Metrics To Evaluate Machine Learning Algorithms in Python

The metrics that you choose to evaluate your machine learning algorithms are very important.

Choice of metrics influences how the performance of machine learning algorithms is measured and compared. They influence how you weight the importance of different characteristics in the results and your ultimate choice of which algorithm to choose.

In this post, you will discover how to select and use different machine learning performance metrics in Python with scikit-learn.

About the Recipes

Various different machine learning evaluation metrics are demonstrated in this post using small code recipes in Python and scikit-learn.

Each recipe is designed to be standalone so that you can copy-and-paste it into your project and use it immediately.

Metrics are demonstrated for both classification and regression type machine learning problems.

• For classification metrics, the Pima Indians onset of diabetes dataset is used as demonstration. This is a binary classification problem where all of the input variables are numeric (update: download from here).
• For regression metrics, the Boston House Price dataset is used as demonstration. this is a regression problem where all of the input variables are also numeric (update: download data from here).

In each recipe, the dataset is downloaded directly.

All recipes evaluate the same algorithms, Logistic Regression for classification and Linear Regression for the regression problems. A 10-fold cross-validation test harness is used to demonstrate each metric, because this is the most likely scenario where you will be employing different algorithm evaluation metrics.

A caveat in these recipes is the cross_val_score function used to report the performance in each recipe.It does allow the use of different scoring metrics that will be discussed, but all scores are reported so that they can be sorted in ascending order (largest score is best).

Some evaluation metrics (like mean squared error) are naturally descending scores (the smallest score is best) and as such are reported as negative by the cross_val_score() function. This is important to note, because some scores will be reported as negative that by definition can never be negative.

You can learn more about machine learning algorithm performance metrics supported by scikit-learn on the page Model evaluation: quantifying the quality of predictions.

Let’s get on with the evaluation metrics.

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Classification Metrics

Classification problems are perhaps the most common type of machine learning problem and as such there are a myriad of metrics that can be used to evaluate predictions for these problems.

In this section we will review how to use the following metrics:

1. Classification Accuracy.
2. Log Loss.
3. Area Under ROC Curve.
4. Confusion Matrix.
5. Classification Report.

1. Classification Accuracy

Classification accuracy is the number of correct predictions made as a ratio of all predictions made.

This is the most common evaluation metric for classification problems, it is also the most misused. It is really only suitable when there are an equal number of observations in each class (which is rarely the case) and that all predictions and prediction errors are equally important, which is often not the case.

Below is an example of calculating classification accuracy.

# Cross Validation Classification Accuracy import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LogisticRegression(solver='liblinear') scoring = 'accuracy' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("Accuracy: %.3f (%.3f)" % (results.mean(), results.std()))

You can see that the ratio is reported.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

This can be converted into a percentage by multiplying the value by 100, giving an accuracy score of approximately 77% accurate.

Accuracy: 0.770 (0.048)

2. Log Loss

Logistic loss (or log loss) is a performance metric for evaluating the predictions of probabilities of membership to a given class.

The scalar probability between 0 and 1 can be seen as a measure of confidence for a prediction by an algorithm. Predictions that are correct or incorrect are rewarded or punished proportionally to the confidence of the prediction.

For more on log loss and it’s relationship to cross-entropy, see the tutorial:

• A Gentle Introduction to Cross-Entropy for Machine Learning

Below is an example of calculating log loss for Logistic regression predictions on the Pima Indians onset of diabetes dataset.

# Cross Validation Classification LogLoss import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LogisticRegression(solver='liblinear') scoring = 'neg_log_loss' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("Logloss: %.3f (%.3f)" % (results.mean(), results.std()))

Smaller log loss is better with 0 representing a perfect log loss.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

As mentioned above, the measure is inverted to be ascending when using the cross_val_score() function.

Logloss: -0.493 (0.047)

3. Area Under ROC Curve

Area Under ROC Curve (or ROC AUC for short) is a performance metric for binary classification problems.

The AUC represents a model’s ability to discriminate between positive and negative classes. An area of 1.0 represents a model that made all predictions perfectly. An area of 0.5 represents a model as good as random.

A ROC Curve is a plot of the true positive rate and the false positive rate for a given set of probability predictions at different thresholds used to map the probabilities to class labels. The area under the curve is then the approximate integral under the ROC Curve.

