PrologMethods/Transformation/nca.md

+# Neighborhood Components Analysis (NCA)
+
+An implementation of neighborhood components analysis, a distance learning technique that can be used for preprocessing. Given a labeled dataset, this uses NCA, which seeks to improve the k-nearest-neighbor classification, and returns the learned distance metric
+
+# Available Predicates
+
+* [nca/20](/PrologMethods/Transformation/nca#nca20)
+
+---
+
+[links/resources](/PrologMethods/Transformation/nca#connected-linksresources)
+
+## **_nca/20_**
+
+Initialize the nca model and the selected optimizer.
+
+Then perform nca on the given data and return the learned distance.
+
+```prolog
+%% part of the predicate definition
+nca(  +string,
+      +float32, +integer, +float32,
+      +integer,
+      +integer, +float32, +float32, +integer, +float32, +float32, +integer,
+      +pointer(float_array), +integer, +integer,
+      +pointer(float_array), +integer,
+      -pointer(float_array), -integer, -integer)
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| optimizerType | +string | Optimizer to use; "sgd" or "lbfgs". | sgd |
+| stepSize | +float | Step size for stochastic gradient descent (alpha). | 0.01 |
+| maxIterations | +integer | Maximum number of iterations for SGD or L-BFGS (0 indicates no limit). | 500000 |
+| tolerance | +float | Maximum tolerance for termination of SGD or L-BFGS. | 1e-7 |
+| shuffle | +integer(bool) |  |  |
+| numBasis | +integer | Number of memory points to be stored for L-BFGS. | 5 |
+| armijoConstant | +float | Armijo constant for L-BFGS. | 0.0001 |
+| wolfe | +float | Wolfe condition parameter for L-BFGS. | 0.9 |
+| maxLineSearchTrials | +integer | Maximum number of line search trials for L-BFGS. | 50 |
+| minStep | +float | Minimum step of line search for L-BFGS. | 1e-20 |
+| maxStep | +float | Maximum step of line search for L-BFGS. | 1e+20 |
+| batchSize | +integer | Batch size for mini-batch SGD. | 50 |
+| data | +matrix | Input dataset to run NCA on. | - |
+| labels | +vector | Labels for input dataset. | - |
+| distance | -matrix | Output matrix for learned distance matrix. | - |
+
+---
+
+# Connected Links/Resources
+
+If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.
+
+* [MLpack::nca_C++\_documentation](https://www.mlpack.org/doc/stable/doxygen/classmlpack_1_1nca_1_1NCA.html)
+* [MLpack::nca_Python_documentation](https://www.mlpack.org/doc/stable/python_documentation.html#nca)
+
+added some of the links from the python documentation
+
+* lmnn
+* [Neighbourhood components analysis on Wikipedia](https://en.wikipedia.org/wiki/Neighbourhood_components_analysis)
+* [Neighbourhood components analysis (pdf)](http://papers.nips.cc/paper/2566-neighbourhood-components-analysis.pdf)
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