Preheat the oven to 325 degrees. In a small bowl, combine graham cracker crumbs, sugar, and melted butter. Stir until the cracker crumbs are moistened and press the mixture with your fingers onto the bottom of a 9-inch springform pan. Bake 10 minutes, then remove the pan from the oven and set it aside to cool completely.
Preheat the oven to 425 degrees. In the large bowl of an electric mixer, cream softened cream cheese and sugar at medium speed just until they are blended. Add eggs, one at a time, beating just until they are mixed, and stir in the vanilla.
Pour all but 1 ¼ cups of the filling into the springform pan and set the pan aside. To the remaining filling, add the pumpkin, cinnamon, ginger, nutmeg, and cloves, beating with an electric mixer just until it is smooth. Spoon dollops of the pumpkin mixture onto the cheesecake filling and gently swirl it through the filling.
Bake 10 minutes at 425 degrees, reduce the heat to 300 degrees, and bake 60 minutes more until the filling is almost set. Turn off the oven, open the oven door slightly, and allow the cheesecake to sit 10 minutes. Remove the cheesecake from the oven, set it on a wire rack 1 hour to cool, then run a sharp knife around the edges. Release the outer band of the springform pan and remove it.
Chill the cheesecake 1 to 2 hours, then slide a metal spatula under the crust and transfer the cheesecake to a serving platter. Cover loosely and chill until ready to serve. Cheesecake may be made 1 to 2 days ahead.