For more on ROC Curves and ROC AUC, see the tutorial:

• How to Use ROC Curves and Precision-Recall Curves for Classification in Python

The example below provides a demonstration of calculating AUC.

# Cross Validation Classification ROC AUC import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LogisticRegression(solver='liblinear') scoring = 'roc_auc' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("AUC: %.3f (%.3f)" % (results.mean(), results.std()))

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

You can see the the AUC is relatively close to 1 and greater than 0.5, suggesting some skill in the predictions.

AUC: 0.824 (0.041)

4. Confusion Matrix

The confusion matrix is a handy presentation of the accuracy of a model with two or more classes.

The table presents predictions on the x-axis and accuracy outcomes on the y-axis. The cells of the table are the number of predictions made by a machine learning algorithm.

For example, a machine learning algorithm can predict 0 or 1 and each prediction may actually have been a 0 or 1. Predictions for 0 that were actually 0 appear in the cell for prediction=0 and actual=0, whereas predictions for 0 that were actually 1 appear in the cell for prediction = 0 and actual=1. And so on.

For more on the confusion matrix, see this tutorial:

• What is a Confusion Matrix in Machine Learning

Below is an example of calculating a confusion matrix for a set of prediction by a model on a test set.

# Cross Validation Classification Confusion Matrix import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import confusion_matrix url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] test_size = 0.33 X_train, X_test, Y_train, Y_test = model_selection.train_test_split(X, Y, test_size=test_size, random_state=7) model = LogisticRegression(solver='liblinear') model.fit(X_train, Y_train) predicted = model.predict(X_test) matrix = confusion_matrix(Y_test, predicted) print(matrix)

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Although the array is printed without headings, you can see that the majority of the predictions fall on the diagonal line of the matrix (which are correct predictions).

[[141  21] [ 41  51]]

5. Classification Report

Scikit-learn does provide a convenience report when working on classification problems to give you a quick idea of the accuracy of a model using a number of measures.

The classification_report() function displays the precision, recall, f1-score and support for each class.

The example below demonstrates the report on the binary classification problem.

# Cross Validation Classification Report import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import classification_report url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] test_size = 0.33 X_train, X_test, Y_train, Y_test = model_selection.train_test_split(X, Y, test_size=test_size, random_state=7) model = LogisticRegression(solver='liblinear') model.fit(X_train, Y_train) predicted = model.predict(X_test) report = classification_report(Y_test, predicted) print(report)

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

You can see good prediction and recall for the algorithm.

precision    recall  f1-score   support           0.0       0.77      0.87      0.82       162         1.0       0.71      0.55      0.62        92   avg / total       0.75      0.76      0.75       254

Regression Metrics

In this section will review 3 of the most common metrics for evaluating predictions on regression machine learning problems:

1. Mean Absolute Error.
2. Mean Squared Error.
3. R^2.

1. Mean Absolute Error

The Mean Absolute Error (or MAE) is the average of the absolute differences between predictions and actual values. It gives an idea of how wrong the predictions were.

The measure gives an idea of the magnitude of the error, but no idea of the direction (e.g. over or under predicting).

You can learn more about Mean Absolute error on Wikipedia.

The example below demonstrates calculating mean absolute error on the Boston house price dataset.

# Cross Validation Regression MAE import pandas from sklearn import model_selection from sklearn.linear_model import LinearRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/housing.data" names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV'] dataframe = pandas.read_csv(url, delim_whitespace=True, names=names) array = dataframe.values X = array[:,0:13] Y = array[:,13] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LinearRegression() scoring = 'neg_mean_absolute_error' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("MAE: %.3f (%.3f)" % (results.mean(), results.std()))

A value of 0 indicates no error or perfect predictions.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Like logloss, this metric is inverted by the cross_val_score() function.

MAE: -4.005 (2.084)

2. Mean Squared Error

The Mean Squared Error (or MSE) is much like the mean absolute error in that it provides a gross idea of the magnitude of error.

Taking the square root of the mean squared error converts the units back to the original units of the output variable and can be meaningful for description and presentation. This is called the Root Mean Squared Error (or RMSE).

You can learn more about Mean Squared Error on Wikipedia.

