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PLSSVM

PLSSVM - Parallel Least Squares Support Vector Machine

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A Support Vector Machine (SVM) is a supervised machine learning model. In its basic form SVMs are used for binary classification tasks. Their fundamental idea is to learn a hyperplane which separates the two classes best, i.e., where the widest possible margin around its decision boundary is free of data. This is also the reason, why SVMs are also called "large margin classifiers". To predict to which class a new, unseen data point belongs, the SVM simply has to calculate on which side of the previously calculated hyperplane the data point lies. This is very efficient since it only involves a single scalar product of the size corresponding to the numer of features of the data set.

strong scaling CPU

However, normal SVMs suffer in their potential parallelizability. Determining the hyperplane boils down to solving a convex quadratic problem. For this, most SVM implementations use Sequential Minimal Optimization (SMO), an inherently sequential algorithm. The basic idea of this algorithm is that it takes a pair of data points and calculates the hyperplane between them. Afterward, two new data points are selected and the existing hyperplane is adjusted accordingly. This procedure is repeat until a new adjustment would be smaller than some epsilon greater than zero.

Some SVM implementations try to harness some parallelization potential by not drawing point pairs but group of points. In this case, the hyperplane calculation inside this group is parallelized. However, even then modern highly parallel hardware can not be utilized efficiently.

Therefore, we implemented a version of the original proposed SVM called Least Squares Support Vector Machine (LS-SVM). The LS-SVMs reformulated the original problem such that it boils down to solving a system of linear equations. For this kind of problem many highly parallel algorithms and implementations are known. We decided to use the Conjugate Gradient (CG) to solve the system of linear equations.

Since one of our main goals was performance, we parallelized the implicit matrix-vector multiplication inside the CG algorithm. To do so, we use multiple different frameworks to be able to target a broad variety of different hardware platforms. The currently available frameworks (also called backends in our PLSSVM implementation) are:

Getting Started

Dependencies

General dependencies:

  • a C++17 capable compiler (e.g. gcc or clang)
  • CMake 3.21 or newer
  • cxxopts ≥ v3.0.0, fast_float, {fmt} ≥ v8.1.1, and igor (all four are automatically build during the CMake configuration if they couldn't be found using the respective find_package call)
  • GoogleTest ≥ v1.11.0 if testing is enabled (automatically build during the CMake configuration if find_package(GTest) wasn't successful)
  • doxygen if documentation generation is enabled
  • Pybind11 ≥ v2.10.3 if Python bindings are enabled
  • OpenMP 4.0 or newer (optional) to speed-up library utilities (like file parsing)
  • multiple Python modules used in the utility scripts, to install all modules use pip install --user -r install/python_requirements.txt

Additional dependencies for the OpenMP backend:

  • compiler with OpenMP support

Additional dependencies for the CUDA backend:

Additional dependencies for the HIP backend:

Additional dependencies for the OpenCL backend:

  • OpenCL runtime and header files

Additional dependencies for the SYCL backend:

  • the code must be compiled with a SYCL capable compiler; currently tested with DPC++ and hipSYCL

Additional dependencies if PLSSVM_ENABLE_TESTING and PLSSVM_GENERATE_TEST_FILE are both set to ON:

Building

Building the library can be done using the normal CMake approach:

git clone https://github.com/SC-SGS/PLSSVM.git
cd PLSSVM 
mkdir build && cd build 
cmake -DPLSSVM_TARGET_PLATFORMS="..." [optional_options] .. 
cmake --build . -j

Target Platform Selection

The CMake option PLSSVM_TARGET_PLATFORMS is used to determine for which targets the backends should be compiled. Valid targets are:

  • cpu: compile for the CPU; an optional architectural specifications is allowed but only used when compiling with DPC++, e.g., cpu:avx2
  • nvidia: compile for NVIDIA GPUs; at least one architectural specification is necessary, e.g., nvidia:sm_86,sm_70
  • amd: compile for AMD GPUs; at least one architectural specification is necessary, e.g., amd:gfx906
  • intel: compile for Intel GPUs; at least one architectural specification is necessary, e.g., intel:skl

At least one of the above targets must be present. If the option PLSSVM_TARGET_PLATFORMS is not present, the targets are automatically determined using the Python3 utility_scripts/plssvm_target_platforms.py script (required Python3 dependencies: argparse, py-cpuinfo, GPUtil, pyamdgpuinfo, and pylspci).

