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Matrix completion and feature imputation algorithms

Project description

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# fancyimpute

A variety of matrix completion and imputation algorithms implemented in Python.

## Usage

from fancyimpute import BiScaler, KNN, NuclearNormMinimization, SoftImpute

# X is the complete data matrix
# X_incomplete has the same values as X except a subset have been replace with NaN

# Use 3 nearest rows which have a feature to fill in each row's missing features
X_filled_knn = KNN(k=3).complete(X_incomplete)

# matrix completion using convex optimization to find low-rank solution
# that still matches observed values. Slow!
X_filled_nnm = NuclearNormMinimization().complete(X_incomplete)

# Instead of solving the nuclear norm objective directly, instead
# induce sparsity using singular value thresholding
X_filled_softimpute = SoftImpute().complete(X_incomplete_normalized)

# print mean squared error for the three imputation methods above
nnm_mse = ((X_filled_nnm[missing_mask] - X[missing_mask]) ** 2).mean()
print("Nuclear norm minimization MSE: %f" % nnm_mse)

softImpute_mse = ((X_filled_softimpute[missing_mask] - X[missing_mask]) ** 2).mean()
print("SoftImpute MSE: %f" % softImpute_mse)

knn_mse = ((X_filled_knn[missing_mask] - X[missing_mask]) ** 2).mean()
print("knnImpute MSE: %f" % knn_mse)

## Algorithms

* `SimpleFill`: Replaces missing entries with the mean or median of each column.

* `KNN`: Nearest neighbor imputations which weights samples using the mean squared difference
on features for which two rows both have observed data.

* `SoftImpute`: Matrix completion by iterative soft thresholding of SVD decompositions. Inspired by the [softImpute]( package for R, which is based on [Spectral Regularization Algorithms for Learning Large Incomplete Matrices]( by Mazumder et. al.

* `IterativeSVD`: Matrix completion by iterative low-rank SVD decomposition. Should be similar to SVDimpute from [Missing value estimation methods for DNA microarrays]( by Troyanskaya et. al.

* `MICE`: Reimplementation of [Multiple Imputation by Chained Equations](

* `MatrixFactorization`: Direct factorization of the incomplete matrix into low-rank `U` and `V`, with an L1 sparsity penalty on the elements of `U` and an L2 penalty on the elements of `V`. Solved by gradient descent.

* `NuclearNormMinimization`: Simple implementation of [Exact Matrix Completion via Convex Optimization](
) by Emmanuel Candes and Benjamin Recht using [cvxpy]( Too slow for large matrices.

* `BiScaler`: Iterative estimation of row/column means and standard deviations to get doubly normalized
matrix. Not guaranteed to converge but works well in practice. Taken from [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](

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