TensorLearn

This is a library for some tensor decomposition and tensor-based methods. This is a project under development and more methods will be added. The current methods are functional.

Installation

Use the package manager pip to install tensorlearn in Python.

pip install tensorlearn

methods

Tensor Train Decomposition

• auto_rank_tt
• tt_to_tensor
• tt_compression_ratio

CANDECOMP/PARAFAC (CP) Decomposition

• cp_als_rand_init
• cp_to_tensor
• cp_compression_ratio

Tucker Decomposition

• tucker_hosvd
• tucker_to_tensor
• tucker_compression_ratio

Tensor Completion using CP and ALS

• cp_completion_als

Tensor Operations

• tensor_resize

• unfold

• tensor_frobenius_norm

Matrix Operations

• error_truncated_svd

• column_wise_kronecker

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<a name="cpcompletionals-id"></a>cp_completion_als

tensorlearn.cp_completion_als(tensor, samples, rank, iteration, cp_iteration=100)

This implementation for tensor completion is based on CP decomposition given a fixed rank.

Arguments

• tensor < array >: The given tensor to be decomposed.
• samples < array >: An array of 0s and 1s where 1s represent observed samples, and 0s indicate missing entries. This array's size must match the dimensions of the tensor.
• rank < int >: The rank for CP decomposition.
• iteration < int >: The iteration for the ALS algorithm.
• cp_iteration < int >: The iteration for initialization.

Return

• weights < array >: the vector of normalization weights (lambda) in CP decomposition

• factors < list of arrays >: factor matrices of CP decomposition

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<a name="autoranktt-id"></a>auto_rank_tt

tensorlearn.auto_rank_tt(tensor, epsilon)

This implementation of tensor-train decomposition determines the ranks automatically based on a given error bound according to Oseledets (2011). Therefore the user does not need to specify the ranks. Instead the user specifies an upper error bound (epsilon) which bounds the error of the decomposition. For more information and details please see the page tensor-train decomposition.

Arguments

• tensor < array >: The given tensor to be decomposed.

• epsilon < float >: The error bound of decomposition in the range [0,1].

Return

• TT factors < list of arrays >: The list includes numpy arrays of factors (or TT cores) according to TT decomposition. Length of the list equals the dimension of the given tensor to be decomposed.

Example

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<a name="cpalsrandinit-id"></a>cp_als_rand_init

tensorlearn.cp_als_rand_init(tensor, rank, iteration, random_seed=None)

This is an implementation of CANDECOMP/PARAFAC (CP) decomposition using alternating least squares (ALS) algorithm with random initialization of factors.

Arguments

• tensor < array >: the given tensor to be decomposed

• rank < int >: number of ranks

• iterations < int >: the number of iterations of the ALS algorithm

• random_seed < int >: the seed of random number generator for random initialization of the factor matrices

Return

• weights < array >: the vector of normalization weights (lambda) in CP decomposition

• factors < list of arrays >: factor matrices of CP decomposition

Example

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<a name="tuckerhosvd-id"></a>tucker_hosvd

tensorlearn.tucker_hosvd(tensor, epsilon)

Arguments

• tensor < array >: the given tensor to be decomposed
• epsilon < float >: The error bound of decomposition in the range [0,1].

Return

• core_factor < array >: Core tensor factor of Tucker
• factor_matrices < list >: A list of factor matrices of Tucker

<a name="tttotensor-id"></a>tt_to_tensor

tensorlearn.tt_to_tensor(factors)

Returns the full tensor given the TT factors

Arguments

• factors < list of numpy arrays >: TT factors

Return

• full tensor < numpy array >

Example

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<a name="ttcr-id"></a>tt_compression_ratio

tensorlearn.tt_compression_ratio(factors)

Returns data compression ratio for tensor-train decompostion

Arguments

• factors < list of numpy arrays >: TT factors

Return

• Compression ratio < float >

Example

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<a name="cptotensor-id"></a>cp_to_tensor

Returns the full tensor given the CP factor matrices and weights

tensorlearn.cp_to_tensor(weights, factors)

Arguments

• weights < array >: the vector of normalization weights (lambda) in CP decomposition

• factors < list of arrays >: factor matrices of the CP decomposition

Return

• full tensor < array >

Example

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<a name="tuckertotensor-id"></a>tucker_to_tensor

Returns the full tensor given the Tucker core factor and factor matrices

tensorlearn.tucker_to_tensor(core_factor,factor_matrices)

Arguments

• core_factor < array >: Core factor of Tucker decomposition

• factor_matrices < list of arrays >: factor matrices of Tucker decomposition

Return

• full tensor < array >

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<a name="cpcr-id"></a>cp_compression_ratio

Returns data compression ratio for CP- decompostion

tensorlearn.cp_compression_ratio(weights, factors)

Arguments

• weights < array >: the vector of normalization weights (lambda) in CP decomposition

• factors < list of arrays >: factor matrices of the CP decomposition

Return

• Compression ratio < float >

Example

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<a name="tuckercr-id"></a>Tucker_compression_ratio

Returns data compression ratio for Tucker decomposition.

tensorlearn.tucker_compression_ratio(core_factor,factor_matrices)

Arguments

• core_factor < array >: Core factor of Tucker decomposition

• factor_matrices < list of arrays >: factor matrices of Tucker decomposition

Return

• Compression ratio < float >

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<a name="tensorresize-id"></a>tensor_resize

tensorlearn.tensor_resize(tensor, new_shape)

This method reshapes the given tensor to a new shape. The new size must be bigger than or equal to the original shape. If the new shape results in a tensor of greater size (number of elements) the tensor fills with zeros. This works similar to numpy.ndarray.resize()

Arguments

• tensor < array >: the given tensor

• new_shape < tuple >: new shape

Return

• tensor < array >: tensor with new given shape

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<a name="unfold-id"></a>unfold

tensorlearn.unfold(tensor, n)

Unfold the tensor with respect to dimension n.

Arguments

• tensor < array >: tensor to be unfolded

• n < int >: dimension based on which the tensor is unfolded

Return

• matrix < array >: unfolded tensor with respect to dimension n

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<a name="tfronorm-id"></a>tensor_frobenius_norm

tensorlearn.tensor_frobenius_norm(tensor)

Calculates the frobenius norm of the given tensor.

Arguments

• tensor < array >: the given tensor

Return

• frobenius norm < float >

Example

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<a name="etsvd-id"></a>error_truncated_svd

tensorlearn.error_truncated_svd(x, error)

This method conducts a compact svd and return sigma (error)-truncated SVD of a given matrix. This is an implementation using numpy.linalg.svd with full_matrices=False. This method is used in TT-SVD algorithm in auto_rank_tt.

Arguments

• x < 2D array >: the given matrix to be decomposed

• error < float >: the given error in the range [0,1]

Return

• r, u, s, vh < int, numpy array, numpy array, numpy array >

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<a name="colwisekron-id"></a>column_wise_kronecker

tensorlearn.column_wise_kronecker(a, b)

Returns the column wise Kronecker product (Sometimes known as Khatri Rao) of two given matrices.

Arguments

• a,b < 2D array >: the given matrices

Return

• column wise Kronecker product < array >

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