Note that when using DPC++ only a single architectural specification for cpu, nvidia or amd is allowed.

python3 utility_scripts/plssvm_target_platforms.py --help
usage: plssvm_target_platforms.py [-h] [--quiet]

optional arguments:
  -h, --help  show this help message and exit
  --quiet     only output the final PLSSVM_TARGET_PLATFORMS string

Example invocation:

python3 utility_scripts/plssvm_target_platforms.py
Intel(R) Core(TM) i9-10980XE CPU @ 3.00GHz: {'avx512': True, 'avx2': True, 'avx': True, 'sse4_2': True}

Found 1 NVIDIA GPU(s):
  1x NVIDIA GeForce RTX 3080: sm_86

Possible -DPLSSVM_TARGET_PLATFORMS entries:
cpu:avx512;nvidia:sm_86

or with the --quiet flag given:

python3 utility_scripts/plssvm_target_platforms.py --quiet
cpu:avx512;intel:dg1

If the architectural information for the requested GPU could not be retrieved, one option would be to have a look at:

Optional CMake Options

The [optional_options] can be one or multiple of:

  • PLSSVM_ENABLE_OPENMP_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for the OpenMP backend and fail if not available
    • AUTO: check for the OpenMP backend but do not fail if not available
    • OFF: do not check for the OpenMP backend

  • PLSSVM_ENABLE_CUDA_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for the CUDA backend and fail if not available
    • AUTO: check for the CUDA backend but do not fail if not available
    • OFF: do not check for the CUDA backend

  • PLSSVM_ENABLE_HIP_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for the HIP backend and fail if not available
    • AUTO: check for the HIP backend but do not fail if not available
    • OFF: do not check for the HIP backend

  • PLSSVM_ENABLE_OPENCL_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for the OpenCL backend and fail if not available
    • AUTO: check for the OpenCL backend but do not fail if not available
    • OFF: do not check for the OpenCL backend

  • PLSSVM_ENABLE_SYCL_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for the SYCL backend and fail if not available
    • AUTO: check for the SYCL backend but do not fail if not available
    • OFF: do not check for the SYCL backend

Attention: at least one backend must be enabled and available!

  • PLSSVM_ENABLE_ASSERTS=ON|OFF (default: OFF): enables custom assertions regardless whether the DEBUG macro is defined or not
  • PLSSVM_THREAD_BLOCK_SIZE (default: 16): set a specific thread block size used in the GPU kernels (for fine-tuning optimizations)
  • PLSSVM_INTERNAL_BLOCK_SIZE (default: 6: set a specific internal block size used in the GPU kernels (for fine-tuning optimizations)
  • PLSSVM_OPENMP_BLOCK_SIZE (default: 64): set a specific block size used in the OpenMP kernels
  • PLSSVM_ENABLE_LTO=ON|OFF (default: ON): enable interprocedural optimization (IPO/LTO) if supported by the compiler
  • PLSSVM_ENABLE_DOCUMENTATION=ON|OFF (default: OFF): enable the doc target using doxygen
  • PLSSVM_ENABLE_PERFORMANCE_TRACKING: enable gathering performance characteristics for the three executables using YAML files; example Python3 scripts to perform performance measurements and to process the resulting YAML files can be found in the utility_scripts/ directory (requires the Python3 modules wrapt-timeout-decorator, pyyaml, and pint)
  • PLSSVM_ENABLE_TESTING=ON|OFF (default: ON): enable testing using GoogleTest and ctest
  • PLSSVM_ENABLE_LANGUAGE_BINDINGS=ON|OFF (default: OFF): enable language bindings

If PLSSVM_ENABLE_TESTING is set to ON, the following options can also be set:

  • PLSSVM_GENERATE_TEST_FILE=ON|OFF (default: ON): automatically generate test files
    • PLSSVM_TEST_FILE_NUM_DATA_POINTS (default: 5000): the number of data points in the test file
    • PLSSVM_TEST_FILE_NUM_FEATURES (default: 2000): the number of features per data point in the test file

If PLSSVM_ENABLE_LANGUAGE_BINDINGS is set to ON, the following option can also be set:

