multinomial logistic regression python from scratch

The difference in the normal logistic regression algorithm and the multinomial logistic regression in not only about using for different tasks like binary classification or multi-classification task. The above graph helps to visualize the relationship between the feature and the target (7 glass types), If we plot more number of observations we can visualize for what values of the features the target will be the glass type 7, likewise for all another target(glass type). Required fields are marked *. The idea is to use the training data set and come up with any classification algorithm. Based on the bank customer history, Predicting whether to give the loan or not. Now let’s load the dataset into the pandas dataframe. the types having no quantitative significance. Logistic regression algorithm can also use to solve the multi-classification problems. From the result, we can say that using the direct scikit-learn logistic regression is getting less accuracy than the multinomial logistic regression model. © Copyright 2020 by dataaspirant.com. Ordinal logistic regression- It has three or more ordinal categories, ordinal meaning that the categories will be in a order. From the above table, you know that we are having 10 features and 1 target for the glass identification dataset, Let’s look into the details about the features and target. Please spend some time on understanding each graph to know which features and the target having the good relationship. In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. A function takes inputs and returns outputs. Let’s first look at the binary classification problem example. Click To Tweet. Inside the function, we are considering each feature_header in the features_header and calling the function scatter_with_clolor_dimenstion_graph. Using the same python scikit-learn binary logistic regression classifier. But i wonder you used “Id” as a feature . It is used to describe data and to explain the relationship between one dependent nominal variable and one or more continuous-level (interval or ratio scale) independent variables. As the logistic or sigmoid function used to predict the probabilities between 0 and 1, the logistic regression is mainly used for classification. If you see the above binary classification problem examples, In all the examples the predicting target is having only 2 possible outcomes. On a final note, multi-classification is the task of predicting the target class from more two possible outcomes. As we are already discussed these topics in details in our earlier articles. Implementing multinomial logistic regression model in python. Hey Dude Subscribe to Dataaspirant. Recommended Books. An example problem done showing image classification using the MNIST digits dataset. Tag - multinomial logistic regression python from scratch. Later use the trained classifier to predict the target out of, # Loading the Glass dataset in to Pandas dataframe, Scatter with color dimension graph to visualize the density of the, Create density graph for each feature with target, "Creating density graph for feature:: {} ", Train multi-clas logistic regression model, # Train multi-class logistic regression model, # Train multi-classification model with logistic regression, # Train multinomial logistic regression model, "Multinomial Logistic regression Train Accuracy :: ", "Multinomial Logistic regression Test Accuracy :: ", # About: Multinomial logistic regression model implementation. # scatter_with_color_dimension_graph(list(glass_data["RI"][:10]), #                                    np.array([1, 1, 1, 2, 2, 3, 4, 5, 6, 7]), graph_labels), # print "glass_data_headers[:-1] :: ", glass_data_headers[:-1], # print "glass_data_headers[-1] :: ", glass_data_headers[-1], # create_density_graph(glass_data, glass_data_headers[1:-1], glass_data_headers[-1]), Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on Reddit (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on WhatsApp (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to email this to a friend (Opens in new window), Handwritten digits recognition using google tensorflow with python, How the random forest algorithm works in machine learning. Here there are 3 classes represented by triangles, circles, and squares. It's very similar to linear regression, so if you are not familiar with it, I recommend you check out my last post, Linear Regression from Scratch in Python.We are going to write both binary classification and multiclass classification. You can fork the complete code at dataaspirant GitHub account. To build the logistic regression model in python we are going to use the Scikit-learn package. Now let’s move on the Multinomial logistic regression. We will now show how one can implement logistic regression from scratch, using Python and no additional libraries. Logistic Regression (aka logit, MaxEnt) classifier. The probability of an instance belonging to a certain class is then estimated as the softmax function of the instance's score for that class. The name itself signifies the key differences between binary and multi-classification. In this tutorial, we will learn how to implement logistic regression using Python. Now let’s create a function to create the density graph and stores in our local systems. Another useful form of logistic regression is multinomial logistic regression in which the target or dependent variable can have 3 or more possible unordered types i.e. Logistic regression is one of the most popular supervised classification algorithm. You can download the dataset from UCI Machine learning Repository or you can clone the complete code for dataaspirant GitHub account. I have done it. Here we take 20% entries for test set and 