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rapidsai
Kernel PCA: C++ Algorithm Implementation
Description
Worked with @garrisonhess to add C++ code for KernelPCA. This implementation of Kernel PCA supports three functions with float/double matrix input:
- kpcaFit()
- Is used to fit model to input data in fit(X) and fit_transform(X) in KernelPCA
- kpcaTransform()
- Called after fit(X). Is used to support transform(Y). X and Y might be different, so we have to compute the centered gram matrix between training data X and test data Y. See sklearn reference.
- kpcaTransformWithFitData()
- Used after kpcaFit() in fit_transform(X). We don't need to calculate the kernel matrix for X, since it's the same input data used in kpcaFit(). See sklearn reference.
Feature request: https://github.com/rapidsai/cuml/issues/1317
Tests were performed on an EC2 g4dn.xlarge instance with CUDA 12.2.
Click here to see environment details
**git*** commit ade61faff6ac261028bc9b8bbca8b7e67be00d16 (HEAD -> fea-kernel-pca, fork/fea-kernel-pca) Author: Tomas Johannesson <[email protected]> Date: Tue Jul 23 22:01:19 2024 -0500 syntax fix **git submodules*** ***OS Information*** DISTRIB_ID=Ubuntu DISTRIB_RELEASE=22.04 DISTRIB_CODENAME=jammy DISTRIB_DESCRIPTION="Ubuntu 22.04.4 LTS" PRETTY_NAME="Ubuntu 22.04.4 LTS" NAME="Ubuntu" VERSION_ID="22.04" VERSION="22.04.4 LTS (Jammy Jellyfish)" VERSION_CODENAME=jammy ID=ubuntu ID_LIKE=debian HOME_URL="https://www.ubuntu.com/" SUPPORT_URL="https://help.ubuntu.com/" BUG_REPORT_URL="https://bugs.launchpad.net/ubuntu/" PRIVACY_POLICY_URL="https://www.ubuntu.com/legal/terms-and-policies/privacy-policy" UBUNTU_CODENAME=jammy Linux ip-172-31-36-86 6.5.0-1020-aws #20~22.04.1-Ubuntu SMP Wed May 1 16:10:50 UTC 2024 x86_64 x86_64 x86_64 GNU/Linux ***GPU Information*** Thu Jul 25 01:28:58 2024 +---------------------------------------------------------------------------------------+ | NVIDIA-SMI 535.183.01 Driver Version: 535.183.01 CUDA Version: 12.2 | |-----------------------------------------+----------------------+----------------------+ | GPU Name Persistence-M | Bus-Id Disp.A | Volatile Uncorr. ECC | | Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. | | | | MIG M. | |=========================================+======================+======================| | 0 Tesla T4 On | 00000000:00:1E.0 Off | 0 | | N/A 32C P8 14W / 70W | 2MiB / 15360MiB | 0% Default | | | | N/A | +-----------------------------------------+----------------------+----------------------+ +---------------------------------------------------------------------------------------+ | Processes: | | GPU GI CI PID Type Process name GPU Memory | | ID ID Usage | |=======================================================================================| | No running processes found | +---------------------------------------------------------------------------------------+ ***CPU*** Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Address sizes: 46 bits physical, 48 bits virtual Byte Order: Little Endian CPU(s): 4 On-line CPU(s) list: 0-3 Vendor ID: GenuineIntel Model name: Intel(R) Xeon(R) Platinum 8259CL CPU @ 2.50GHz CPU family: 6 Model: 85 Thread(s) per core: 2 Core(s) per socket: 2 Socket(s): 1 Stepping: 7 BogoMIPS: 4999.99 Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid aperfmperf tsc_known_freq pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single pti fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid mpx avx512f avx512dq rdseed adx smap clflushopt clwb avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves ida arat pku ospke avx512_vnni Hypervisor vendor: KVM Virtualization type: full L1d cache: 64 KiB (2 instances) L1i cache: 64 KiB (2 instances) L2 cache: 2 MiB (2 instances) L3 cache: 35.8 MiB (1 instance) NUMA node(s): 1 NUMA node0 CPU(s): 0-3 Vulnerability Gather data sampling: Unknown: Dependent on hypervisor status Vulnerability Itlb multihit: KVM: Mitigation: VMX unsupported Vulnerability L1tf: Mitigation; PTE Inversion Vulnerability Mds: Vulnerable: Clear CPU buffers attempted, no microcode; SMT Host state unknown Vulnerability Meltdown: Mitigation; PTI Vulnerability Mmio stale data: Vulnerable: Clear CPU buffers attempted, no microcode; SMT Host state unknown Vulnerability Retbleed: Vulnerable Vulnerability Spec rstack overflow: Not affected Vulnerability Spec store bypass: Vulnerable Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Retpolines; STIBP disabled; RSB filling; PBRSB-eIBRS Not affected; BHI Retpoline Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Not affected ***CMake*** /home/ubuntu/miniconda3/envs/cuml_dev/bin/cmake cmake version 3.29.6 CMake suite maintained and supported by Kitware (kitware.com/cmake). ***g++*** /home/ubuntu/miniconda3/envs/cuml_dev/bin/g++ g++ (conda-forge gcc 11.4.0-12) 11.4.0 Copyright (C) 2021 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ***nvcc*** /home/ubuntu/miniconda3/envs/cuml_dev/bin/nvcc nvcc: NVIDIA (R) Cuda compiler driver Copyright (c) 2005-2023 NVIDIA Corporation Built on Tue_Aug_15_22:02:13_PDT_2023 Cuda compilation tools, release 12.2, V12.2.140 Build cuda_12.2.r12.2/compiler.33191640_0 ***Python*** /home/ubuntu/miniconda3/envs/cuml_dev/bin/python Python 3.11.9 ***Environment Variables*** PATH : /home/ubuntu/miniconda3/envs/cuml_dev/bin:/home/ubuntu/miniconda3/condabin:/opt/amazon/openmpi/bin:/opt/amazon/efa/bin:/usr/local/cuda-12.1/bin:/usr/local/cuda-12.1/include:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin LD_LIBRARY_PATH : 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Notes for Reviewers
Cython wrapper PR contains more varied unit and manual tests: https://github.com/rapidsai/cuml/pull/5988
C++ unit test reference
Sklearn script to generate C++ test reference data
import numpy as np from sklearn.decomposition import KernelPCA, PCAInput data
n_rows = 3 n_cols = 2 n_components = 2 data = np.array([ [1.0, 4.0], [2.0, 2.0], [5.0, 1.0] ])
Kernel Parameters
class KernelParams: def init(self, kernel, degree=3, gamma=1.0, coef0=1): self.kernel = kernel self.degree = degree self.gamma = gamma self.coef0 = coef0
Define kernel parameters
lin_kern = KernelParams(kernel='linear', degree=0, gamma=0, coef0=0) poly_kern = KernelParams(kernel='poly', degree=3, gamma=1.0/2.0, coef0=1) rbf_kern = KernelParams(kernel='rbf', degree=0, gamma=1.0/2.0, coef0=0)
Function to compute and print kernel matrices
def compute_and_print_kernel_matrices(data, kernel_params, n_components): kpca = KernelPCA(n_components=n_components, kernel=kernel_params.kernel, degree=kernel_params.degree, gamma=kernel_params.gamma, coef0=kernel_params.coef0)