The example below provides a demonstration of calculating mean squared error.

# Cross Validation Regression MSE import pandas from sklearn import model_selection from sklearn.linear_model import LinearRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/housing.data" names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV'] dataframe = pandas.read_csv(url, delim_whitespace=True, names=names) array = dataframe.values X = array[:,0:13] Y = array[:,13] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LinearRegression() scoring = 'neg_mean_squared_error' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("MSE: %.3f (%.3f)" % (results.mean(), results.std()))

This metric too is inverted so that the results are increasing.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Remember to take the absolute value before taking the square root if you are interested in calculating the RMSE.

MSE: -34.705 (45.574)

3. R^2 Metric

The R^2 (or R Squared) metric provides an indication of the goodness of fit of a set of predictions to the actual values. In statistical literature, this measure is called the coefficient of determination.

This is a value between 0 and 1 for no-fit and perfect fit respectively.

You can learn more about the Coefficient of determination article on Wikipedia.

The example below provides a demonstration of calculating the mean R^2 for a set of predictions.

# Cross Validation Regression R^2 import pandas from sklearn import model_selection from sklearn.linear_model import LinearRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/housing.data" names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV'] dataframe = pandas.read_csv(url, delim_whitespace=True, names=names) array = dataframe.values X = array[:,0:13] Y = array[:,13] kfold = model_selection.KFold(n_splits=10, random_state=7, shuffle=True) model = LinearRegression() scoring = 'r2' results = model_selection.cross_val_score(model, X, Y, cv=kfold, scoring=scoring) print("R^2: %.3f (%.3f)" % (results.mean(), results.std()))

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

You can see that the predictions have a poor fit to the actual values with a value close to zero and less than 0.5.

R^2: 0.203 (0.595)

Summary

In this post, you discovered metrics that you can use to evaluate your machine learning algorithms.

You learned about 3 classification metrics:

• Accuracy.
• Log Loss.
• Area Under ROC Curve.

Also 2 convenience methods for classification prediction results:

• Confusion Matrix.
• Classification Report.

And 3 regression metrics:

• Mean Absolute Error.
• Mean Squared Error.
• R^2.

Do you have any questions about metrics for evaluating machine learning algorithms or this post? Ask your question in the comments and I will do my best to answer it.

Spot-Check Classification Machine Learning Algorithms in Python with scikit-learn

 Spot-checking is a way of discovering which algorithms perform well on your machine learning problem.

You cannot know which algorithms are best suited to your problem before hand. You must trial a number of methods and focus attention on those that prove themselves the most promising.

In this post you will discover 6 machine learning algorithms that you can use when spot checking your classification problem in Python with scikit-learn.

Algorithm Spot Checking

You cannot know which algorithm will work best on your dataset before hand.

You must use trial and error to discover a short list of algorithms that do well on your problem that you can then double down on and tune further. I call this process spot checking.

The question is not:

What algorithm should I use on my dataset?

Instead it is:

What algorithms should I spot check on my dataset?

You can guess at what algorithms might do well on your dataset, and this can be a good starting point.

I recommend trying a mixture of algorithms and see what is good at picking out the structure in your data.

• Try a mixture of algorithm representations (e.g. instances and trees).
• Try a mixture of learning algorithms (e.g. different algorithms for learning the same type of representation).
• Try a mixture of modeling types (e.g. linear and nonlinear functions or parametric and nonparametric).

Let’s get specific. In the next section, we will look at algorithms that you can use to spot check on your next machine learning project in Python.

Algorithms Overview

We are going to take a look at 6 classification algorithms that you can spot check on your dataset.

2 Linear Machine Learning Algorithms:

1. Logistic Regression
2. Linear Discriminant Analysis

4 Nonlinear Machine Learning Algorithms:

1. K-Nearest Neighbors
2. Naive Bayes
3. Classification and Regression Trees
4. Support Vector Machines

Each recipe is demonstrated on the Pima Indians onset of Diabetes dataset. This is a binary classification problem where all attributes are numeric.

You can learn more about the dataset here:

• Dataset File.
• Dataset Details

Each recipe is complete and standalone. This means that you can copy and paste it into your own project and start using it immediately.