  • PLSSVM_ENABLE_PYTHON_BINDINGS=ON|OFF (default: PLSSVM_ENABLE_LANGUAGE_BINDINGS): enable Python bindings using Pybind11

If PLSSVM_ENABLE_PYTHON_BINDINGS is set to ON, the following options can also be set:

  • PLSSVM_PYTHON_BINDINGS_PREFERRED_REAL_TYPE (default: double): the default real_type used if the generic plssvm.Model and plssvm.DataSet Python classes are used
  • PLSSVM_PYTHON_BINDINGS_PREFERRED_LABEL_TYPE (default: std::string): the default label_type used if the generic plssvm.Model and plssvm.DataSet Python classes are used

If the SYCL backend is available additional options can be set.

  • PLSSVM_ENABLE_SYCL_HIPSYCL_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for hipSYCL as implementation for the SYCL backend and fail if not available
    • AUTO: check for hipSYCL as implementation for the SYCL backend but do not fail if not available
    • OFF: do not check for hipSYCL as implementation for the SYCL backend

  • PLSSVM_ENABLE_SYCL_DPCPP_BACKEND=ON|OFF|AUTO (default: AUTO):

    • ON: check for DPC++ as implementation for the SYCL backend and fail if not available
    • AUTO: check for DPC++ as implementation for the SYCL backend but do not fail if not available
    • OFF: do not check for DPC++ as implementation for the SYCL backend

To use DPC++ for SYCL simply set the CMAKE_CXX_COMPILER to the respective DPC++ clang executable during CMake invocation.

If the SYCL implementation is DPC++ the following additional options are available:

  • PLSSVM_SYCL_BACKEND_DPCPP_USE_LEVEL_ZERO (default: OFF): use DPC++'s Level-Zero backend instead of its OpenCL backend
  • PLSSVM_SYCL_BACKEND_DPCPP_GPU_AMD_USE_HIP (default: ON): use DPC++'s HIP backend instead of its OpenCL backend for AMD GPUs
  • PLSSVM_SYCL_BACKEND_DPCPP_ENABLE_AOT (default: ON): enable Ahead-of-Time (AOT) compilation for the specified target platforms

If more than one SYCL implementation is available the environment variables PLSSVM_SYCL_HIPSYCL_INCLUDE_DIR and PLSSVM_SYCL_DPCPP_INCLUDE_DIR must be set to the respective SYCL include paths. Note that those paths must not be present in the CPLUS_INCLUDE_PATH environment variable or compilation will fail.

  • PLSSVM_SYCL_BACKEND_PREFERRED_IMPLEMENTATION (dpcpp|hipsycl): specify the preferred SYCL implementation if the sycl_implementation_type option is set to automatic; additional the specified SYCL implementation is used in the plssvm::sycl namespace, the other implementations are available in the plssvm::dpcpp and plssvm::hipsycl namespace respectively

Running the tests

To run the tests after building the library (with PLSSVM_ENABLE_TESTING set to ON) use:

ctest

Generating test coverage results

To enable the generation of test coverage reports using locv the library must be compiled using the custom Coverage CMAKE_BUILD_TYPE. Additionally, it's advisable to use smaller test files to shorten the ctest step.

cmake -DCMAKE_BUILD_TYPE=Coverage -DPLSSVM_TARGET_PLATFORMS="..." \
      -DPLSSVM_TEST_FILE_NUM_DATA_POINTS=100 \
      -DPLSSVM_TEST_FILE_NUM_FEATURES=50 ..
cmake --build . -- coverage

The resulting html coverage report is located in the coverage folder in the build directory.

Creating the documentation

If doxygen is installed and PLSSVM_ENABLE_DOCUMENTATION is set to ON the documentation can be build using

cmake --build . -- doc

The documentation of the current state of the main branch can be found here.

Installing

The library supports the install target:

cmake --build . -- install

Afterward, the necessary exports should be performed:

export CMAKE_PREFIX_PATH=${CMAKE_INSTALL_PREFIX}/share/plssvm/cmake:${CMAKE_PREFIX_PATH}
export MANPATH=${CMAKE_INSTALL_PREFIX}/share/man:$MANPATH

export PATH=${CMAKE_INSTALL_PREFIX}/bin:${PATH}
export LD_LIBRARY_PATH=${CMAKE_INSTALL_PREFIX}/lib:${LD_LIBRARY_PATH}

Usage

Generating artificial data

The repository comes with a Python3 script (in the utility_scripts/ directory) to simply generate arbitrarily large data sets.