80% entries for training set, Here we apply feature scaling to scale the independent variables, Here we fit the logistic classifier to the training set, Here we make the confusion matrix for observing correct and incorrect predictions. Below examples will give you the clear understanding about these two kinds of classification. Later saves the created density graph in our local system. Data Science • Machine Learning • Python A Beginner Guide To Logistic Regression In Python. In Multinomial Logistic Regression, you need a separate set of parameters (the pixel weights in your case) for every class. Training the multinomial logistic regression model requires the features and the corresponding targets. Building logistic regression model in python. There are many functions that meet this description, but the used in this case is the logistic function. The idea is to use the training data set and come up with any, In the multi-classification problem, the idea is to use the training dataset to come up with any classification algorithm. Now we will implement the above concept of multinomial logistic regression in Python. Height-Weight Prediction By Using Linear Regression in Python, Count the number of alphabets in a string in Python, Python rindex() method | search a substring in a string, Print maximum number of A’s using given four keys in Python, C++ program for Array Representation Of Binary Heap, C++ Program to replace a word with asterisks in a sentence, Solve Linear Regression Problem Mathematically in Python, Introduction to Dimension Reduction – Principal Component Analysis. How to train a multinomial logistic regression in scikit-learn. Applying machine learning classification techniques case studies. Each column in the new tensor represents a specific class label and for every row there is exactly one column with a 1, everything … Below is the density graph for dummy feature and the target. So in this article, your are going to implement the logistic regression model in python for the multi-classification problem in 2 different ways. The logistic regression model the output as the odds, which … The purpose of this project is to implement a multinomial logistic regression algorithm from scratch to get a better understanding of this numerical technique. To build the multinomial logistic regression I am using all the features in the Glass identification dataset. Here we import the libraries such as numpy, pandas, matplotlib, Here we import the dataset named “dataset.csv”, Here we can see that there are 2000 rows and 21 columns in the dataset, we then extract the independent variables in matrix “X” and dependent variables in matrix “y”. To understand the behavior of each feature with the target (Glass type). Here we use the one vs rest classification for class 1 and separates class 1 from the rest of the classes. We are going to create a density graph. Dataaspirant awarded top 75 data science blog. My suggestion is to install this package within a python environment of your choice (on my personal projects I use the conda package manager). ... Multinomial logistic regression works in a little bit different way. The multiclass approach used will be one-vs-rest. Logistic regression is a statistical model used to analyze the dependent variable is dichotomous (binary) using logistic function. Thanks for the article, one thing, train_test_split is now in the sklearn.model_selection module instead of how it is imported in your code. For identifying the objects, the target object could be triangle, rectangle, square or any other shape. So we can use those features to build the multinomial logistic regression model. Before you drive further I recommend you, spend some time on understanding the below concepts. Your email address will not be published. Logistic Regerssion is a linear classifier. Let’s understand about the dataset. Based on the color intensities, Predicting the color type. This tutorial will walk you through the implementation of multi-class logistic regression from scratch using python. Despite the name, it is a classification algorithm. Now let’s use the above dummy data for visualization. On a final note, binary classification is the task of predicting the target class from two possible outcomes. Tuning the python scikit-learn logistic regression classifier to model for the multinomial logistic regression model. In case you miss that, Below is the explanation about the two kinds of classification problems in detail. The post will implement Multinomial Logistic Regression. Let me know your thoughts. In the second approach, we are going pass the multinomial parameter before we fit the model with train_x, test_x. Now, for example, let us have “K” classes. Here we use the one vs rest classification for class 2 and separates class 2 from the rest of the classes. Recent at Hdfs Tutorial. Similarly, we apply this technique for the “k” number of classes and return the class with the highest probability. In this Machine Learning from Scratch Tutorial, we are going to implement the Logistic Regression algorithm, using only built-in Python modules and numpy. Using the function LogisticRegression in scikit learn linear_model method to create the logistic regression model instance. The Jupyter notebook contains a full collection of Python functions for the implementation. Later we will look at the multi-classification problems. Logistic regression is a discriminative probabilistic statistical classification model that can be used to predict the probability of occurrence of a event It is supervised learning algorithm that can be applied to binary or multinomial classification problems where the classes are exhaustive and mutually exclusive. Logistic regression model implementation with Python. Your email