1. Threshold randomly, not friendly when new observation on the threshold.
2. Focus on the edge of the cluster, use the midpoint between them as threshold. Not friendly when the outlier observation is close to the opposite cluster.
3. Allow misclassifications. Using cross-validation to determine how many misclassifications and observations to allow inside of Soft Margin to get the best classification.
4. When the data are 3 dimensional, the support vector classifier is a 2-dimensional plane. In mathematical jargon, a plane is a "flat affine 2-Dimensional subspace". When the data are in 4 or more dimensions, the Support Vector Classifier is a hyperplane. In mathematical jargon, a hyperplane is a "flat affine subspace".
5. Features of Support Vector Classifiers: handle outliers and overlapping classifications
6. Features of Support Vector Machines: handle tons of overlap.
Start with data in a relatively low dimension, move the data into a higher dimension(eg: square the data), find the support vector classifier that separates the higher dimensional data into two groups.
7. How do we decide how to transform the data? Kernel function
Terminology
Margin: The shortest distance between the observations and the threshold.
Maximal Margin Classifier: The largest distance between the edge of the clusters and the threshold. Sensitive to outliers in the training data which makes them pretty lame.
Bias/Variance Tradeoff: High bias in training data causes low variance in new data.
Soft margin: When misclassification is allowed, the distance between the observations and the threshold.
Cross-validation:
Support vector: the observations on the edge and within the soft margin.
Hyperplane: all flat affine subspace are called hyperplanes. Generally, we only use the term when we cannot draw it on paper.
Kernel functions: polynomial kernel, radial kernel. d(the degree of the polynomial)
The kernel trick:
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