In order to use all functionality, the following Python3 modules must be installed: argparse, timeit, numpy, pandas, sklearn, arff, matplotlib, mpl_toolkits, and humanize.

python3 utility_scripts/generate_data.py --help
usage: generate_data.py [-h] --output OUTPUT --format FORMAT [--problem PROBLEM] --samples SAMPLES [--test_samples TEST_SAMPLES] --features FEATURES [--plot]

optional arguments:
  -h, --help            show this help message and exit
  --output OUTPUT       the output file to write the samples to (without extension)
  --format FORMAT       the file format; either arff or libsvm
  --problem PROBLEM     the problem to solve; one of: blobs, blobs_merged, planes, planes_merged, ball
  --samples SAMPLES     the number of training samples to generate
  --test_samples TEST_SAMPLES
                        the number of test samples to generate; default: 0
  --features FEATURES   the number of features per data point
  --plot                plot training samples; only possible if 0 < samples <= 2000 and 1 < features <= 3

An example invocation generating a data set consisting of blobs with 1000 data points with 200 features each could look like:

python3 generate_data.py --output data_file --format libsvm --problem blobs --samples 1000 --features 200

Training

./plssvm-train --help
LS-SVM with multiple (GPU-)backends
Usage:
  ./plssvm-train [OPTION...] training_set_file [model_file]

  -t, --kernel_type arg         set type of kernel function. 
                                         0 -- linear: u'*v
                                         1 -- polynomial: (gamma*u'*v + coef0)^degree 
                                         2 -- radial basis function: exp(-gamma*|u-v|^2) (default: 0)
  -d, --degree arg              set degree in kernel function (default: 3)
  -g, --gamma arg               set gamma in kernel function (default: 1 / num_features)
  -r, --coef0 arg               set coef0 in kernel function (default: 0)
  -c, --cost arg                set the parameter C (default: 1)
  -e, --epsilon arg             set the tolerance of termination criterion (default: 0.001)
  -i, --max_iter arg            set the maximum number of CG iterations (default: num_features)
  -b, --backend arg             choose the backend: automatic|openmp|cuda|hip|opencl|sycl (default: automatic)
  -p, --target_platform arg     choose the target platform: automatic|cpu|gpu_nvidia|gpu_amd|gpu_intel (default: automatic)
      --sycl_kernel_invocation_type arg
                                choose the kernel invocation type when using SYCL as backend: automatic|nd_range|hierarchical (default: automatic)
      --sycl_implementation_type arg
                                choose the SYCL implementation to be used in the SYCL backend: automatic|dpcpp|hipsycl (default: automatic)
      --performance_tracking arg
                                the output YAML file where the performance tracking results are written to; if not provided, the results are dumped to stderr
      --use_strings_as_labels   use strings as labels instead of plane numbers
      --use_float_as_real_type  use floats as real types instead of doubles
      --verbosity               choose the level of verbosity: full|timing|libsvm|quiet (default: full)
  -q, --quiet                   quiet mode (no outputs regardless the provided verbosity level!)
  -h, --help                    print this helper message
  -v, --version                 print version information
      --input training_set_file
                                
      --model model_file

The help message only print options available based on the CMake invocation. For example, if CUDA was not available during the build step, it will not show up as possible backend in the description of the --backend option.

The most minimal example invocation is:

./plssvm-train /path/to/data_file

An example invocation using the CUDA backend could look like:

./plssvm-train --backend cuda --input /path/to/data_file

Another example targeting NVIDIA GPUs using the SYCL backend looks like:

./plssvm-train --backend sycl --target_platform gpu_nvidia --input /path/to/data_file

The --backend=automatic option works as follows:

  • if the gpu_nvidia target is available, check for existing backends in order cuda 🠦 hip 🠦 opencl 🠦 sycl
  • otherwise, if the gpu_amd target is available, check for existing backends in order hip 🠦 opencl 🠦 sycl
  • otherwise, if the gpu_intel target is available, check for existing backends in order sycl 🠦 opencl
  • otherwise, if the cpu target is available, check for existing backends in order sycl 🠦 opencl 🠦 openmp

Note that during CMake configuration it is guaranteed that at least one of the above combinations does exist.