# Fit and transform data transformed_data = kpca.fit_transform(data) # Print results print(f"transformed_data for {kernel_params.kernel} kernel:\n{transformed_data}") print(f"eigenvalues_ for {kernel_params.kernel} kernel:\n{kpca.eigenvalues_}") print(f"eigenvectors_ for {kernel_params.kernel} kernel:\n{kpca.eigenvectors_}")Compute and print kernel matrices for linear, polynomial, and RBF kernels
kernels = [lin_kern, poly_kern, rbf_kern] for kernel_params in kernels: compute_and_print_kernel_matrices(data, kernel_params, n_components)
Output from script and C++ expected values are below. Note that C++ matrices are in column order while Python w. numpy uses row order. Sklearn linear kernel:
transformed_data for linear kernel:
[[-2.32318647 -0.39794495]
[-0.35170213 0.65716145]
[ 2.6748886 -0.25921649]]
eigenvalues_ for linear kernel:
[12.67591879 0.65741454]
eigenvectors_ for linear kernel:
[[-0.65252078 -0.49079864]
[-0.0987837 0.81049889]
[ 0.75130448 -0.31970025]]
C++ test reference:
std::vector<float> lin_trans_data_ref_h = {-2.32318647,-0.35170213, 2.6748886, -0.39794495, 0.65716145,-0.25921649};
std::vector<float> lin_eigenvalues_ref_h = {12.6759, 0.6574};
std::vector<float> lin_eigenvectors_ref_h = {-0.6525, -0.0987, 0.7513, -0.4907, 0.8105, -0.3197};
Sklearn poly kernel:
transformed_data for poly kernel:
[[-22.97601835 -8.84385051]
[-10.85540799 11.24260772]
[ 33.83142634 -2.39875721]]
eigenvalues_ for poly kernel:
[1790.30271016 210.36395651]
eigenvectors_ for poly kernel:
[[-0.54301464 -0.6097555 ]
[-0.25655644 0.77514222]
[ 0.79957107 -0.16538672]]
C++ test reference:
std::vector<float> poly_trans_data_ref_h = {-22.9760, -10.8554, 33.8314, -8.8438, 11.2426, -2.3987};
std::vector<float> poly_eigenvalues_ref_h = {1790.3207, 210.3639};
std::vector<float> poly_eigenvectors_ref_h = {-0.5430, -0.2565, 0.7995, -0.6097, 0.7751, -0.1653};
Sklearn rbf kernel:
transformed_data for rbf kernel:
[[-0.43907684 -0.66248897]
[-0.38619599 0.69140675]
[ 0.82527283 -0.02891778]]
eigenvalues_ for rbf kernel:
[1.02301105 0.91777117]
eigenvectors_ for rbf kernel:
[[-0.43411058 -0.69153067]
[-0.38182784 0.72171613]
[ 0.81593842 -0.03018545]]
C++ test reference:
std::vector<float> rbf_trans_data_ref_h = {-0.4391, -0.3862, 0.8253, -0.6624, 0.6914, -0.0289};
std::vector<float> rbf_eigenvalues_ref_h = {1.0230, 0.9177};
std::vector<float> rbf_eigenvectors_ref_h = {-0.4341, -0.3818, 0.8159, -0.6915, 0.7217, -0.0301};
Definition of Done Criteria Checklist
C++ Checklist
Design
- [x] Existing prims are used wherever possible
- [x] Array inputs and outputs to algorithms are accepted on device
- [x] New prims created wherever there is potential for reuse across different algorithms or prims
- [x] User-facing API is stateless and follows the plain-old data (POD) design paradigm
- [x] Public API contains a C-Wrapper around the stateless API
- [x] ~~(optional) Public API contains an Scikit-learn-like stateful wrapper around the stateless API~~
Testing
- [x] ~~Prims: GTests with different inputs~~
- [x] Algorithms: End-to-end GTests with different inputs and different datasets
Documentation
- [x] Complete and comprehensive Doxygen strings explaining the public API, restrictions, and gotchas. Any array parameters should also note whether the underlying memory is host or device.
- [x] Array inputs/outputs should also mention their expected size/dimension.
- [x] If there are references to the underlying algorithm, they must be cited too.
