## Developer Guide and Reference

• 2021.2
• 03/26/2021
• Public Content
Contents

# Support Vector Machine Classifier (SVM)

Support Vector Machine (SVM) classification is among popular classification algorithms. It belongs to a family of generalized linear classification problems.
 Operation Computational methods Programming Interface

## Mathematical formulation

Training
Given
n
feature vectors of size
p
and a vector of class labels , where describes the class to which the feature vector belongs, the problem is to build a two-class Support Vector Machine (SVM) classifier.
The SVM model is trained using the Sequential minimal optimization (SMO) method [Boser92]} for reduced to the solution of the quadratic optimization problem
with ,
i = 1, …, n
, , where
e
is the vector of ones,
C
is the upper bound of the coordinates of the vector ,
Q
is a symmetric matrix of size with , and is a kernel function.
Working subset of α updated on each iteration of the algorithm is based on the Working Set Selection (WSS) 3 scheme [Fan05]. The scheme can be optimized using one of these techniques or both:
• Cache
: the implementation can allocate a predefined amount of memory to store intermediate results of the kernel computation.
• Shrinking
: the implementation can try to decrease the amount of kernel related computations (see [Joachims99]).
The solution of the problem defines the separating hyperplane and corresponding decision function , where only those that correspond to non-zero appear in the sum, and
b
is a bias. Each non-zero is called a classification coefficient and the corresponding is called a support vector.
Training method:
smo
In
smo
training method, all vectors from the training dataset are used for each iteration.
Training method:
thunder
In
thunder
training method, the algorithm iteratively solves the convex optimization problem with the linear constraints by selecting the fixed set of active constrains (working set) and applying Sequential Minimal Optimization (SMO) solver to the selected subproblem. The description of this method is given in Algorithm [Wen2018].
Inference methods:
smo
and
thunder
smo
and
thunder
inference methods perform prediction in the same way:
Given the SVM classifier and
r
feature vectors , the problem is to calculate the signed value of the decision function , . The sign of the value defines the class of the feature vector, and the absolute value of the function is a multiple of the distance between the feature vector and the separating hyperplane.

## Examples

oneAPI DPC++
Batch Processing:
oneAPI C++
Batch Processing:
Python* with DPC++ support
Batch Processing:

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.