使用js使用pca算法
时间: 2023-07-11 21:17:57 浏览: 61
在JavaScript中实现PCA算法的具体步骤如下:
1. 计算数据的协方差矩阵。
```javascript
function covarianceMatrix(data) {
const { length: n } = data;
const means = data.reduce((acc, row) => acc.map((x, i) => x + row[i] / n), Array(data[0].length).fill(0));
return data.reduce((acc, row) => acc.map((x, i) => x.map((y, j) => y + (row[i] - means[i]) * (row[j] - means[j]) / (n - 1))), Array(data[0].length).fill().map(() => Array(data[0].length).fill(0)));
}
```
2. 计算协方差矩阵的特征值和特征向量。
```javascript
function eigen(covarianceMatrix) {
const { length: n } = covarianceMatrix;
const { eigenvectors, eigenvalues } = numeric.eig(covarianceMatrix);
return eigenvalues.map((eigenvalue, i) => [eigenvalue, eigenvectors.map((row) => row[i])]);
}
```
3. 对特征值进行降序排序,并选取前k个特征向量。
```javascript
function sortEigen(eigen, k = eigen.length) {
return eigen.sort(([a], [b]) => b - a).slice(0, k).map(([, eigenvector]) => eigenvector);
}
```
4. 将原始数据投影到选取的特征向量上,得到降维后的数据。
```javascript
function transform(data, eigenvectors) {
const { length: n } = data;
const { length: k } = eigenvectors;
return data.map((row) => eigenvectors.map((eigenvector) => eigenvector.reduce((acc, x, i) => acc + x * row[i], 0) / Math.sqrt(n - 1)));
}
```
完整的PCA算法实现代码如下:
```javascript
function pca(data, k = data[0].length) {
const cov = covarianceMatrix(data);
const eig = sortEigen(eigen(cov), k);
return transform(data, eig);
}
function covarianceMatrix(data) {
const { length: n } = data;
const means = data.reduce((acc, row) => acc.map((x, i) => x + row[i] / n), Array(data[0].length).fill(0));
return data.reduce((acc, row) => acc.map((x, i) => x.map((y, j) => y + (row[i] - means[i]) * (row[j] - means[j]) / (n - 1))), Array(data[0].length).fill().map(() => Array(data[0].length).fill(0)));
}
function eigen(covarianceMatrix) {
const { length: n } = covarianceMatrix;
const { eigenvectors, eigenvalues } = numeric.eig(covarianceMatrix);
return eigenvalues.map((eigenvalue, i) => [eigenvalue, eigenvectors.map((row) => row[i])]);
}
function sortEigen(eigen, k = eigen.length) {
return eigen.sort(([a], [b]) => b - a).slice(0, k).map(([, eigenvector]) => eigenvector);
}
function transform(data, eigenvectors) {
const { length: n } = data;
const { length: k } = eigenvectors;
return data.map((row) => eigenvectors.map((eigenvector) => eigenvector.reduce((acc, x, i) => acc + x * row[i], 0) / Math.sqrt(n - 1)));
}
```
其中,`numeric`是一个JavaScript数值计算库,可以通过npm安装。