randomly select the centroid for each cluster. Let’s say we want to have 2 clusters, so k is equal to 2 here. We then randomly select the centroid:

Here, the red and green circles represent the centroid for these clusters.

**Step 3: Assign all the points to the closest cluster centroid**

Once we have initialized the centroids, we assign each point to the closest cluster centroid:

Here you can see that the points which are closer to the red point are assigned to the red cluster whereas the points which are closer to the green point are assigned to the green cluster.

**Step 4: Re-compute the centroids of newly formed clusters**

Now, once we have assigned all of the points to either cluster, the next step is to compute the centroids of newly formed clusters:

Here, the red and green crosses are the new centroids.

**Step 5: Repeat steps 3 and 4**

We then repeat steps 3 and 4:

*The step of computing the centroid and assigning all the points to the cluster based on their distance from the centroid is a single iteration*. But wait – when should we stop this process? It can’t run till eternity, right?

**Stopping Criteria for K-Means Clustering**:

There are essentially three stopping criteria that can be adopted to stop the K-means algorithm:

- Centroids of newly formed clusters do not change
- Points remain in the same cluster
- Maximum number of iterations are reached

#### References

- www.edureka.co 2. simplilearn.com 3. geeksforgeeks.org 4. elitedatascience.com 5. analyticsvidhya.com 6. guru99.com 7. intellipaat.com 8. towardsdatascience.com 9 mygreatlearning.com 10 mindmajix.com 11 toptal.com 12 glassdoor.co.in 13 udacity.com 14 educba.com 15 analyticsindiamag.com 16 ubuntupit.com 17 javatpoint.com 18 quora.com 19 hackr.io 20 kaggle.com

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