Support vectors refer to the training of data concentrations from the nearest sample point of the classification super plane, which directly determines the location of the classification's decision boundary. According to the google developer machine learning glossary released in 2017, the support vector maximizes the margin between the positive and negative classes by mapping the input data vector to a higher dimension。
The non-support vector does not have an impact on the final form of the classification boundary, so only the supporting vector parameters will need to be retained after model training has been completed. This feature significantly reduces the computational complexity of algorithms at the projection stage。
Algorithmic principles
In supporting the realization of vectors, algorithms identify support vectors by:
1.
Map raw data into high-dimensional feature space to solve linear inseparability
2.
Construct cams to solve the optimal separation super plane
3.
Screening of training samples at the interval boundary as a support vector
The introduction of nuclear methods allows algorithms to process non-linear disaggregated data. Calculating the internality of high-dimensional space through nuclear functions in order to avoid the problem of the dimension disaster caused by a visible mapping. This process reinforces the ability to demonstrate vector support in complex classification missions。
Math foundation
The spacing maximise principle is the mathematical core that supports vector selection. (xi, yi)}$us$ \min{w, b}\frac}2+c\sum{i}=Xi i$, of which $w is the hyper plane vector, $\Xi i is a loose variable and $c is a punitive parameter. The formula is solved by the lagrands multiplier method, which is ultimately linked only to the non-zero value of the lagrands multiplier corresponding to the support vector。
The application of the hinge loss function ensures that the algorithm presents a non-linear relationship between punishment for classification error and spacing: $$l(y i) = \\max(0, 1 - y i (w\cdot x i + b)) $ $$, which does not allow the correct classification sample far from the decision-making boundary to contribute to the updating of model parameters。
Physical interpretation of the report
Within the framework of statistical learning theory, the physical characteristics of supporting vectors are:
Visibility analysis of characterization space shows that support vectors tend to be concentrated in transition areas with changes in class density, and these sample points carry key scaling information on data distribution。
Application and development bulletin
Machine learning methods based on support vectors have important applications in the following areas:
As in-depth learning develops, supporting the integration of vector machines and neural networks has resulted in new hybrid model structures. By supporting vector-bound decision-making boundaries of the neural network, such models increase interpretability while maintaining the expression of deep characteristics。
