Tapkee is a C++ template library for dimensionality reduction with some bias on spectral methods. The Tapkee origins from the code developed during GSoC 2011 as the part of the Shogun machine learning toolbox. The project aim is to provide efficient and flexible standalone library for dimensionality reduction which can be easily integrated to existing codebases. Tapkee leverages capabilities of effective Eigen3 linear algebra library and optionally makes use of the ARPACK eigensolver. The library uses CoverTree and VP-tree data structures to compute nearest neighbors. To achieve greater flexibility we provide a callback interface which decouples dimension reduction algorithms from the data representation and storage schemes.

The library is distributed under permissive BSD 3-clause license (except a few rather optional parts that are distributed under other open sources licenses, see Licensing section of this document). If you use this software in any publication we would be happy if you cite the following paper:

Sergey Lisitsyn and Christian Widmer and Fernando J. Iglesias Garcia. Tapkee: An Efficient Dimension Reduction Library. Journal of Machine Learning Research, 14: 2355-2359, 2013.

To get started with dimension reduction you may try the borsch script that embeds common datasets (swissroll, helix, scurve) using the Tapkee library and outputs it with the help of Matplotlib library. To use the script build the sample application (see the Application section for more details) and call borsch with the following command:

./examples/borsch [swissroll|helix|scurve|...] [lle|isomap|...]

You may also try out an minimal example using make minimal (examples/minimal) and the RNA example using make rna (examples/rna). There are also a few graphical examples. To run MNIST digits embedding example use make mnist (examples/mnist), to run promoters embedding example use make promoters (examples/promoters) and to run embedding for faces dataset use make faces (examples/faces). All graphical examples require Matplotlib which can be usually installed with a package manager. The promoters example also has non-trivial dependency on Shogun machine learning toolbox (minimal version is 2.1.0). We also provide some examples of usage Tapkee in Shogun as make langs (examples/langs) example.

API

We provide an interface based on the method chaining technique. The chain starts from the call of the initialize() method and followed with the withParameters(const ParametersSet&) call which is used to provide parameters like the method to use and its settings. The provided argument is formed with the following syntax:

(keyword1=value1, keyword2=value2)

Such syntax is possible due to comma operator overloading which groups all assigned keywords in the comma separated list.

Keywords are defined in the tapkee namespace. Currently, the following keywords are defined: method, eigen_method, neighbors_method, num_neighbors, target_dimension, diffusion_map_timesteps, gaussian_kernel_width, max_iteration, spe_global_strategy, spe_num_updates, spe_tolerance, landmark_ratio, nullspace_shift, klle_shift, check_connectivity, fa_epsilon, progress_function, cancel_function, sne_perplexity, sne_theta. See the documentation for their detailed meaning.

As an example of parameters setting, if you want to use the Isomap algorithm with the number of neighbors set to 15:

tapkee::initialize().withParameters((method=Isomap,num_neighbors=15))

Please note that the inner parentheses are necessary as it uses the comma operator which appears to be ambiguous in this case.

Next, with initialized parameters you may either embed the provided matrix with:

tapkee::initialize().withParameters((method=Isomap,num_neighbors=15)).
                    .embedUsing(matrix);

Or provide callbacks (kernel, distance and features) using any combination of the withKernel(KernelCallback), withDistance(DistanceCallback) and withFeatures(FeaturesCallback) member functions:

tapkee::initialize().withParameters((method=Isomap,num_neighbors=15))
                    .withKernel(kernel_callback)
                    .withDistance(distance_callback)
                    .withFeatures(features_callback)

Once callbacks are initialized you may either embed data using an STL-compatible sequence of indices or objects (that supports the begin() and end() methods to obtain the corresponding iterators) with the embedUsing(Sequence) member function or embed the data using a sequence range with the embedRange(RandomAccessIterator, RandomAccessIterator) member function.