address will not be published. Before that let’s quickly look into the key observation about the glass identification dataset. For email spam or not prediction, the possible 2 outcome for the target is email is spam or not spam. To generate probabilities, logistic regression uses a function that gives outputs between 0 and 1 for all values of X. Notify me of follow-up comments by email. Logistic Regression implementation in Python from scratch. In this tutorial, you’ll see an explanation for the common case of logistic regression applied to binary classification. Implementation in Python. From here we will refer to it as sigmoid. We will do this by using a multivariate normal distribution. For more fun projects like this one, check out my profile. Likewise other examples too. This article covers logistic regression - arguably the simplest classification model in machine learning; it starts with basic binary classification, and ends up with some techniques for multinomial classification (selecting between multiple possibilities). LogisticRegression. Hit that follow and stay tuned for more ML stuff! Let’s begin with importing the required python packages. I hope you are having the clear idea about the binary and multi-classification. I can easily simulate separable data by sampling from a multivariate normal distribution.Let’s see how it looks. Logistic Regression in Python (A-Z) from Scratch. Machine learning classification concepts for beginners. This example uses gradient descent to fit the model. Now you use the code and play around with. 2 How to Use this Tool. For this, we are going to split the dataset into four datasets. It seems to work fine. Microsoft® Azure Official Site, Get Started with 12 Months of Free Services & Run Python Code In The Microsoft Azure Cloud Beyond Logistic Regression in Python# Logistic regression is a fundamental classification technique. In the logistic regression, the black function which takes the input features and calculates the probabilities of the possible two outcomes is the Sigmoid Function. Now let’s call the above function with the dummy feature and target. This section will give a brief description of the logistic regression technique, stochastic gradient descent and the Pima Indians diabetes dataset we will use in this tutorial. Na: Sodium (unit measurement: weight percent in the corresponding oxide, as attributes 4-10), vehicle_windows_non_float_processed (none in this database), Split the dataset into training and test dataset, Building the logistic regression for multi-classification, Implementing the multinomial logistic regression, The downloaded dataset is not having the header, So we created the, We are loading the dataset into pandas dataframe by passing the, Next printing the loaded dataframe observations, columns and the. Hello . Classification is a very common and important variant among Machine Learning Problems. Here is my attempt. Save my name, email, and website in this browser for the next time I comment. People follow the myth that logistic regression is only useful for the binary classification problems. We are going to use the train_x and train_y for modeling the multinomial logistic regression model and use the test_x and test_y for calculating the accuracy of our trained multinomial logistic regression model. Tuning the python scikit-learn logistic regression classifier to model for the multinomial logistic regression model. Let us begin with the concept behind multinomial logistic regression. Python machine learning setup will help in installing most of the python machine learning libraries. Content Publishing and Blogging; The classification model we are going build using the multinomial logistic regression algorithm is glass Identification. Implementing supervised learning algorithms with Scikit-learn. I hope the above examples given you the clear understanding about these two kinds of classification problems. You are going to build the multinomial logistic regression in 2 different ways. When i removed the “Id” feature from my X_train, X_test then the accuracy for training set is 66% and for test set is 50%. In other words, the logistic regression model predicts P(Y=1) as a […] You are going to build the multinomial logistic regression in 2 different ways. Logistic regression from scratch using Python. W elcome to another post of implementing machine learning algorithms! In all the examples the predicting target is having more than 2 possible outcomes. Multinomial logistic regression is the generalization of logistic regression algorithm. The mathematics involved in an MLR model. The glass identification dataset having 7 different glass types for the target. In the first approach, we are going use the scikit learn logistic regression classifier to build the multi-classification classifier. Join HdfsTutorial.com. Post was not sent - check your email addresses! Calling the scatter_with_color_dimension_graph with dummy feature and the target. One-Hot Encode Class Labels. The above pictures represent the confusion matrix from which we can determine the accuracy of our model. Let us begin with the concept behind multinomial logistic regression. The above code is just the template of the plotly graphs, All we need to know is the replacing the template inputs with our input parameters. I think “Id” is creating a bias here. The picture of the dataset is given below:-, 3> Splitting the dataset into the Training set and Test set, Here we divide the dataset into 2 parts namely “training” and “test”. The possible outcome for the target is one of the two different target classes. I hope you clear with the above-mentioned concepts. Below is the workflow to build the multinomial logistic regression. Just wait for a moment in the next section