The --target_platform=automatic option works for the different backends as follows:

  • OpenMP: always selects a CPU
  • CUDA: always selects an NVIDIA GPU (if no NVIDIA GPU is available, throws an exception)
  • HIP: always selects an AMD GPU (if no AMD GPU is available, throws an exception)
  • OpenCL: tries to find available devices in the following order: NVIDIA GPUs 🠦 AMD GPUs 🠦 Intel GPUs 🠦 CPU
  • SYCL: tries to find available devices in the following order: NVIDIA GPUs 🠦 AMD GPUs 🠦 Intel GPUs 🠦 CPU

The --sycl_kernel_invocation_type and --sycl_implementation_type flags are only used if the --backend is sycl, otherwise a warning is emitted on stderr. If the --sycl_kernel_invocation_type is automatic, the nd_range invocation type is always used, except for hipSYCL on CPUs where the hierarchical formulation is used instead (if hipSYCL wasn't build with omp.accelerated). If the --sycl_implementation_type is automatic, the used SYCL implementation is determined by the PLSSVM_SYCL_BACKEND_PREFERRED_IMPLEMENTATION cmake flag.

Predicting

./plssvm-preidct --help
LS-SVM with multiple (GPU-)backends
Usage:
  ./plssvm-preidct [OPTION...] test_file model_file [output_file]

  -b, --backend arg             choose the backend: automatic|openmp|cuda|hip|opencl|sycl (default: automatic)
  -p, --target_platform arg     choose the target platform: automatic|cpu|gpu_nvidia|gpu_amd|gpu_intel (default: automatic)
      --sycl_implementation_type arg
                                choose the SYCL implementation to be used in the SYCL backend: automatic|dpcpp|hipsycl (default: automatic)
      --performance_tracking arg
                                the output YAML file where the performance tracking results are written to; if not provided, the results are dumped to stderr
      --use_strings_as_labels   use strings as labels instead of plane numbers
      --use_float_as_real_type  use floats as real types instead of doubles
      --verbosity               choose the level of verbosity: full|timing|libsvm|quiet (default: full)
  -q, --quiet                   quiet mode (no outputs regardless the provided verbosity level!)
  -h, --help                    print this helper message
  -v, --version                 print version information
      --test test_file          
      --model model_file        
      --output output_file

An example invocation could look like:

./plssvm-preidct --backend cuda --test /path/to/test_file --model /path/to/model_file

Another example targeting NVIDIA GPUs using the SYCL backend looks like:

./plssvm-preidct --backend sycl --target_platform gpu_nvidia --test /path/to/test_file --model /path/to/model_file

The --target_platform=automatic and --sycl_implementation_type flags work like in the training (./plssvm-train) case.

Scaling

LS-SVM with multiple (GPU-)backends
Usage:
  ./plssvm-scale [OPTION...] input_file [scaled_file]

  -l, --lower arg               lower is the lowest (minimal) value allowed in each dimension (default: -1)
  -u, --upper arg               upper is the highest (maximal) value allowed in each dimension (default: 1)
  -f, --format arg              the file format to output the scaled data set to (default: libsvm)
  -s, --save_filename arg       the file to which the scaling factors should be saved
  -r, --restore_filename arg    the file from which previous scaling factors should be loaded
      --performance_tracking arg
                                the output YAML file where the performance tracking results are written to; if not provided, the results are dumped to stderr
      --use_strings_as_labels   use strings as labels instead of plane numbers
      --use_float_as_real_type  use floats as real types instead of doubles
      --verbosity               choose the level of verbosity: full|timing|libsvm|quiet (default: full)
  -q, --quiet                   quiet mode (no outputs regardless the provided verbosity level!)
  -h, --help                    print this helper message
  -v, --version                 print version information
      --input input_file        
      --scaled scaled_file

An example invocation could look like:

./plssvm-scale -l -0.5 -u 1.5 --input /path/to/input_file --scaled /path/to/scaled_file

An example invocation to scale a train and test file in the same way looks like:

./plssvm-scale -l -1.0 -u 1.0 -s scaling_parameter.txt train_file.libsvm train_file_scaled.libsvm
./plssvm-scale -r scaling_parameter.txt test_file.libsvm test_file_scaled.libsvm

For more information see the man pages for plssvm-train, plssvm-predict, and plssvm-scale (which are installed via cmake --build . -- install).