As a summary - a few examples:

TapkeeOutput output = initialize()
    .withParameters((method=Isomap,num_neighbors=15))
    .embedUsing(matrix);

TapkeeOutput output = initialize()
    .withParameters((method=Isomap,num_neighbors=15))
    .withDistance(distance_callback)
    .embedUsing(indices);

TapkeeOutput output = initialize()
    .withParameters((method=Isomap,num_neighbors=15))
    .withDistance(distance_callback)
    .embedRange(indices.begin(),indices.end());

Minimal example

A minimal working example of a program that uses the library is:

#include <tapkee/tapkee.hpp>
#include <tapkee/callbacks/dummy_callbacks.hpp>

using namespace std;
using namespace tapkee;

struct MyDistanceCallback
{
	ScalarType distance(IndexType l, IndexType r) { return abs(l-r); } 
}; 

int main(int argc, const char** argv)
{
	const int N = 100;
	vector<IndexType> indices(N);
	for (int i=0; i<N; i++) indices[i] = i;

	MyDistanceCallback d;

	TapkeeOutput output = tapkee::initialize() 
	   .withParameters((method=MultidimensionalScaling,target_dimension=1))
	   .withDistance(d)
	   .embedUsing(indices);

	cout << output.embedding.transpose() << endl;
	return 0;
}

This example require Tapkee to be in the include path. With Linux compilers you may do that with the -I/path/to/tapkee/headers/folder key.

Integration

There are a few issues related to including the Tapkee library to your code. First, if your library already includes Eigen3 (and only if) - you might need to let Tapkee know about that with the following define:

#define TAPKEE_EIGEN_INCLUDE_FILE <path/to/your/eigen/include/file.h>

Please note that if you don't include Eigen3 in your project there is no need to define that variable - in this case Eigen3 will be included by Tapkee. This issue comes from the need of including the Eigen3 library only once when using some specific parameters (like debug and extensions).

If you are able to use less restrictive licenses (such as LGPLv3) you may define the following variable:

• TAPKEE_USE_LGPL_COVERTREE to use Covertree code by John Langford.

When compiling your software that includes Tapkee be sure Eigen3 headers are in include path and your code is linked against ARPACK library (-larpack key for g++ and clang++).

For an example of integration you may check Tapkee adapter in Shogun.

When working with installed headers you may check which version of the library do you have with checking the values of TAPKEE_WORLD_VERSION, TAPKEE_MAJOR_VERSION and TAPKEE_MINOR_VERSION defines.

We welcome any integration so please contact authors if you have got any questions. If you have successfully used the library please also let authors know about that - mentions of any applications are very appreciated.

Customization

Tapkee is designed to be highly customizable with preprocessor definitions.

If you want to use float as internal numeric type (default is double) you may do that with definition of #define TAPKEE_CUSTOM_NUMTYPE float before including defines header.

If you use some non-standard STL-compatible realization of vector, map and pair you may redefine them with TAPKEE_INTERNAL_VECTOR, TAPKEE_INTERNAL_PAIR, TAPKEE_INTERNAL_MAP (they are set to std::vector, std::pair and std::map by default otherwise).

You may define TAPKEE_USE_FIBONACCI_HEAP or TAPKEE_USE_PRIORITY_QUEUE to select which data structure should be used in the shortest paths computing algorithm. By default a priority queue is used.

Other properties can be loaded from some provided header file using #define TAPKEE_CUSTOM_PROPERTIES. Currently such file should define only one variable - COVERTREE_BASE which defines the base of the CoverTree (default is 1.3).

Command line application

Tapkee comes with a sample application which can be used to construct low-dimensional representations of dense feature matrices. For more information on its usage please run:

./bin/tapkee_cli -h

The application takes plain ASCII file containing dense matrix (each vector is a column and each line contains values of some feature). The output of the application is stored into the provided file in the same format (each line is feature).

