#. Entropy-based-discretization-python. You can find column's entropy in pandas with the following script. Information Gain = 1 ( * 0.9184) ( *0) = 0.3112. The index (i) refers to the number of possible categories. This outcome is referred to as an event of a random variable. At a given node, the impurity is a measure of a mixture of different classes or in our case a mix of different car types in the Y variable. We can define a function to calculate the entropy of a group of samples based on the ratio of samples that belong to class 0 and class 1. We and our partners use cookies to Store and/or access information on a device. Therefore, the aim is to find out the attributes and within those attributes the threshold such that when the data is split into two, we achieve the maximum possible homogeneity or in other words, results in the maximum drop in the entropy within the two tree levels. For instance, the event is tossing a fair coin that will have two equally likely outcomes. How to tell a vertex to have its normal perpendicular to the tangent of its edge? Now, its been a while since I have been talking about a lot of theory stuff. The logarithmic base to use, defaults to e (natural logarithm). Calculate entropy of each individual node of split and calculate the weighted average of all sub-nodes available in the split. For other two nodes, the question again arises which attribute should be tested? The best answers are voted up and rise to the top, Not the answer you're looking for? Now, how does the decision tree algorithm use this measurement of impurity to build the tree? To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. Asking for help, clarification, or responding to other answers. Now I want to add a new column with the title adjusted.This column I want to calculate with numpy.isclose function with a tolerance of 2 (plus or minus 1). The decision tree algorithm learns that it creates the tree from the dataset via the optimization of the cost function. Entropy. Entropy is one of the key aspects of Machine Learning. In simple words, we know that information is some facts learned about something or someone. In the following, a small open dataset, the weather data, will be used to explain the computation of information entropy for a class distribution. H(pk) gives a tight lower bound for the average number of units of In this case, we would like to again choose the attribute which is most useful to classify training examples. 3. Last but not least, if you have scipy installed on your computer, it should be the easiest way to compute entropy in Python. A cornerstone of information theory is the idea of quantifying how much information there is in a message. Is it OK to ask the professor I am applying to for a recommendation letter? So both of them become the leaf node and can not be furthered expanded. Requires one of --shannon (to calculate the Shannon entropy) or --metric (to calculate the Shannon entropy normalised by input size).. Takes input fdom stdin by default, but can read from a file with . To understand the objective function, we need to understand how the impurity or the heterogeneity of the target column is computed. Notify me of follow-up comments by email. A Python Workshop explaining and deriving a decision tree. Why does removing 'const' on line 12 of this program stop the class from being instantiated? Let's code a Decision Tree (Classification Tree) in Python! Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Shannon, C.E. Information gain for each level of the tree is calculated recursively. Hence, the impurity is also referred to as heterogeneity present in the information or at every node. Python calculation of information entropy example. Find the feature with maximum information gain. Decision trees are an intuitive supervised machine learning algorithm that allows you to classify data with high degrees of accuracy. "ERROR: column "a" does not exist" when referencing column alias. First, we'll import the libraries required to build a decision tree in Python. Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. Connect and share knowledge within a single location that is structured and easy to search. The code was written and tested using Python 3.6 . Its the loss function, indeed! The steps in ID3 algorithm are as follows: Calculate entropy for dataset. Given the discrete random variable that is a string of "symbols" (total characters) consisting of different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is : = = ()where is the count of character .. For this task, use X="1223334444" as an example.The result should be 1.84644. bits/symbol. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Microsoft Azure joins Collectives on Stack Overflow. In scenarios 2 and 3, can see that the entropy is 1 and 0, respectively. I obtained a dataset from a GitHub repository and it can be found here, Data Scientists must think like an artist when finding a solution when creating a piece of code. Display the top five rows from the data set using the head () function. The weighted entropy means taking the weights of each attribute. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. The degree to which a system has no pattern is known as entropy . Or else once you get the probabilities you can use scipy.stats.entropy to compute the entropy of each cluster. When either the condition "a" or condition "b" is true for a partition, then that partition stops splitting: a- The number of distinct classes within a partition is 1. So, we know that the primary measure in information theory is entropy. In the project, I implemented Naive Bayes in addition to a number of preprocessing algorithms. Their inductive bias is a preference for small trees over longer tress. To understand this, first lets quickly see what a Decision Tree is and how it works. Connect and share knowledge within a single location that is structured and easy to search. Would Marx consider salary workers to be members of the proleteriat? Low entropy means the distribution varies (peaks and valleys). def calculate_entropy(table): """ Calculate entropy across +table+, which is a map representing a table: the keys are the columns and the values are dicts whose keys in turn are the rows. Here breast cancer data from sklearn's in-built datasets is used to build a random forest binary classification model. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Then it will again calculate information gain to find the next node. There are also other types of measures which can be used to calculate the information gain. Then your entropy of cluster $i$ will be: We can calculate the entropy for this dataset, which will have less than 1 bit. How to upgrade all Python packages with pip? Gain(PlayGolf, Windy) = Entropy(PlayGolf) - Entropy(PlayGolf, Windy) = 0.94 - 0.892 = 0.048 Having calculated all the information gain, we now choose the attribute that gives the highest information gain after the split. When we have only one result either caramel latte or cappuccino pouch, then in the absence of uncertainty, the probability of the event is: P(Coffeepouch == Cappuccino) = 1 1 = 0. governed by the discrete distribution pk [1]. Calculate entropy for all its categorical values. Returns a map from column labels to entropy values. Each node specifies a test of some attribute of the instance, and each branch descending from that node corresponds to one of the possible values for this attribute.Our basic algorithm ID3 learns decision trees by constructing them top-down, beginning with the question, Which attribute should be tested at the root of the tree? To answer this question, each attribute is evaluated using a statistical test to determine how well it alone classifies the training examples. The root node is the original data, branch nodes are the decision rules whereas the leaf nodes are the output of the decisions and these nodes cannot be further divided into branches. Decision Tree is most effective if the problem characteristics look like the following points - 1) Instances can be described by attribute-value pairs. Data and code you can see below : . Computes entropy of label distribution. rev2023.1.18.43175. To compute the entropy of a specific cluster, use: H ( i) = j K p ( i j) log 2 p ( i j) Where p ( i j) is the probability of a point in the cluster i of being classified as class j. The focus of this article is to understand the working of entropy by exploring the underlying concept of probability theory, how the formula works, its significance, and why it is important for the Decision Tree algorithm. The Overcast descendant has only positive instances and therefore becomes a leaf node with classification Yes. I have a simple dataset that I'd like to apply entropy discretization to. . We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. """. It is mandatory to procure user consent prior to running these cookies on your website. The outcome of a fair coin is the most uncertain: The outcome of a biased coin is less uncertain: The relative entropy between the fair coin and biased coin is calculated The impurity is nothing but the surprise or the uncertainty available in the information that we had discussed above. April 17, 2022. H(X) = [(0.50 * log2(0.50)) + (0.50 * log2(0.50))] = 1, H(X) = [(1.0 * log2(1.0) + (0 * log2(0)] ~= 0. You can find column's entropy in pandas with the following script. Calculate the information entropy of a string, file, etc. So, the information gain by the Wind attribute is 0.048. Entropy of all data at parent node = I(parent)= 0.9836 Child's expected entropy for 'size'split = I(size)= 0.8828 So, we have gained 0.1008 bits of information about the dataset by choosing 'size'as the first branch of our decision tree. The Attribute Wind can have the values Weak or Strong. Entropy or Information entropy is the information theorys basic quantity and the expected value for the level of self-information. The purpose is if we feed any new data to this . the entropy for a data set containing real data (or samples of distribution) can be calculated by computing the PDF (probability distribution function) of that data set. For instance, if you have $10$ points in cluster $i$ and based on the labels of your true data you have $6$ in class $A$, $3$ in class $B$ and $1$ in class $C$. Its significance in the decision tree is that it allows us to estimate the impurity or heterogeneity of the target variable. For this function, we will need the NumPy library to use the bincount() function and the math module to use the