Efficient $\chi ^{2}$ Kernel Linearization via Random Feature Maps.

Area of Science:

• Machine Learning
• Computer Vision

Background:

• Explicit feature mapping linearizes additive kernels like the chi-squared (χ²) kernel for Support Vector Machines (SVMs).
• High-dimensional feature mapping can cause computational challenges in large-scale SVM training.

Purpose of the Study:

• To develop an efficient method for approximating the χ² kernel linearization using random feature maps.
• To address computational challenges in large-scale χ² kernel SVMs.

Main Methods:

• Utilized sparse random projection to reduce feature map dimensionality.
• Preserved kernel approximation capability while reducing computational cost.
• Extended the method to handle χ² multiple kernel SVMs.

Main Results:

• Achieved significant speed-up in training χ² kernel SVMs.
• Maintained high testing accuracy comparable to exact methods.
• Demonstrated effectiveness on large-scale image classification tasks.

Conclusions:

• The proposed random feature map method offers an efficient and accurate approach for large-scale χ² kernel SVM learning.
• This technique effectively balances computational efficiency and predictive performance.