Implementing (slow) string kernel

Author: helq

string_kernel.py

@@ -0,0 +1,81 @@
+import numpy as np
+
+# Kernel defined by Lodhi et al. (2002)
+def ssk(s, t, n, lbda, accum=False):
+    dynamic = {}
+
+    def k_prim(s, t, i):
+        # print( "k_prim({},{},{})".format(s, t, i) )
+        if i == 0:
+            # print( "k_prim({},{},{}) => 1".format(s, t, i)  )
+            return 1.
+        if min(len(s), len(t)) < i:
+            # print( "k_prim({},{},{}) => 0".format(s, t, i)  )
+            return 0.
+        if (s,t,i) in dynamic:
+            return dynamic[(s,t,i)]
+
+        x = s[-1]
+        s_ = s[:-1]
+        indices = [i for i, e in enumerate(t) if e == x]
+        toret = lbda * k_prim(s_, t, i) \
+              + sum( k_prim(s_, t[:j], i-1) * (lbda**(len(t)-j+1)) for j in indices )
+        # print( "k_prim({},{},{}) => {}".format(s, t, i, toret) )
+        dynamic[(s,t,i)] = toret
+        return toret
+
+    def k(s, t, n):
+        # print( "k({},{},{})".format(s, t, n) )
+        if n <= 0:
+            raise "Error, n must be bigger than zero"
+        if min(len(s), len(t)) < n:
+            # print( "k({},{},{}) => 0".format(s, t, n) )
+            return 0.
+        x = s[-1]
+        s_ = s[:-1]
+        indices = [i for i, e in enumerate(t) if e == x]
+        toret = k(s_, t, n) \
+              + lbda**2 * sum( k_prim(s_, t[:j], n-1) for j in indices )
+        # print( "k({},{},{}) => {}".format(s, t, n, toret) )
+        return toret
+
+    if accum:
+        toret = sum( k(s, t, i) for i in range(1, min(n,len(s),len(t))+1) )
+    else:
+        toret = k(s, t, n)
+
+    # print( len(dynamic) )
+    return toret
+
+def string_kernel(xs, ys, n, lbda):
+    if len(xs.shape) != 2 or len(ys.shape) != 2 or xs.shape[1] != 1 or ys.shape[1] != 1:
+        raise "The shape of the features is wrong, it must be (n,1)"
+
+    lenxs, lenys = xs.shape[0], ys.shape[0]
+
+    mat = np.zeros( (lenxs, lenys) )
+    for i in range(lenxs):
+        for j in range(lenys):
+            mat[i,j] = ssk(xs[i,0], ys[j,0], n, lbda, accum=True)
+
+    mat_xs = np.zeros( (lenxs, 1) )
+    mat_ys = np.zeros( (lenys, 1) )
+
+    for i in range(lenxs):
+        mat_xs[i] = ssk(xs[i,0], xs[i,0], n, lbda, accum=True)
+    for j in range(lenys):
+        mat_ys[j] = ssk(ys[j,0], ys[j,0], n, lbda, accum=True)
+
+    return np.divide(mat, np.sqrt(mat_ys.T * mat_xs))
+
+if __name__ == '__main__':
+    print("Testing...")
+    lbda = .6
+    assert abs( ssk("cat", "cart", 4, lbda, accum=True) - (3*lbda**2 + lbda**4 + lbda**5 + 2*lbda**7) ) < 1e-6
+    assert ssk("science is organized knowledge", "wisdom is organized life", 4, 1, accum=True) == 20538.0
+
+    xs = np.array( ["cat", "car", "cart", "camp", "shard"] ).reshape( (5,1) )
+    ys = np.array( ["a", "cd"] ).reshape( (2,1) )
+    assert string_kernel(xs, xs, 2, 1.)[0,0] == 1.
+
+    print( string_kernel(xs, ys, 2, 1.) )