Hakan Çelik· Hakan Çelik · OpenCV / Machine Learning · 2 dk okuma
Understanding SVM
Understanding SVM
Goal
In this chapter we will see an intuitive understanding of SVM.
Theory
Linearly Separable Data
Consider an image below which has two types of data, red and blue. We find a line, f(x) = ax₁ + bx₂ + c which divides both the data to two regions. When we get a new test_data X, just substitute it in f(X). If f(X) > 0, it belongs to blue group, else it belongs to red group. We can call this line as Decision Boundary.
So what SVM does is to find a straight line (or hyperplane) with largest minimum distance to the training samples. These points closest to the decision boundary are called Support Vectors and the lines passing through them are called Support Planes.
Non-Linearly Separable Data
Consider some data which can’t be divided into two with a straight line. For example, one-dimensional data where ‘X’ is at -3 & +3 and ‘O’ is at -1 & +1. If we map this data set with a function f(x) = x², we get ‘X’ at 9 and ‘O’ at 1 which are linear separable.
In general, it is possible to map points in a d-dimensional space to some D-dimensional space (D > d) to check the possibility of linear separability. The kernel function helps compute the dot product in the high-dimensional (kernel) space by performing computations in the low-dimensional input (feature) space.
SVM in OpenCV
import cv2 as cv
import numpy as np
# Training data
labels = np.array([1, 1, -1, -1])
trainingData = np.matrix([[501, 10], [255, 10], [501, 255], [10, 501]], dtype=np.float32)
# Create SVM and train
svm = cv.ml.SVM_create()
svm.setType(cv.ml.SVM_C_SVC)
svm.setKernel(cv.ml.SVM_LINEAR)
svm.setTermCriteria((cv.TERM_CRITERIA_MAX_ITER, 100, 1e-6))
svm.train(trainingData, cv.ml.ROW_SAMPLE, labels)