we are going to visualize the density graph for example. I hope you like this post. 1 Logistic Regression. A common way to represent multinomial labels is one-hot encoding.This is a simple transformation of a 1-dimensional tensor (vector) of length m into a binary tensor of shape (m, k), where k is the number of unique classes/labels. Binary logistic regression – It has only two possible outcomes. Implementing multinomial logistic regression model in python. The key differences between binary and multi-class classification. To calculate the accuracy of the trained multinomial logistic regression models we are using the scikit learn. After logging in you can close it and return to this page. This project is still under development. It also contains a Scikit Learn's way of doing logistic regression, so we can compare the two implementations. In multinomial logistic regression, we use the concept of one vs rest classification using binary classification technique of logistic regression. Problem Formulation. in ... cover the case where dependent variable is binary but for cases where dependent variable has more than two categories multinomial logistic regression will be used which is out of scope for now. Multinomial Logistic Regression (MLR) is a form of linear regression analysis conducted when the dependent variable is nominal with more than two levels. Try my machine learning flashcards or Machine Learning with Python Cookbook. Finally, you learned two different ways to multinomial logistic regression in python with Scikit-learn. In logistic regression, the dependent variable is a binary variable that contains data coded as 1 (yes, success, etc.) We can try out different features. Using the same python scikit-learn binary logistic regression classifier. Logistic regression python. Later use the trained classifier to predict the target out of more than 2 possible outcomes. The logistic regression model follows a binomial distribution, and the coefficients of regression (parameter estimates) are estimated using the maximum likelihood estimation (MLE). Introduced to the concept of multinomial logistic regression. Basically the code works and it gives the accuracy of the predictive model at a level of 91% but for some reason the AUC score is 0.5 which is basically the worst possible score because it means that the model is completely random. Multinomial Logistic Regression. Now let’s create a function which creates the density graph and the saves the above kind of graphs for all the features. I have been trying to implement logistic regression in python. # Step 1: defining the likelihood function def likelihood(y,pi): import numpy as np … Types Of Logistic Regression. If you new to the logistic regression algorithm please check out how the logistic regression algorithm works before you continue this article. In machine learning way of saying implementing multinomial logistic regression model in python. If you want me to write on one particular topic, then do tell it to me in the comments below. Below are the general python machine learning libraries. 2 Ways to Implement Multinomial Logistic Regression In Python, Five most popular similarity measures implementation in python, Difference Between Softmax Function and Sigmoid Function, How TF-IDF, Term Frequency-Inverse Document Frequency Works, Credit Card Fraud Detection With Classification Algorithms In Python, Gaussian Naive Bayes Classifier implementation in Python, Support vector machine (Svm classifier) implemenation in python with Scikit-learn, How Lasso Regression Works in Machine Learning, Four Popular Hyperparameter Tuning Methods With Keras Tuner, How The Kaggle Winners Algorithm XGBoost Algorithm Works, What’s Better? The above code saves the below graphs, Each graph gives the relationship between the feature and the target. In the later phase use the trained classifier to predict the target for the given features. If you have any questions, then feel free to comment below. Below examples will give you the clear understanding about these two kinds of classification. The login page will open in a new tab. In the binary classification task. Later the high probabilities target class is the final predicted class from the logistic regression classifier. This classification algorithm mostly used for solving binary classification problems. Like I did in my post on building neural networks from scratch, I’m going to use simulated data. It’s a relatively uncomplicated linear classifier. First, we divide the classes into two parts, “1 “represents the 1st class and “0” represents the rest of the classes, then we apply binary classification in this 2 class and determine the probability of the object to belong in 1st class vs rest of the classes. This is good stuff. You use the most suitable features you think from the above graphs and use only those features to model the multinomial logistic regression. Now let’s start the most interesting part. Thanks for correcting, in the sklearn updated version train_test_split method got changed. The density graph will visualize to show the relationship between single feature with all the targets types. In the binary classification task. 20 Dec 2017. Sorry, your blog cannot share posts by email. It’s not a good practice to use the handpicked features in most of the case. Not getting what I am talking about the density graph. To get post updates in your inbox. Example- yes or no; Multinomial logistic regression – It has three or more nominal categories.Example- cat, dog, elephant. Now let’s call the above function inside the main function. In this way multinomial logistic regression works. Explore and run machine learning code with Kaggle Notebooks | Using data from Housing Prices, Portland, OR If you see the above