diff --git a/classifier/linear_model.py b/classifier/linear_model.py
index 99fd07c..d0d538b 100644
--- a/classifier/linear_model.py
+++ b/classifier/linear_model.py
@@ -1,17 +1,86 @@
+# initialization procedure: https://towardsdatascience.com/weight-initialization-techniques-in-neural-networks-26c649eb3b78
+
 class Perceptron:
 
-    def __init__(self, label):
+    def __init__(self, label, input_dim, output_dim, step_size, num_classes=1):
         self.classifier_label = label
-        pass
+        self.input_len = input_dim
+        self.output_len = output_dim
+        self.sigmoid = lambda z : 1/(1+exp(-z))
+        self.num_classes = num_classes
+        self.multi_class = num_classes > 1
+        self.vexp = np.vectorize(exp)
+
+
+
+
+    def fit(self, X, y, weights=None, step_size=0.01, batch_size=10):
+        """
+        initializes training data and hyperparameters
+        """
+        # init weights and step_size
+        assert X.shape[0] == y.shape[0]
+        self.train_nobs = X.shape[0]
+        if weights not None:
+            self.W = weights
+        else:
+            self.W = np.random.randn(self.input_len, self.num_classes)*sqrt(2/(1+self.input_len))
+        self.step_size = step_size
+        self.batch_size = batch_size
+        self. shuffler = np.random.randn(self.train_nobs)
+        self.X = X[self.shuffler]
+        self.y = y[self.shuffler]
+
 
-    def fit(self, X, y, weights=None):
-        pass
 
     def predict(self, X):
-        pass
+        """
+        takes a test set and returns predictions
+        """
+        if self.multi_class:
+            return self.softmax(X.dot(self.W))
+        else:
+            return self.sigmoid(X.dot(self.W))
+
+    def train(self, num_epochs=1, cost_funct='cross_ent'):
+        """
+        implements backpropagation algorithm
+        """
+        batches = [(n,n+self.batch_size) for n in range(self.input_len)]
+        for a,b in batches:
+            XW = X.dot(self.W)
+            preds = self.predict(self.X[a:b])
+            #cost = self.cost(self.y[a:b], preds, funct=cost_funct)
+            cost_deriv = preds - self.y
+            self.W = self.W - self.step_size *
+            if self.multi_class:
+                act_deriv = self.soft_deriv(XW)
+            else:
+                act_deriv = self.sigmoid(XW)(1-self.sigmoid(XW))
+            update = X.dot(act_deriv).dot(cost_deriv)
+            self.W = self.W - self.step_size * update
+
+
+    def softmax(self, vector):
+        denom = np.sum(self.vexp(vector))
+        return np.array(self.vexp(exp))/denom
+
+    def cost(self, y, yhat, funct='cross_ent'):
+        if funct == 'cross_ent':
+            return np.sum(np.vectorize(log)(yhat) * y)
 
+    def soft_deriv(self, inputs):
+        size = max(*inputs.shape)
+        deriv = np.zeros((size,size))
+        for i in range(size):
+            for j in range(size):
+                if i==j:
+                    deriv[i,j] = self.sigmoid(inputs[j])(1-self.sigmoid(inputs[i]))
+                else:
+                    deriv[i, j] = -self.sigmoid(inputs[j]) * self.sigmoid(inputs[i])
+        return deriv
 
-class MultiClassPerceptron:
+#class MultiClassPerceptron(Perceptron):
 
-    def __init__(self):
-        pass
+#    def __init__(self):
+#        pass