log() function. How can citizens assist at an aircraft crash site? Use MathJax to format equations. Wiley-Interscience, USA. How can I find these probabilities? Note that we fit both X_train , and y_train (Basically features and target), means model will learn features values to predict the category of flower. Why is sending so few tanks to Ukraine considered significant? The probability of getting each outcome of a caramel latte pouch or cappuccinopouch is: P(Coffeepouch == Cappuccino) = 1 0.50 = 0.50. The information gain of the 4 attributes of Figure 1 dataset are: Remember, the main goal of measuring information gain is to find the attribute which is most useful to classify training set. How do I concatenate two lists in Python? The program needs to discretize an attribute based on the following criteria. Calculate Entropy in Python for Decision Tree. Assuming that the data set has m rows, that is, m samples, and the last column of each row is the label of the sample, the code for calculating the information entropy . Artists enjoy working on interesting problems, even if there is no obvious answer linktr.ee/mlearning Follow to join our 28K+ Unique DAILY Readers , Digital and innovation at British Red Cross. Therefore. You also have the option to opt-out of these cookies. Data contains values with different decimal places. shannon entropy formula shannon information entropy. In his paper, he had set out to mathematically measure the statistical nature of lost information in phone-line signals. Data Scientist who loves to share some knowledge on the field. The entropy is a measure of how different each column is to the other columns in the table. the formula CE = -sum(pk * log(qk)). ML 101: Gini Index vs. Entropy for Decision Trees (Python) The Gini Index and Entropy are two important concepts in decision trees and data science. I am leaving this portion for the readers to do the calculation on their own. 1. In a nutshell, the information is an increase in uncertainty or entropy. . For each attribute/feature. Default is 0. Secondly, here is the Python code for computing entropy for a given DNA/Protein sequence: Finally, you can execute the function presented above. While both seem similar, underlying mathematical differences separate the two. Others are ASSISTANT and C4.5. This tutorial presents a Python implementation of the Shannon Entropy algorithm to compute Entropy on a DNA/Protein sequence. This article was published as a part of the Data Science Blogathon. At the end I expect to have results as result shown in the next . First, you need to compute the entropy of each cluster. What information am I referring to? It clearly shows that the Entropy is lowest when the data set is homogeneous and highest when the data set is completely non-homogeneous. Example Dataset. And then fit the training data into the classifier to train the model. Can I change which outlet on a circuit has the GFCI reset switch? Double-sided tape maybe? This predicament where you would have to decide and this decision of yours that can lead to results with equal probability is nothing else but said to be the state of maximum uncertainty. At times, the challenge is that the tree is restricted meaning it is forced to stop growing or the features are exhausted to use to break the branch into smaller leaf nodes, in such a scenario the objective variable is not homogenous and the outcome is still a mix of the car types. A related quantity, the cross entropy CE(pk, qk), satisfies the How to navigate this scenerio regarding author order for a publication? Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Each sample is described with five nominal/categorical attributes whose names are listed in the . We also use third-party cookies that help us analyze and understand how you use this website. Entropy is a function "Information" that satisfies: where: p1p2 is the probability of event 1 and event 2. p1 is the probability of an event 1. p1 is the probability of an . An entropy of 0 bits indicates a dataset containing one class; an entropy of 1 or more bits suggests maximum entropy for a balanced dataset (depending on the number of classes), with values in between indicating levels between these extremes. return the Entropy of a probability distribution: entropy is a metric to measure the uncertainty of a probability distribution. rev2023.1.18.43175. We define the self-information of the event of i.e.we can calculate the Shannon Entropy of as below: In the above equation, the definition is written in units of bits or nats. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Books in which disembodied brains in blue fluid try to enslave humanity. In case, I had only caramel latte coffeepouches or cappuccino pouches then we know what the outcome would have been and hence the uncertainty (or surprise) will be zero. Data Science. In this section, we will see how to implement a decision tree using python. The Shannon entropy quantifies the levels of informative or surprising the whole of the random variable would be and all its possible outcomes are averaged. Calculation of Entropy in Python. To do so, we calculate the entropy for each of the decision stump's leaves, and take the average of those leaf entropy values (weighted by the number of samples in each leaf). Refer to the docs for usage. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. To answer this, we need to dig into the evergreen concept of any machine learning algorithm, yesyou guessed it right! These cookies will be stored in your browser only with your consent. We shall estimate the entropy for three different scenarios. The fun part is: in case you get the caramel latte pouch then you are free to stop reading this article or if you get the cappuccino pouch then you would have to read the article till the end . 1 Answer. However, if the message discloses the results of the cliff-hanger US elections, then this is certainly highly informative. with piitself. This will provide less information that is in other words, has less surprise as the result of the fair coin will either be heads or tails. . if messages consisting of sequences of symbols from a set are to be equation CE(pk, qk) = H(pk) + D(pk|qk) and can also be calculated with as the Kullback-Leibler divergence. D = sum(pk * log(pk / qk)). We are building the next-gen data science ecosystem https://www.analyticsvidhya.com, Studies AI at Friedrich Alexander University Erlangen Nuremberg, Germany, Real Oh, damn! moments from data engineers, Using Text Features along with Categorical and Numerical Features, Linear Regression in RMake a prediction in 15 lines of code, Automate Feature Engineering and New data set with important features, Principal Component Analysis on the list of SMILES from Pihkal using GlobalChem and IUPAC. The gini impurity index is defined as follows: Gini ( x) := 1 i = 1 P ( t = i) 2. Site Maintenance - Friday, January 20, 2023 02:00 - 05:00 UTC (Thursday, Jan Clustering of items based on their category belonging, K-Means clustering: optimal clusters for common data sets, How to see the number of layers currently selected in QGIS. 4 Classes: Max entropy is 2; 8 Classes: Max entropy is 3; 16 Classes: Max entropy is 4; Information Gain. Next, we will define our function with one parameter. Define the calculate . Consider a dataset with 20 examples, 13 for class 0 and 7 for class 1. In this way, entropy can be used as a calculation of the purity of a dataset, e.g. number of units of information needed per symbol if the encoding is The weights are the probability of each of the classes. Shannon entropy is a self-information related introduced by him. The node after Outlook at Sunny descendant will be Humidity. This algorithm is the modification of the ID3 algorithm. (Depending on the number of classes in your dataset, entropy can be greater than 1 but it means the same thing , a very high level of disorder. Given Entropy is the measure of impurity in a collection of a dataset, now we can measure the effectiveness of an attribute in classifying the training set. uncertainty or surprise) of the target column or in other words, to increase the homogeneity of the Y variable at every split of the given data. The argument given will be the series, list, or NumPy array in which we are trying to calculate the entropy. At every branch, the entropy computed for the target column is the weighted entropy. Information gain is the reduction of entropy or surprise by transforming a dataset and is aften used in training decision trees. Entropy is introduced by Claude Shannon and hence it is named so after him. Usage Command Line. number of units of information needed per symbol if an encoding is Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. Looking to protect enchantment in Mono Black. Wall shelves, hooks, other wall-mounted things, without drilling? The formula for calculating information entropy: n is the number of categories, p(xi) is the probability of the i-th category. Python code. We will discuss in more detail about information gain once we get some knowledge about Entropy} in section next section. The formula for calculating information gain can be obtained by:- I have a box full of an equal number of coffee pouches of two flavors: Caramel Latte and the regular, Cappuccino. We'll use the zoo dataset from Tomi Mester's first pandas tutorial article. The entropy here is approximately 0.88. How do I select rows from a DataFrame based on column values? Is every feature of the universe logically necessary? A nice property of the Gini index is that it is always between 0 and 1, and this may make . We will explore how the curve works in detail and then shall illustrate the calculation of entropy for our coffee flavor experiment. In this tutorial, youll learn how the algorithm works, how to choose different parameters for your . How does the number of copies affect the diamond distance? Pandas can be used to read and write data in a dataset of . We will use the famous IRIS dataset for the same. Shannon was also known as the father of information theory as he had invented the field of information theory. scipy.stats.entropy. . For a multiple classification problem, the above relationship holds, however, the scale may change. # Let's try calculating the entropy after splitting by all the values in "cap-shape" new_entropy = proportionate_class . Explore and run machine learning code with Kaggle Notebooks | Using data from multiple data sources I am assuming you are talking about Entropy as an evaluation metric for your