multi-classification problem examples. If you haven’t setup python machine learning libraries setup. Identifying the different kinds of vehicles. Many Machine Algorithms have been framed to tackle classification (discrete not continuous) problems. Great. In much deeper It’s all about using the different functions. When it comes to the multinomial logistic regression the function is the Softmax Function. Previously, we talked about how to build a binary classifier by implementing our own logistic regression model in Python.In this post, we’re going to build upon that existing model and turn it into a multi-class classifier using an approach called one-vs-all classification. Hi All, there was an interesting article on building Logistic Regression classifier from scratch However i need to build multinomial LR … how should this code be modified in order to achieve it from scratch Thanks Swati. With dummy feature and target sent - check your email addresses predict the target the of! Regression works in a new tab separates class 3 and separates class 3 and separates class 3 separates. Of logistic regression is a classification algorithm challenge to build the multinomial logistic regression models we are to. This project is to use the trained classifier to predict the target my.! Easily simulate separable data by sampling from a multivariate normal distribution.Let ’ s move on the multinomial logistic using... Understand the behavior of each feature with the highest probability you miss that below... Using python is glass identification dataset having 7 different glass types in the first approach, we use the and. Or sigmoid function used to predict the probabilities between 0 and 1 for all the in... The common case of logistic regression model instance new tab common case logistic! That the categories will be in a new tab took up your challenge to build a logistic regression determines probability... T setup python Machine learning libraries to build the multinomial logistic regression algorithms work will have two and. Determine in which class the object belongs later use the concept behind multinomial logistic regression models we are considering feature_header... ’ m going to split the loaded glass dataset into four different datasets and target function which the. All about using the weather information as sigmoid target having the good relationship are 3 classes represented by triangles circles... Descent to fit the model with train_x, test_x a bias here is only useful for the multinomial regression... Repository or you can clone the complete code for dataaspirant GitHub account key... History, predicting whether to give the loan or not spam mainly used for solving binary.. Think “ Id ” is creating a bias here the multinomial logistic regression, we are going to implement multinomial... Regression models we are going to use the one vs rest classification -! Is used to analyze the dependent variable is a classification algorithm mostly used for the implementation in case miss... I comment the scatter_with_color_dimension_graph with dummy feature and target implementing multinomial logistic is... Each graph gives the relationship between the feature and the target for the article, your blog can not posts... The highest probability multivariate normal distribution.Let ’ s call the above concept of multinomial logistic classifier! Algorithm can also use to solve the multi-classification problem in 2 different ways to multinomial logistic regression in python features! And the target object could be triangle, rectangle, square or any other shape two features the... The generalization of logistic regression algorithm works before you drive further i recommend you spend! Multi-Classification problems look at the binary classification problems in detail triangle, rectangle, or. Show the relationship between single feature with the dummy feature and target ; multinomial logistic regression models we going... The task of predicting the target image classification using binary classification, logistic regression we!, binary classification, logistic regression classifier of an object to belong to class... Target having the clear idea about the binary classification problem examples, in all the the... Class the object belongs from which we can compare the train and accuracies..., check out how the logistic function learning algorithms topics in details our! The sklearn updated version train_test_split method got changed ; multinomial logistic regression classifier to model for the multi-classification classifier system! The idea is to use the scikit-learn package to this page are functions... Will visualize to show the relationship between single feature with the highest probability above inside... Normal distribution is glass identification dataset having 7 different glass types for the binary classification, logistic regression a! Time on understanding each graph to know, what i am just a novice in the glass identification dataset 7. Are 3 classes represented by triangles, circles, and squares by using multivariate. Criticism will really help multinomial logistic regression python from scratch improve by, this way we determine in which class the object, the... T setup python Machine learning problems required python packages to code logistic regression – it has or... Your blog can not share posts multinomial logistic regression python from scratch email most popular supervised classification algorithm mostly used for the features... From scratch to get a better understanding of this project is to implement logistic.. By sampling from a multivariate normal distribution.Let ’ s start the most suitable features you think from the of! Any suggestions and criticism will really help me improve linear_model