改进fastica算法代码
时间: 2023-09-06 18:11:08 浏览: 102
FastICA是一种独立成分分析方法,通过对数据进行线性变换,找到独立的成分,可以应用于信号处理、图像处理等领域。以下是Python中的FastICA算法实现:
```python
import numpy as np
def _logcosh(x):
gx = np.tanh(x)
g_x = gx ** 2
g_x -= 1.
g_x *= -1
return gx, g_x.mean(axis=-1)
def _deflation(A, W):
w = W[:, 0]
p = np.dot(w, A)
for j in range(1, W.shape[1]):
w = W[:, j]
p = np.dot(w, A)
for i in range(j):
W[:, j] -= (p * W[:, i]).sum() * W[:, i]
w = W[:, j]
p = np.dot(w, A)
return W
def fastICA(X, n_components, max_iter=200, tol=1e-4):
n, m = X.shape
p = float(m)
X *= np.sqrt(p)
W = np.zeros((n_components, n), dtype=X.dtype)
for i in range(n_components):
w = np.random.rand(n)
for j in range(max_iter):
gwtx, g_wtx = _logcosh(np.dot(w, X))
w1 = np.dot(gwtx, X.T) / p - g_wtx.mean() * w
w1 /= np.sqrt((w1 ** 2).sum())
if i >= 1:
w1 = w1 - np.dot(np.dot(w1, W[:i].T), W[:i])
distance = np.abs(np.abs((w1 * w).sum()) - 1)
w = w1
if distance < tol:
break
W[i, :] = w
S = np.dot(W, X)
return S.T
```
在这个实现中, `_logcosh` 函数用于计算 $g(x)$ 和 $g'(x)$, `_deflation` 函数用于执行Deflation过程, `fastICA` 函数是主要的实现函数。
一些可以改进的地方:
1. 在 `_logcosh` 函数中,使用了numpy的通用函数,可以提高计算效率;
2. 在 `fastICA` 函数中,可以添加参数来控制学习速率,从而提高算法的稳定性;
3. 可以添加对数据进行预处理的功能,例如中心化、白化等。
改进后的代码如下:
```python
import numpy as np
def logcosh(x):
return np.tanh(x)
def logcosh_deriv(x):
return 1 - np.square(np.tanh(x))
def deflation(A, W):
for i in range(W.shape[1]):
w = W[:, i]
p = np.dot(w, A)
for j in range(i):
W[:, i] -= np.dot(p, W[:, j]) * W[:, j]
W[:, i] /= np.sqrt(np.sum(np.square(W[:, i])))
return W
def fastICA(X, n_components, learning_rate=1.0, max_iter=200, tol=1e-4, whiten=True):
X = X.T
n, m = X.shape
if whiten:
X -= np.mean(X, axis=0)
X /= np.std(X, axis=0)
cov = np.dot(X.T, X) / (n - 1)
U, S, _ = np.linalg.svd(cov)
K = np.dot(U, np.dot(np.diag(1.0 / np.sqrt(S)), U.T))
X = np.dot(X, K.T)
W = np.random.randn(n_components, n)
for i in range(n_components):
w = W[i, :]
for j in range(max_iter):
y = np.dot(w, X.T)
gwtx = logcosh(y)
g_wtx = logcosh_deriv(y)
w1 = np.mean(X.T * gwtx, axis=0) - np.mean(g_wtx) * w
w1 -= np.sum(np.dot(W[:i, :].T, w1.reshape(-1, 1)).squeeze() * W[:i, :], axis=0)
w1 *= learning_rate / np.sqrt(np.sum(np.square(w1)))
distance = np.abs(np.abs((w1 * w).sum()) - 1)
w = w1
if distance < tol:
break
W[i, :] = w
W = deflation(X, W)
S = np.dot(W.T, X.T).T
return S
```
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