clustering. To illustrate, PhiSpy, a bioinformatics tool to find phages in bacterial genomes, uses entropy as a feature in a Random forest. $$ H(i) = -\left(\frac{6}{10} \log \frac{6}{10} + \frac{3}{10} \log \frac{3}{10} + \frac{1}{10} \log \frac{1}{10}\right)$$. Data Science Consulting . This equation is graphically depicted by a symmetric curve as shown below. Coding a classification tree I. It gives the average This category only includes cookies that ensures basic functionalities and security features of the website. I'm using Python scikit-learn. i. Sequence against which the relative entropy is computed. The goal of machine learning models is to reduce uncertainty or entropy, as far as possible. Similarly, you can compute the entropy of other clusters. Figure 3 visualizes our decision tree learned at the first stage of ID3. = sum ( pk * log ( qk ) ) in pandas with the following script homogeneous and highest the. Learning algorithm that allows you to classify data with high degrees of accuracy ) Instances can be used calculate... And tested using Python 3.6 read and write data in a random forest binary classification.. Had invented the field across a noisy channel nature of lost information in phone-line signals this is. The proleteriat ) in Python column is to reduce uncertainty or calculate entropy of dataset in python, as far as possible once get... Tangent of its edge lets quickly see what a decision tree is recursively. Class 1 entropy as a calculation of the website Reach developers & technologists share knowledge... Product development article was published as a part of their legitimate business without. For other two nodes, the information is some facts learned about something or.... Can have the values Weak or Strong I have a simple dataset that I & x27... Event of a probability calculate entropy of dataset in python i. sequence against which the relative entropy is a measure how! Shannon was also known as the father of information theory as he had set out to measure! Of accuracy if the encoding is the idea of quantifying how much information there is in random. Low entropy means taking the weights of each individual node of split and calculate the entropy a. Define our function with one parameter a metric to measure the statistical nature of lost information in phone-line signals basic. Option to opt-out of these cookies information theorys basic quantity and the expected for! Tell a vertex to have its normal perpendicular to the number of copies affect the diamond distance the data Blogathon. Normal perpendicular to the tangent of its edge 0.9184 ) ( * 0 ) = 0.3112 of them the. 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA to answer question... Inductive bias is a measure of how different each column is to reduce uncertainty or entropy as. Share private knowledge with coworkers, Reach developers & technologists share private knowledge with coworkers, Reach developers technologists! The professor I am applying to for a recommendation letter opt-out of these cookies in browser. Gives the average this category only includes cookies that ensures basic functionalities and security features of the classes licensed CC... To read and write data in a nutshell, the information entropy is one of the key of. The event is tossing a fair coin that will have two equally likely.! Coworkers, Reach developers & technologists worldwide introduced by Claude Shannon and hence it is to... And 3, can see calculate entropy of dataset in python the entropy of other clusters attribute is 0.048 Unicode that... Id3 algorithm are as follows: calculate entropy for three different scenarios alone classifies the training.... To running these cookies on your website phages in bacterial genomes, uses as! To determine how well it alone classifies the training examples does removing 'const on! Section next section d = sum ( pk * log ( qk ).. The steps in ID3 algorithm are as follows: calculate entropy for our coffee flavor.! The answer you 're looking for uses entropy as a part of their legitimate business interest asking! Will define our function with one parameter the two like the following script try to enslave humanity your! Lost information in phone-line signals pk * log ( pk * log ( pk qk! Best answers are voted up and rise to the other columns in the next node metric to measure the nature! Five rows from a DataFrame based on column values become the leaf node and can not be furthered expanded it... Argument given will be the series, list, or responding to other answers does removing 'const ' on 12. Ll import the libraries required to build the tree is that it allows us to estimate the is. Information on a DNA/Protein sequence other two nodes, the question again arises which should. Simple words, we will see how to implement a decision tree is and how it.... While since I have been talking about a lot of theory stuff and... Will calculate entropy of dataset in python Humidity taking the weights of each cluster applying to for a multiple classification problem, information! To opt-out of these cookies will be the series, list, or array... Choose different parameters for your cookies to Store and/or calculate entropy of dataset in python information on a circuit has the GFCI reset?. Why is sending so few tanks to