Support Vector Machine

Support Vector Machines are a class of learning algorithms initially defined for discrimination, that is, predicting a binary qualitative variable. They were then generalized to the forecast of a quantitative variable. They are based on the search for the optimal margin hyperplane which, where possible, classifies or separates the data correctly while being as far as possible from all observations.

Given a set of points, a subset of a larger set (space), in which each of them belongs to one of two possible categories, an algorithm based on SVM constructs a model capable of predicting whether a new point (with unknown category) belongs to one category or the other. As with most supervised classification methods, input data (points) are viewed as a p-dimensional vector.

The SVM looks for a hyperplane that optimally separates the points of one class from the other, which could have been previously projected into a space of superior dimensionality.

This concept of « optimal separation » is where the fundamental characteristic of SVM resides: this type of algorithm seeks the hyperplane that has the maximum distance (margin) with the points that are closest to it. This is also why SVMs are sometimes known as maximum margin classifiers. In this way, the points of the vector that are labeled with a category will be on one side of the hyperplane and the cases that are in the other category will be on the other side.

The SVM algorithms belong to the family of linear classifiers. They can also be considered a special case of Tikhonov regularization. Models based on SVMs are closely related to neural networks. Using a kernel function, they result in an alternative training method for polynomial classifiers, radial base functions and multilayer perceptron.

The kernel trick is commonly used with a linear classifier (as an SVM) in order to classify non linearly distributed data. The idea is to transform the representation space of the input data into a larger dimension space, where a linear classifier can be used and obtain good performance. Linear discrimination in the large space (also called redescription space) is equivalent to nonlinear discrimination in the original space. There are multiple different kernel functions (sigmoid, polynomial, laplacian, etc) among which the most used one is the RBF gaussian function. In the following use case, we use a gaussian RBF kernel function SVM to build a classifier for detecting a human presence in a room.

USE CASE : ROOM OCCUPANCY DETECTION

In this use case, the goal is to build a model that predicts the presence of an individual in a room according to the temperature, humidity and CO2 levels recorded by sensors in the room. The model is built by training a SVM classifier on a dataset of 9753 rows providing the occupancy status of the room (1 iff human presence, otherwise 0) according to the room temperature (ranging from 19.5 to 24.39 C°), the humidity ratio (ranging from 00.33% to 0.58%) and the CO2 level (ranging 484.67 from to 2076.5). Here follows the first 40 rows of the dataset :

Dataset of individual presence in a room according to levels of temperature, CO2 and humidity.

Dataset of individual presence in a room according to levels of temperature, CO2 and humidity.

And here the full dataset in CSV format :

Temperature,CO2,HumidityRatio,Occupancy
21.76,1029.666667,0.005021011,1
21.79,1000,0.005008581,1
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21.89,1060.5,0.005137857,1
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