Unit test results
C++ Test Results
(cuml_dev) ubuntu@ip-172-31-36-86:~/cuml$ ./cpp/build/test/SG_KPCA_TEST Running main() from /home/ubuntu/cuml/cpp/build/_deps/gtest-src/googletest/src/gtest_main.cc [==========] Running 36 tests from 6 test suites. [----------] Global test environment set-up. [----------] 6 tests from KPcaTests/KPcaTestEigenvaluesF [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/0 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/0 (430 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/1 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/2 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/3 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/4 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesF.Result/5 [ OK ] KPcaTests/KPcaTestEigenvaluesF.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestEigenvaluesF (442 ms total)[----------] 6 tests from KPcaTests/KPcaTestEigenvectorsF [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/0 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/0 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/1 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/2 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/3 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/4 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsF.Result/5 [ OK ] KPcaTests/KPcaTestEigenvectorsF.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestEigenvectorsF (13 ms total)
[----------] 6 tests from KPcaTests/KPcaTestTransDataF [ RUN ] KPcaTests/KPcaTestTransDataF.Result/0 [ OK ] KPcaTests/KPcaTestTransDataF.Result/0 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataF.Result/1 [ OK ] KPcaTests/KPcaTestTransDataF.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataF.Result/2 [ OK ] KPcaTests/KPcaTestTransDataF.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataF.Result/3 [ OK ] KPcaTests/KPcaTestTransDataF.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataF.Result/4 [ OK ] KPcaTests/KPcaTestTransDataF.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataF.Result/5 [ OK ] KPcaTests/KPcaTestTransDataF.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestTransDataF (13 ms total)
[----------] 6 tests from KPcaTests/KPcaTestEigenvaluesD [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/0 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/0 (9 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/1 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/2 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/3 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/4 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvaluesD.Result/5 [ OK ] KPcaTests/KPcaTestEigenvaluesD.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestEigenvaluesD (23 ms total)
[----------] 6 tests from KPcaTests/KPcaTestEigenvectorsD [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/0 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/0 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/1 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/2 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/3 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/4 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestEigenvectorsD.Result/5 [ OK ] KPcaTests/KPcaTestEigenvectorsD.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestEigenvectorsD (16 ms total)
[----------] 6 tests from KPcaTests/KPcaTestTransDataD [ RUN ] KPcaTests/KPcaTestTransDataD.Result/0 [ OK ] KPcaTests/KPcaTestTransDataD.Result/0 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataD.Result/1 [ OK ] KPcaTests/KPcaTestTransDataD.Result/1 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataD.Result/2 [ OK ] KPcaTests/KPcaTestTransDataD.Result/2 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataD.Result/3 [ OK ] KPcaTests/KPcaTestTransDataD.Result/3 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataD.Result/4 [ OK ] KPcaTests/KPcaTestTransDataD.Result/4 (2 ms) [ RUN ] KPcaTests/KPcaTestTransDataD.Result/5 [ OK ] KPcaTests/KPcaTestTransDataD.Result/5 (2 ms) [----------] 6 tests from KPcaTests/KPcaTestTransDataD (16 ms total)
[----------] Global test environment tear-down [==========] 36 tests from 6 test suites ran. (525 ms total) [ PASSED ] 36 tests.
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Thanks for the PR. I've given it a look over and I think it's shaping up well. Most of the things are minor, but important to maintenance and quality. Looking forward to having this feature.
Small question- what data scales are you targeting? The unfortunate thing about the naive implementation of kernel algorithms is that they require n^2 space, whereas there are some ways we can make them scale by computing more on the fly (and even sparsifying the kernel gramm by using nearest neighbors methods). Our Kernel APIs also allow for caching and tiling so if we can use an iterative solver, we can scale to much larger datasets without having to resort to multiple GPUs.
Thank you for the review. I have started incorporating most of the requested changes, but still working one replacing one of the raw kernels and tests. I just hit a busy period, so I probably won't be able to make the updates until beginning of October.
Regarding your question on targeted data scales: I observed the algorithm being memory bound in benchmarking. It would be great to be able to support larger matrices. Could we aim for this for V2 of the algorithm? I might need some guidance on the changes needed for kernel caching + tiling.