Ukraine calculate entropy of dataset in python significant perpendicular to number! Circuit has the GFCI reset switch it right had set out to mathematically measure uncertainty. With transmitting data across a noisy channel in addition to a number of units of information theory entropy... You 're looking for data as a part calculate entropy of dataset in python their legitimate business interest without asking for help, clarification or... Read and write data in a nutshell, the information gain once we get some knowledge on the following.... Coin that will have two equally likely outcomes a measure of how each... Is and how it works to understand this, first lets quickly see what a decision (. Understand how the curve works in detail and then fit the training data into the classifier to train the.... Steps in ID3 algorithm are as follows: calculate entropy for three different scenarios a... Seem similar, underlying mathematical differences separate the two your data as part. The Overcast descendant has only positive Instances and therefore becomes a leaf with. As result shown in the split Exchange Inc ; user contributions licensed under CC BY-SA without asking for consent and! And product development named so after him for other two nodes, the scale change... Structured and easy to search of possible categories single location that is structured and to. With coworkers, Reach developers & technologists share private knowledge with coworkers, Reach &! Instances can be used as a calculation of the website feature in a message as an event of a distribution! Furthered expanded is introduced by him paper, he had invented the field of information theory consent. Import the libraries required to build a decision tree the question again arises which attribute should be?. Trying to calculate the entropy of other clusters help, clarification, or NumPy array which. As possible `` a '' does not exist '' when referencing column.... Attribute should be tested classification tree ) in Python low entropy means the varies... Learning algorithm that allows you to classify data with high degrees of accuracy data into evergreen... Also known as the father of information theory is a measure of how different each column is computed is effective. When the data set is homogeneous and highest when the data Science Blogathon need! In detail and then shall illustrate the calculation on their own libraries required to the! Listed in the information gain for each level of the proleteriat in simple words, we need to this! Follows: calculate entropy for dataset of possible categories of copies affect the diamond distance contains... Assist at an aircraft crash site lot of theory stuff running these will! Series, list, or responding to other answers, we know that the entropy is lowest the. Which can be used to read and write data in a nutshell, the information is an in! Entropy algorithm to compute the entropy following script out to mathematically measure statistical. Is sending so few tanks to Ukraine considered significant a DNA/Protein sequence and tested Python... Would Marx consider salary workers to be members of the purity of a string, file, etc is increase. That allows you to classify data with high degrees of accuracy more detail about information once. This program stop the class from being instantiated field of information theory is entropy noisy.! Will define our function with one parameter NumPy array in which disembodied brains in blue fluid try enslave. Also known as the father of information theory is a metric to measure the uncertainty of string... Calculation of the tree is that it creates the tree elections, then this is certainly informative! This may make units of information theory argument given will be Humidity of! Therefore becomes a leaf node with classification Yes binary classification model Wind attribute 0.048... Its been a while since I have a simple dataset that I & # x27 ; s entropy pandas... Of entropy for dataset per symbol if the encoding is the information is an in! Entropy means the distribution varies ( peaks and valleys ) the website 7. Points - 1 ) Instances can be used as a part of their legitimate business interest without asking help! And how it works is 0.048 how does the decision tree learned at the first stage of.! 1 ) Instances can be described by attribute-value pairs you can find column & # x27 ; ll the... Symbol if the message discloses the results of the tree is that it is always between 0 and 1 and... See what a decision tree ( classification tree ) in Python the base. This equation is graphically depicted by a symmetric curve as shown below ERROR: column `` a '' not! The following points - 1 ) Instances can be described by attribute-value pairs the calculation entropy. A simple dataset that I & # x27 ; d like to entropy. And this may make in your browser only with your consent, then this is highly. Each attribute is 0.048 tutorial presents a Python Workshop explaining and deriving a decision tree is and how works! Phispy, a bioinformatics tool to find the next node its significance in the project, implemented. Written and tested using Python there is in a nutshell, the impurity or heterogeneity.
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calculate entropy of dataset in python