A test harness using 10-fold cross validation is used to demonstrate how to spot check each machine learning algorithm and mean accuracy measures are used to indicate algorithm performance.

The recipes assume that you know about each machine learning algorithm and how to use them. We will not go into the API or parameterization of each algorithm.

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Linear Machine Learning Algorithms

This section demonstrates minimal recipes for how to use two linear machine learning algorithms: logistic regression and linear discriminant analysis.

1. Logistic Regression

Logistic regression assumes a Gaussian distribution for the numeric input variables and can model binary classification problems.

You can construct a logistic regression model using the LogisticRegression class.

# Logistic Regression Classification import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] seed = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = LogisticRegression() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.76951469583

2. Linear Discriminant Analysis

Linear Discriminant Analysis or LDA is a statistical technique for binary and multi-class classification. It too assumes a Gaussian distribution for the numerical input variables.

You can construct an LDA model using the LinearDiscriminantAnalysis class.

# LDA Classification import pandas from sklearn import model_selection from sklearn.discriminant_analysis import LinearDiscriminantAnalysis url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] seed = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = LinearDiscriminantAnalysis() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.773462064252

Nonlinear Machine Learning Algorithms

This section demonstrates minimal recipes for how to use 4 nonlinear machine learning algorithms.

1. K-Nearest Neighbors

K-Nearest Neighbors (or KNN) uses a distance metric to find the K most similar instances in the training data for a new instance and takes the mean outcome of the neighbors as the prediction.

You can construct a KNN model using the KNeighborsClassifier class.

# KNN Classification import pandas from sklearn import model_selection from sklearn.neighbors import KNeighborsClassifier url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] random_state = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = KNeighborsClassifier() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.726555023923

2. Naive Bayes

Naive Bayes calculates the probability of each class and the conditional probability of each class given each input value. These probabilities are estimated for new data and multiplied together, assuming that they are all independent (a simple or naive assumption).

When working with real-valued data, a Gaussian distribution is assumed to easily estimate the probabilities for input variables using the Gaussian Probability Density Function.

You can construct a Naive Bayes model using the GaussianNB class.

# Gaussian Naive Bayes Classification import pandas from sklearn import model_selection from sklearn.naive_bayes import GaussianNB url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] seed = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = GaussianNB() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.75517771702

3. Classification and Regression Trees

Classification and Regression Trees (CART or just decision trees) construct a binary tree from the training data. Split points are chosen greedily by evaluating each attribute and each value of each attribute in the training data in order to minimize a cost function (like Gini).

You can construct a CART model using the DecisionTreeClassifier class.

# CART Classification import pandas from sklearn import model_selection from sklearn.tree import DecisionTreeClassifier url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] seed = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = DecisionTreeClassifier() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.692600820232

4. Support Vector Machines

Support Vector Machines (or SVM) seek a line that best separates two classes. Those data instances that are closest to the line that best separates the classes are called support vectors and influence where the line is placed. SVM has been extended to support multiple classes.

Of particular importance is the use of different kernel functions via the kernel parameter. A powerful Radial Basis Function is used by default.

You can construct an SVM model using the SVC class.

# SVM Classification import pandas from sklearn import model_selection from sklearn.svm import SVC url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" names = ['preg', 'plas', 'pres', 'skin', 'test', 'mass', 'pedi', 'age', 'class'] dataframe = pandas.read_csv(url, names=names) array = dataframe.values X = array[:,0:8] Y = array[:,8] seed = 7 kfold = model_selection.KFold(n_splits=10, random_state=seed) model = SVC() results = model_selection.cross_val_score(model, X, Y, cv=kfold) print(results.mean())

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

Running the example prints the mean estimated accuracy.

0.651025290499

Summary

In this post you discovered 6 machine learning algorithms that you can use to spot-check on your classification problem in Python using scikit-learn.

Specifically, you learned how to spot-check:

2 Linear Machine Learning Algorithms

1. Logistic Regression
2. Linear Discriminant Analysis

4 Nonlinear Machine Learning Algorithms

1. K-Nearest Neighbors
2. Naive Bayes
3. Classification and Regression Trees
4. Support Vector Machines

Do you have any questions about spot checking machine learning algorithms or about this post? Ask your questions in the comments section below and I will do my best to answer them.