@@ -15,10 +15,10 @@
**NTFk** methodology allows for automatic identification of the optimal number of features (signals) present in multi-dimensional data arrays (tensors).
The number of features (tensor rank / multi-rank) along different dimensions can be estimated jointly and independently.
-**NMFk** can be applied to perform various types of analyses of multi-dimensional data:
+**SmartTensors** can be applied to perform various types of analyses of multi-dimensional data:
- Feature extraction (**FE**)
- Blind source separation (**BSS**)
-- Detection of disruptions / anomalies
+- Detection of disruptions/anomalies
- Image recognition
- Text mining
- Data classification
@@ -26,14 +26,14 @@ The number of features (tensor rank / multi-rank) along different dimensions can
- Discovery of unknown dependencies and phenomena
- Development of reduced-order/surrogate models
- Identification of dependencies between model inputs and outputs
-- Guiding the development of physics models representing the ML analyzed data
+- Guiding the development of physics models representing the ML-analyzed data
- Blind predictions
- Optimization of data acquisition (optimal experimental design)
- Labeling of datasets for supervised ML analyses
**NTFk** provides high-performance computing capabilities to solve problems with Shared and Distributed Arrays in parallel.
-The parallelization allows for utilization of multi-core / multi-processor environments.
+The parallelization allows for the utilization of multi-core / multi-processor environments.
GPU and TPU accelerations are available through existing Julia packages.
**NTFk** can be employed to perform tensor decomposition using CP (Candecomp/Parafac) and Tucker methods.
@@ -44,15 +44,15 @@ GPU and TPU accelerations are available through existing Julia packages.
* Wotao Yin's [BCU](https://www.math.ucla.edu/~wotaoyin/papers/bcu/matlab.html)
* [TensorLab](https://www.tensorlab.net)
-**NTFk** provides also interface to Jean Kossaifi's [Python TensorLy](http://tensorly.org/stable/index.html).
+**NTFk** provides also an interface to Jean Kossaifi's [Python TensorLy](http://tensorly.org/stable/index.html).
-**NTFk** can perform high-performance computing tensor decomposition analyses using TensorFlow, PyTorch and MXNET.
+**NTFk** can perform high-performance computing tensor decomposition analyses using TensorFlow, PyTorch, and MXNET.
-**NTFk** methodology and applications are discussed in the the papers and presentations listed below.
+**NTFk** methodology and applications are discussed in the papers and presentations listed below.
-Tensor network decompositions can be be performed using SmartTensors' [**NTNk**](https://github.com/SmartTensors/NTNk.jl) package.
+Tensor network decompositions can be performed using SmartTensors' [**NTNk**](https://github.com/SmartTensors/NTNk.jl) package.
-Matrix factorization can be be performed using SmartTensors' [**NMFk**](https://github.com/SmartTensors/NMFk.jl) package.
+Matrix factorization can be performed using SmartTensors' [**NMFk**](https://github.com/SmartTensors/NMFk.jl) package.
## Awards
@@ -74,7 +74,7 @@ Pkg.add("NTFk")
```
to access the latest released version.
-To utilize the latest updates (commits) use:
+To utilize the latest updates (commits), use:
```julia
import Pkg
@@ -138,7 +138,7 @@ Some of the decomposition models can theoretically lead to unique solutions unde
When these conditions are not satisfied, additional minimization constraints can assist the factorization.
A popular approach is to add sparsity and nonnegative constraints.
Sparsity constraints on the elements of G reduce the number of features and their mixing (by having as many zero entries as possible).
-Nonnegativity enforces parts-based representation of the original data which also allows the Tensor Decomposition results for
and
to be easily interrelated [Cichocki et al, 2009](https://books.google.com/books?hl=en&lr=&id=KaxssMiWgswC&oi=fnd&pg=PR5&ots=Lta2adM6LV&sig=jNPDxjKlON1U3l46tZAYH92mvAE#v=onepage&q&f=false).
+Nonnegativity enforces parts-based representation of the original data, which also allows the Tensor Decomposition results for
and
to be easily interrelated [Cichocki et al, 2009](https://books.google.com/books?hl=en&lr=&id=KaxssMiWgswC&oi=fnd&pg=PR5&ots=Lta2adM6LV&sig=jNPDxjKlON1U3l46tZAYH92mvAE#v=onepage&q&f=false).
## Examples
@@ -153,7 +153,7 @@ tsize = (5, 10, 15)
tucker_orig = NTFk.rand_tucker(csize, tsize; factors_nonneg=true, core_nonneg=true)
```
-After that, we can compose a tensor based on this Tucker decomposition:
+After that, we can compose a tensor-based on this Tucker decomposition:
```julia
import TensorDecompositions
@@ -163,7 +163,7 @@ T_orig .*= 1000
```
Applying **NTFk**, we can find the unknown core size of the tensor using the tensor by itself as an input only.
-To do this, we explore a series of core sizes and we identify the optimal one:
+To do this, we explore a series of core sizes and identify the optimal one:
```julia
sizes = [csize, (1,3,4), (3,3,4), (2,2,4), (2,4,4), (2,3,3), (2,3,5)]
@@ -184,9 +184,9 @@ tucker_estimated, csize_estimated = NTFk.analysis(T_orig, sizes, 3; eigmethod=[f
[ Info: Estimated true core size based on the reconstruction: (2, 3, 4)
```
-The final **NTFk** result is the estimated core size `(2,3,4)` which as expected matches the original unknown core size.
+The final **NTFk** result is the estimated core size `(2,3,4)`, which, as expected, matches the original unknown core size.
-**NTFk** also produces a Tucker deconstruction of this tensor with core size `(2,3,4)` which is stored as `tucker_estimated[ibest]`
+**NTFk** also produces a Tucker deconstruction of this tensor with core size `(2,3,4)`, which is stored as `tucker_estimated[ibest]`
## Notebooks:
@@ -217,8 +217,8 @@ The analyzed datasets include model outputs, laboratory experimental data, and f
- Induced seismicity
- Phase separation of co-polymers
- Oil / Gas extraction from unconventional reservoirs
-- Geothermal exploration and produciton
-- Geologic carbon storages
+- Geothermal exploration and production
+- Geologic carbon storage
- Wildfires
## Videos:
@@ -291,7 +291,7 @@ Julia uses git for package management.
Julia uses git and curl to install the necessary packages.
-It is important to set proxies if needed:
+It is important to set proxies, if needed:
```bash
export ftp_proxy=http://proxyout.
:8080
@@ -312,7 +312,7 @@ export https_proxy=http://proxyout.lanl.gov:8080
export no_proxy=.lanl.gov
```
-Proxies can be also set up directly in the Julia REPL as well:
+Proxies can also be set up directly in the Julia REPL:
```julia
ENV["ftp_proxy"] = "http://proxyout.lanl.gov:8080"
@@ -332,7 +332,7 @@ ENV["https_proxy"] = ""
ENV["no_proxy"] = ""
```
-In some situations, you may need to add in the `.gitconfig` file in your home directory:
+In some situations, you may need to add the `.gitconfig` file in your home directory:
```
[url "git@github.com:"]
@@ -352,4 +352,4 @@ git config --global url."https://".insteadOf git://
git config --global url."http://".insteadOf git://
git config --global url."git@gitlab.com:".insteadOf https://gitlab.com/
git config --global url."git@github.com:".insteadOf https://github.com/
-```
\ No newline at end of file
+```
-**NTFk** is one of the tools in the **SmartTensors** ML framework ([smarttensors.com](https://smarttensors.com)).
+**NTFk** is a module of the **SmartTensors** ML framework ([smarttensors.com](https://smarttensors.com)).