Combine all ingredients except vanilla in heavy large saucepan.
Cook over medium heat until mixture thickens, stirring occasionally, about 5 minutes.
Cool slightly. Transfer to processor. Add vanilla. Puree until smooth.
Strain into medium bowl. Separate 1/2 cup and use in the cran-raspberry compote.
Cover with plastic. Refrigerate at least 6 hours or freeze for 1.5 hours.
Spray 10-inch-diameter spring-form cheesecake baking pan with 2 3/4 inch-high sides with non-stick spray.
Wrap outside of pan with 2 layers of heavy-duty foil.
Blend Special K cereal, Z Sweet, brown sugar, cinnamon and unsalted butter in a food processor until moist clumps form (about 5 minutes).
Press crumb mixture onto bottom of pan.
Position rack in center of oven and preheat to 350 degrees F.
Using an electric mixer, beat cream cheese in large bowl until fluffy. Beat in Z Sweet and pudding mix. Beat in eggs one at a time. Mix in sour cream and vanilla.
Transfer 1/3 of filling to prepared crust.
Dollop 1/3 of cranberry puree atop filling. Repeat layering of filling and puree 2 more times.
Using a knife, swirl puree through filling, creating marbled design.
Place spring form pan in large roasting pan. Pour enough boiling water to come half way up sides of spring form pan.
Bake until cheesecake puffs around edges, about 1 hour 15 minutes.
Turn off oven. Let cake stand in oven 1 hour, leaving oven door open.
Transfer cake to rack. Run knife around pan sides to loosen cake. Cool completely. Remove foil from pan sides.
Cover cake and chill overnight. (Can be made 2 days ahead. Keep refrigerated.)
Remove pan sides. Serve cake with cran-raspberry compote.
Combine all ingredients except vanilla extract in a heavy medium saucepan.
Simmer over medium heat until mixture thickens, about 10 minutes.
Remove from heat. Cool slightly. Stir in vanilla.
Cool to room temperature.
Cover and refrigerate until cold, at least 6 hours.