Example code for usage as library

A simple C++ program (main.cpp) using this library could look like:

#include "plssvm/core.hpp"

#include <exception>
#include <iostream>
#include <vector>

int main() {
    try {
      
        // create a new C-SVM parameter set, explicitly overriding the default kernel function
        const plssvm::parameter params{ plssvm::kernel_type = plssvm::kernel_function_type::polynomial };

        // create two data sets: one with the training data scaled to [-1, 1] 
        // and one with the test data scaled like the training data
        const plssvm::data_set<double> train_data{ "train_file.libsvm", { -1.0, 1.0 } };
        const plssvm::data_set<double> test_data{ "test_file.libsvm", train_data.scaling_factors()->get() };

        // create C-SVM using the default backend and the previously defined parameter
        const auto svm = plssvm::make_csvm(params);

        // fit using the training data, (optionally) set the termination criterion
        const plssvm::model model = svm->fit(train_data, plssvm::epsilon = 10e-6);

        // get accuracy of the trained model
        const double model_accuracy = svm->score(model);
        std::cout << "model accuracy: " << model_accuracy << std::endl;

        // predict the labels
        const std::vector<int> label = svm->predict(model, test_data);

        // write model file to disk
        model.save("model_file.libsvm");
        
    } catch (const plssvm::exception &e) {
        std::cerr << e.what_with_loc() << std::endl;
    } catch (const std::exception &e) {
        std::cerr << e.what() << std::endl;
    }

    return 0;
}

With a corresponding minimal CMake file:

cmake_minimum_required(VERSION 3.16)

project(LibraryUsageExample
        LANGUAGES CXX)

find_package(plssvm CONFIG REQUIRED)

add_executable(prog main.cpp)

target_compile_features(prog PUBLIC cxx_std_17)
target_link_libraries(prog PUBLIC plssvm::plssvm-all)

Using the Python bindings

Roughly the same can be achieved using our Python bindings with the following Python script:

import plssvm

try:
    # create a new C-SVM parameter set, explicitly overriding the default kernel function
    params = plssvm.Parameter(kernel_type=plssvm.KernelFunctionType.POLYNOMIAL)
  
    # create two data sets: one with the training data scaled to [-1, 1]
    # and one with the test data scaled like the training data
    train_data = plssvm.DataSet("train_data.libsvm", scaling=(-1.0, 1.0))
    test_data = plssvm.DataSet("test_data.libsvm", scaling=train_data.scaling_factors())
  
    # create C-SVM using the default backend and the previously defined parameter
    svm = plssvm.CSVM(params)
  
    # fit using the training data, (optionally) set the termination criterion
    model = svm.fit(train_data, epsilon=10e-6)
  
    # get accuracy of the trained model
    model_accuracy = svm.score(model)
    print("model accuracy: {}".format(model_accuracy))
  
    # predict labels
    label = svm.predict(model, test_data)
  
    # write model file to disk
    model.save("model_file.libsvm")
except plssvm.PLSSVMError as e:
    print(e)
except RuntimeError as e:
    print(e)

Note: it may be necessary to set PYTHONPATH to the lib folder in the PLSSVM install path.

We also provide Python bindings for a plssvm.SVC class that offers the same interface as the sklearn.svm.SVC class. Note that currently not all functionality has been implemented in PLSSVM. The respective functions will throw a Python AttributeError if called.

Citing PLSSVM

If you use PLSSVM in your research, we kindly request you to cite:

@inproceedings{9835379,
  author={Van Craen, Alexander and Breyer, Marcel and Pfl\"{u}ger, Dirk},
  booktitle={2022 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)}, 
  title={PLSSVM: A (multi-)GPGPU-accelerated Least Squares Support Vector Machine}, 
  year={2022},
  volume={},
  number={},
  pages={818-827},
  doi={10.1109/IPDPSW55747.2022.00138}
}

For a full list of all publications involving PLSSVM see our Wiki Page.

License

The PLSSVM library is distributed under the MIT license.