To compile the application please use CMake. The workflow of compilation Tapkee with CMake is usual. When using Unix-based systems you may use the following command to compile the Tapkee application:

mkdir build && cd build && cmake [definitions] .. && make

There are a few cases when you'd want to put some definitions:

• To enable unit-tests compilation add to -DBUILD_TESTS=1 to [definitions] when building. Please note that building unit-tests require googletest. If you are running Ubuntu you may install libgtest-dev package for that. Otherwise, if you have gtest sources around you may provide them as -DGTEST_SOURCE_DIR and -DGTEST_INCLUDES_DIR. If may also download gtest with the following command:

  wget http://googletest.googlecode.com/files/gtest-1.6.0.zip && unzip -q gtest-1.6.0.zip && cd gtest-1.6.0 && cmake . && make && cd .. && rm gtest-1.6.0.zip

  Downloaded sources will be used by Tapkee on build. To run tests use make test command (or better 'ctest -VV').

• To let make script store test coverage information using GCOV and add a target for output test coverage in HTML with LCOV add the -DUSE_GCOV=1 flag to [definitions].

• To enable precomputation of kernel/distance matrices which can speed-up algorithms (but requires much more memory) add -DPRECOMPUTED=1 to [definitions] when building.

• To build application without parts licensed by LGPLv3 use -DGPL_FREE=1 definition.

The library requires Eigen3 to be available in your path. The ARPACK library is also highly recommended to achieve best performance. On Debian/Ubuntu these packages can be installed with

sudo apt-get install libeigen3-dev libarpack2-dev

If you are using Mac OS X and Macports you can install these packages with

sudo port install eigen3 && sudo port install arpack`

In case you want to use some non-default compiler use CC=your-C-compiler CXX=your-C++-compiler cmake [definitions] .. when running cmake.

Directory contents

The repository of Tapkee contains the following directories:

• src/ that contains simple command-line application (src/cli) and CMake module finders (src/cmake).
• includes/ that contains the library itself in the includes/tapkee subdirectory.
• test/ that contains unit-tests in the test/unit subdirectory and a few helper scripts.
• examples/ that contains a few examples including already mentioned (these examples are supposed to be called through make as described above, e.g. make minimal).
• data/ a git submodule that contains data required for examples. To initialize this submodule use git submodule update --init.
• doc/ that contains Doxygen interface file which is used to generate HTML documentation of the library. Calling doxygen doc/Doxyfile will generate it in this folder.

Once built, the root will also contain the following directories:

• bin that contains binaries (tapkee_cli that is command line application and various tests with common naming test_*)
• lib that contains gtest shared libraries.

Need help?

If you need any help or advice don't hesitate to send an email or fire an issue at github.

Supported platforms

Tapkee is tested to be fully functional on Linux (ICC, GCC, Clang compilers) and Mac OS X (GCC and Clang compilers). It also compiles under Windows natively (MSVS 2012 compiler) with a few known issues. In general, Tapkee uses no platform specific code and should work on other systems as well. Please let us know if you have successfully compiled or have got any issues on any other system not listed above.

Supported dimension reduction methods

Tapkee provides implementations of the following dimension reduction methods (urls to descriptions provided):

• Locally Linear Embedding and Kernel Locally Linear Embedding (LLE/KLLE)
• Neighborhood Preserving Embedding (NPE)
• Local Tangent Space Alignment (LTSA)
• Linear Local Tangent Space Alignment (LLTSA)
• Hessian Locally Linear Embedding (HLLE)
• Laplacian eigenmaps
• Locality Preserving Projections
• Diffusion map
• Isomap and landmark Isomap
• Multidimensional scaling and landmark Multidimensional scaling (MDS/lMDS)
• Stochastic Proximity Embedding (SPE)
• PCA and randomized PCA
• Kernel PCA (kPCA)
• Random projection
• Factor analysis
• t-SNE
• Barnes-Hut-SNE

Licensing

The library is distributed under the BSD 3-clause license.

Exceptions are:

• Barnes-Hut-SNE code by Laurens van der Maaten which is distributed under the BSD 4-clause license.

• Covertree code by John Langford and Dinoj Surendran which is distributed under the LGPLv3 license.

• EZOptionsParser by Remik Ziemlinski which is distributed under the MIT license.