LostTech.TensorFlow : API Documentation

An Estimator for Weighted Matrix Factorization, using the WALS method.

WALS (Weighted Alternating Least Squares) is an algorithm for weighted matrix factorization. It computes a low-rank approximation of a given sparse (n x m) matrix `A`, by a product of two matrices, `U * V^T`, where `U` is a (n x k) matrix and `V` is a (m x k) matrix. Here k is the rank of the approximation, also called the embedding dimension. We refer to `U` as the row factors, and `V` as the column factors. See tensorflow/contrib/factorization/g3doc/wals.md for the precise problem formulation.

The training proceeds in sweeps: during a row_sweep, we fix `V` and solve for `U`. During a column sweep, we fix `U` and solve for `V`. Each one of these problems is an unconstrained quadratic minimization problem and can be solved exactly (it can also be solved in mini-batches, since the solution decouples across rows of each matrix). The alternating between sweeps is achieved by using a hook during training, which is responsible for keeping track of the sweeps and running preparation ops at the beginning of each sweep. It also updates the global_step variable, which keeps track of the number of batches processed since the beginning of training. The current implementation assumes that the training is run on a single machine, and will fail if `config.num_worker_replicas` is not equal to one. Training is done by calling `self.fit(input_fn=input_fn)`, where `input_fn` provides two tensors: one for rows of the input matrix, and one for rows of the transposed input matrix (i.e. columns of the original matrix). Note that during a row sweep, only row batches are processed (ignoring column batches) and vice-versa. Also note that every row (respectively every column) of the input matrix must be processed at least once for the sweep to be considered complete. In particular, training will not make progress if some rows are not generated by the `input_fn`.

For prediction, given a new set of input rows `A'`, we compute a corresponding set of row factors `U'`, such that `U' * V^T` is a good approximation of `A'`. We call this operation a row projection. A similar operation is defined for columns. Projection is done by calling `self.get_projections(input_fn=input_fn)`, where `input_fn` satisfies the constraints given below.

The input functions must satisfy the following constraints: Calling `input_fn` must return a tuple `(features, labels)` where `labels` is None, and `features` is a dict containing the following keys:

TRAIN: * `WALSMatrixFactorization.INPUT_ROWS`: float32 SparseTensor (matrix). Rows of the input matrix to process (or to project). * `WALSMatrixFactorization.INPUT_COLS`: float32 SparseTensor (matrix). Columns of the input matrix to process (or to project), transposed.

INFER: * `WALSMatrixFactorization.INPUT_ROWS`: float32 SparseTensor (matrix). Rows to project. * `WALSMatrixFactorization.INPUT_COLS`: float32 SparseTensor (matrix). Columns to project. * `WALSMatrixFactorization.PROJECT_ROW`: Boolean Tensor. Whether to project the rows or columns. * `WALSMatrixFactorization.PROJECTION_WEIGHTS` (Optional): float32 Tensor (vector). The weights to use in the projection.

EVAL: * `WALSMatrixFactorization.INPUT_ROWS`: float32 SparseTensor (matrix). Rows to project. * `WALSMatrixFactorization.INPUT_COLS`: float32 SparseTensor (matrix). Columns to project. * `WALSMatrixFactorization.PROJECT_ROW`: Boolean Tensor. Whether to project the rows or columns.