# 数学编程|MATH3017W1-01 Mathematical Programming代写 southampton代写

We address the task of estimating a classification function which assigns a given vector $x \in R^{n}$ into one of two disjoint point sets $\mathcal{A}$ or $\mathcal{B}$ in $n$-dimensional feature space. We have $\mathcal{X}=R^{n}, \mathcal{Y}={0,1}$ and the classification function has the following form.
$$g(x)= \begin{cases}1 & \text { if } x \in \mathcal{A} \ 0 & \text { if } x \in \mathcal{B}\end{cases}$$
We represent the $m$ elements of the finite point set $\mathcal{A} \subset R^{n}$ as the matrix $A \in R^{m \times n}$ where each element of $\mathcal{A}$ is represented by a row in $A$. Similarly, we represent the $k$ elements of the finite point set $\mathcal{B}$ as $B \in R^{k \times n}$. We attempt to discriminate between the points of $\mathcal{A}$ and $\mathcal{B}$ by constructing a separating plane:

$$\hat{g}(x)=\sum_{j=1}^{N} w_{j} f_{j}(x) .$$
By sampling the elements of $\mathcal{F}$ at the data points $x^{1}, x^{2}, \ldots, x^{M}$, the problem of estimating the coefficients $w_{j}$ in (19) reduces to solving the linear system:
$$A w=b$$

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