Self-organizing Maps (SOM) in Python

使用4x4 SOM網路，將英文字母 “A~L” 進行分類與辨識。

• 用matplotlib 印出
  

設定SOM 網路4x4個神經元，每個神經元含35個w。

並計算$q(x)$優勝神經元，並轉換成座標。

$$q(x) = \min\limits_{\forall j} ||X - w_{j}||_2$$

w = np.random.randn(k, 35)  # (16,35)
N = np.zeros([len(X), k])  # (12,16)

for i in range(len(X)):  # 12
    for j in range(len(w)):  # 16
        N[i, j] = (np.linalg.norm(X[i] - w[j]))  # (12,16)

rq = np.zeros([len(X), 1, 2])  # (12,1,2)
for i in range(12):
    x = np.argmin(N[i, :])  # (12,1) 12 data 距 16 neuron最小距離 index (0~15)
    p = lambda x: (x // 4, x % 4)  # 轉成4x4的座標
    rq[i, :, :] = np.array([p(x)])  # 輸入與最短神經元的座標(12,1,2)

• 建立16個神經元的初始座標

  ri = np.zeros([k, 1, 2])
  for i in range(k):
      q = lambda x: (x // 4, x % 4)
      ri[i] = np.array(q(i))  # ri 4*4 座標 (16,1,2)  [0,0],[0,1]...->[3,3]

• 利用迴圈更新Weight

$h_{qj}(k) = exp(\displaystyle\frac{||r_j-r_q||_2}{2R^2(k)})$

$w_j(k+1) = w_j(k) + _\Delta w_j$

$_\Delta w_j = \eta(k)h_{qj}(k)(x(k)-w_j(k))$

h = np.zeros([len(rq), len(ri)])  # 初始h(12,16)
for k in range(Epochs):
    lr = lr0 * np.exp(-k / t2)
    R = R0 * np.exp(-k / t)
    for q in range(len(rq)):  # X 12
        for j in range(len(ri)):  # 16
            d = ((np.linalg.norm(ri[j] - rq[q]))**2)
            h[q, j] = np.exp(-d / (2 * (R**2)))
    for q in range(len(X)):  # X 12
        for j in range(len(w)):  # 16
            w_grad = lr * h[q, j] * (X[q, :] - w[j, :])
            w[j, :] = w[j, :] + w_grad  #(16, 35)

Result

- 利用matshow印出w的結果 :

一開始的結果只能看出”F” “L” “C”

經過調整參數及 Epochs = 10000後
能明顯看出更多字母。

相關參數:
$R_0 = 1.5$
$lr_0 = 0.1$
$lr = \frac{\displaystyle lr_0}{\displaystyle exp(R_0)}$
$ $
$t = \frac{\displaystyle 1000}{\displaystyle exp(\frac{-k}{t_2})}$
$t2 = 1000$

def Draw_w(m, x=4, y=4):
    fig = plt.figure()
    m = np.reshape(m, (len(m), 7, 5))
    for num in range(len(m)):
        ax = fig.add_subplot(x, y, num + 1)  #num + 1: 1~16
        ax.matshow(1 - m[num, :, :], cmap=plt.cm.gray)
    plt.tight_layout()
    plt.show()

Full Python code in my Github