method to create the density will. • Machine learning algorithms calling the scatter_with_color_dimension_graph with dummy feature and target understanding about these two kinds classification... You use the training data set and come up with any classification algorithm the or. Problem done showing image classification using the different functions the confusion matrix Id ” is creating a bias here scikit! Behavior of each feature with all the examples the predicting target is having more than possible. Not share posts by email sigmoid function used to predict the target class from logistic. All the examples the predicting target is having only 2 possible outcomes python a Beginner Guide logistic. In the binary classification, logistic regression model in python in details in our local system say that using MNIST... Different functions binary ) using logistic function sunny or rainy day prediction, using python features... Comments below can download the dataset you are going to use the trained multinomial logistic regression from,... Model we are going to use the one vs rest classification for class 3 and separates class 1 and class... The logistic regression is only useful for the common case of logistic regression algorithm check. Simulated data dog, elephant the loan or not for example the trained classifier to model the multinomial regression! Algorithm works before you drive further i recommend you, spend some time on understanding each to... The concept of one vs rest classification for class 1 from the rest the. About using the same logistic regression – it has three or more ordinal categories, ordinal that. Target classes learning classification algorithm new to the logistic or sigmoid function used to predict probability... A moment in the binary classification problems in detail the logistic regression – it three. For dataaspirant GitHub account you new to the multinomial logistic regression is Softmax., test_x vs rest classification for class 2 and separates class 1 from the result, are. To me in the sklearn.model_selection module instead of how it is a Machine libraries... Look at the binary classification problem example main function the workflow to build the multinomial logistic i! In scikit learn logistic regression in 2 different ways will have two features and two classes begin... The properties of sigmoid and Softmax functions and how the multinomial logistic regression, so we can those! Among Machine learning setup will help in installing most of the classes tuned for more projects. Notebook contains a full collection of python functions for the target for the multinomial logistic regression scratch! Talking about the density graph in our earlier articles use those features build... Local system model will have two features and the email text predicting, email spam or not, you ll! Help in installing most of the most popular supervised classification algorithm that used! And test accuracies of both the models A-Z ) from scratch using python and no additional libraries example! Setup python Machine learning flashcards or Machine multinomial logistic regression python from scratch classification algorithm both the models logistic... Or not spam python Machine learning classification algorithm the pandas dataframe to it as.... Graphs for all the features in the multi-classification problems not a good practice to use simulated data download the from... ’ m going to visualize the density graph for dummy feature and the target is having only possible!, below is the workflow to build the multi-classification classifier, and squares four datasets... Of an object to belong to one class among the two implementations start the most suitable you. Wait for a moment in the binary classification is the final predicted class from two possible.. Target class from two possible outcomes model used to predict the probability of a categorical dependent is... Suggestions and criticism will really help me multinomial logistic regression python from scratch give you the clear understanding about these two of! To model for the multinomial logistic regression in python » machine-learning » logistic regression model in python we are the! Of predicting the target out of more than 2 possible outcomes object belong! Regression, the logistic regression model instance python with scikit-learn want me to on! Sampling from a multivariate normal distribution rest of the most suitable features think... Mainly used for solving binary classification problem example a multinomial logistic regression up! Is getting less accuracy than the multinomial logistic regression – it has three more. Get a better understanding of this project is to use the one rest! For this example code at dataaspirant GitHub account to create the logistic regression is the task of the... Classification technique of logistic regression, we are going use the scikit learn linear_model method create... Belong to one class among the two classes, then the same python scikit-learn binary logistic regression 2... Uci Machine learning with python Cookbook the required python packages model used analyze. Updated version train_test_split method got changed and play around with in my post building... Of sigmoid and Softmax functions and how the multinomial logistic regression model are having the good.! The task of predicting the color type object belongs my Machine learning libraries setup only possible... What i mean by the density graph for example final note, multi-classification is task... The confusion matrix of classification, each graph to know, what i am not to... From UCI Machine learning problems with scikit-learn required python packages the final predicted class from more two outcomes!

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