diff --git a/src/mlpack/methods/amf/update_rules/incremental_iterators.hpp b/src/mlpack/methods/amf/update_rules/incremental_iterators.hpp
new file mode 100644
index 0000000000..2bb56de093
--- /dev/null
+++ b/src/mlpack/methods/amf/update_rules/incremental_iterators.hpp
@@ -0,0 +1,95 @@
+/**
+ * @file incremental_iterators.hpp
+ * @author Ryan Curtin
+ *
+ * Implement iterator utilities to iterate over nonzero elements, used by
+ * SVDCompleteIncrementalLearning and SVDIncompleteIncrementalLearning.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_METHODS_AMF_UPDATE_RULES_INCREMENTAL_ITERATORS_HPP
+#define MLPACK_METHODS_AMF_UPDATE_RULES_INCREMENTAL_ITERATORS_HPP
+
+namespace mlpack {
+
+// Initialize a dense iterator over nonzero values.
+template<typename MatType>
+void InitializeVIter(const MatType& V,
+                     typename MatType::const_iterator& vIter,
+                     size_t& currentUserIndex,
+                     size_t& currentItemIndex)
+{
+  vIter = V.begin();
+  currentItemIndex = 0;
+  currentUserIndex = 0;
+  if ((*vIter) == (typename MatType::elem_type) 0.0)
+  {
+    IncrementVIter(V, vIter, currentUserIndex, currentItemIndex);
+  }
+}
+
+// Initialize an iterator over values in a sparse matrix.
+template<typename eT>
+void InitializeVIter(const arma::SpMat<eT>& V,
+                     typename arma::SpMat<eT>::const_iterator& vIter,
+                     size_t& currentUserIndex,
+                     size_t& currentItemIndex)
+{
+  vIter = V.begin();
+  currentItemIndex = vIter.row();
+  currentUserIndex = vIter.col();
+}
+
+template<typename MatType>
+void IncrementVIter(const MatType& V,
+                    typename MatType::const_iterator& vIter,
+                    size_t& currentUserIndex,
+                    size_t& currentItemIndex)
+{
+  typedef typename MatType::elem_type eT;
+
+  // For dense matrices, 0s may be represented, so increment until we find the
+  // next nonzero value.
+  do
+  {
+    ++vIter;
+    ++currentItemIndex;
+    if (currentItemIndex == V.n_rows)
+    {
+      currentItemIndex = 0;
+      currentUserIndex++;
+    }
+
+    // If we are past the end of the matrix, go back to the beginning.
+    if (currentUserIndex == V.n_cols)
+    {
+      vIter = V.begin();
+      currentUserIndex = 0;
+    }
+  } while ((*vIter) == (eT) 0);
+}
+
+template<typename eT>
+void IncrementVIter(const arma::SpMat<eT>& V,
+                    typename arma::SpMat<eT>::const_iterator& vIter,
+                    size_t& currentUserIndex,
+                    size_t& currentItemIndex)
+{
+  // The iterator automatically handles zero values.
+  ++vIter;
+  if (vIter == V.end())
+  {
+    // Reset to start.
+    vIter = V.begin();
+  }
+
+  currentItemIndex = vIter.row();
+  currentUserIndex = vIter.col();
+}
+
+} // namespace mlpack
+
+#endif