Make the Apple-Apricot Compote: Combine the apples, brown sugar, lemon juice, ginger, and mustard in a small saucepan over medium-low heat and cook, stirring occasionally, for 10 minutes.
Add the apricots, raisins, and 1/4 cup water, cover, and cook for 10 more minutes.
Lightly mash the compote with the back of a wooden spoon, cover, and cook for 5 more minutes.
Transfer to a bowl and set aside.
Make the Latkes: Place small batches of grated potatoes in the center of a dish towel, gather up the sides of the towel, and wring excess liquid from the potatoes.
Transfer potatoes to a large bowl and repeat with the remaining potatoes.
Add the remaining ingredients to the potatoes, mix well, and set aside.
Heat 1/4 inch of vegetable oil in a 12-inch skillet over medium heat.
Add the potato mixture by the 1/4 cupful to the hot oil, lightly flatten pancakes with a spatula, and cook latkes until golden -- about 5 minutes.
Turn over and cook until heated through and golden brown -- about 5 more minutes.