added regularization

Author: akagam1

Neural Networks/OneVsAll-Digit Recognition.ipynb

@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 153,
+   "execution_count": 2,
    "id": "aeaa3bba",
    "metadata": {},
    "outputs": [
@@ -240,7 +240,7 @@
        "[5 rows x 785 columns]"
       ]
      },
-     "execution_count": 153,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "id": "6c91a3f5",
    "metadata": {},
    "outputs": [
@@ -324,7 +324,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 4,
    "id": "26597be5",
    "metadata": {},
    "outputs": [],
@@ -336,7 +336,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 141,
+   "execution_count": 5,
    "id": "a1f43228",
    "metadata": {},
    "outputs": [
@@ -346,7 +346,7 @@
        "(5000, 785)"
       ]
      },
-     "execution_count": 141,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -361,37 +361,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 142,
+   "execution_count": 10,
    "id": "fa042365",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def gradDesc(theta,x,y,m):\n",
+    "def gradDesc(theta,x,y,m,lambda_):\n",
     "    h = sigmoid(x*theta)\n",
     "    grad = np.transpose(x)*(h-np.transpose(y))\n",
+    "    grad[1:,:] = grad[1:,:] + (lambda_/m)*theta[1:,:]\n",
     "    return grad/m\n",
     "\n",
-    "def oneVall(x,y,alpha,itr):\n",
+    "def oneVall(x,y,alpha,itr,lambda_):\n",
     "    m,n = x.shape\n",
     "    theta = np.transpose(np.matrix(np.zeros(n)))\n",
     "    x = np.matrix(x)\n",
     "    y = np.matrix(y)\n",
     "    for i in range(itr):\n",
-    "        theta = theta - alpha*gradDesc(theta,x,y,m)\n",
+    "        theta = theta - alpha*gradDesc(theta,x,y,m,lambda_)\n",
     "    return np.array(np.transpose(theta))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 147,
+   "execution_count": 15,
    "id": "d31d0b48",
    "metadata": {},
    "outputs": [],
    "source": [
     "all_theta = np.array([np.zeros(785)])\n",
     "for j in range(num_labels):\n",
     "    yIn = (y == j).astype(int)\n",
-    "    temp = oneVall(x,yIn,0.00000001,1000)\n",
+    "    temp = oneVall(x,yIn,0.00000001,1000,100)\n",
     "    all_theta = np.append(all_theta, temp, axis=0)\n",
     "    #all_theta = np.vstack([all_theta,temp])\n",
     "all_theta.shape\n",
@@ -400,7 +401,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 154,
+   "execution_count": 16,
    "id": "1b610409",
    "metadata": {},
    "outputs": [
@@ -433,7 +434,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 163,
+   "execution_count": 17,
    "id": "37e5c59c",
    "metadata": {},
    "outputs": [],
@@ -443,7 +444,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 164,
+   "execution_count": 18,
    "id": "fbb3bb20",
    "metadata": {},
    "outputs": [