Improve convergence system for MiniBatch algorithm

[PyDataBlog]

Fixes #113

Improve the convergence system for the MiniBatch algorithm in src/mini_batch.jl and add corresponding tests in test/test90_minibatch.jl.

• Adaptive Batch Size Mechanism

  • Implement an adaptive batch size mechanism that adjusts based on the convergence rate.
  • Modify the batch size dynamically during the iterations.

• Early Stopping Criteria

  • Introduce early stopping criteria by monitoring the change in cluster assignments and the stability of centroids.
  • Add a check to stop the algorithm if the labels and centroids remain unchanged over iterations.

• Tests for New Features

  • Add tests for the adaptive batch size mechanism to ensure it adjusts the batch size correctly based on the convergence rate.
  • Add tests for early stopping criteria to ensure the algorithm stops when the change in cluster assignments or the stability of centroids is detected.
  • Add tests for improved initialization of centroids to ensure the algorithm converges successfully.

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Benchmark result

# Judge result # Benchmark Report for */home/runner/work/ParallelKMeans.jl/ParallelKMeans.jl* ## Job Properties * Time of benchmarks: - Target: 21 Oct 2024 - 18:21 - Baseline: 21 Oct 2024 - 18:22 * Package commits: - Target: 16881e - Baseline: 500f7a * Julia commits: - Target: 3b76b2 - Baseline: 3b76b2 * Julia command flags: - Target: None - Baseline: None * Environment variables: - Target: None - Baseline: None ## Results A ratio greater than `1.0` denotes a possible regression (marked with :x:), while a ratio less than `1.0` denotes a possible improvement (marked with :white_check_mark:). Only significant results - results that indicate possible regressions or improvements - are shown below (thus, an empty table means that all benchmark results remained invariant between builds). | ID | time ratio | memory ratio | |------------------------------------------|------------------------------|--------------| | `["distance", "100kx10"]` | 1.65 (5%) :x: | 1.00 (1%) | | `["distance", "100kx3"]` | 1.51 (5%) :x: | 1.00 (1%) | | `["kmeans", "10x100_000x10x1 Hammerly"]` | 0.89 (5%) :white_check_mark: | 1.00 (1%) | | `["kmeans", "10x100_000x3x1 Hammerly"]` | 0.94 (5%) :white_check_mark: | 1.00 (1%) | | `["kmeans", "10x100_000x3x2 Hammerly"]` | 0.89 (5%) :white_check_mark: | 1.00 (1%) | ## Benchmark Group List Here's a list of all the benchmark groups executed by this job: - `["distance"]` - `["kmeans"]` ## Julia versioninfo ### Target ``` Julia Version 1.6.7 Commit 3b76b25b64 (2022-07-19 15:11 UTC) Platform Info: OS: Linux (x86_64-pc-linux-gnu) Ubuntu 22.04.5 LTS uname: Linux 6.5.0-1025-azure #26~22.04.1-Ubuntu SMP Thu Jul 11 22:33:04 UTC 2024 x86_64 x86_64 CPU: AMD EPYC 7763 64-Core Processor: speed user nice sys idle irq #1 2591 MHz 670 s 0 s 82 s 2700 s 0 s #2 2445 MHz 688 s 0 s 93 s 2666 s 0 s #3 3243 MHz 584 s 0 s 89 s 2780 s 0 s #4 2445 MHz 231 s 0 s 86 s 3130 s 0 s Memory: 15.606491088867188 GB (12445.23828125 MB free) Uptime: 347.47 sec Load Avg: 1.03 0.65 0.28 WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-11.0.1 (ORCJIT, generic) ``` ### Baseline ``` Julia Version 1.6.7 Commit 3b76b25b64 (2022-07-19 15:11 UTC) Platform Info: OS: Linux (x86_64-pc-linux-gnu) Ubuntu 22.04.5 LTS uname: Linux 6.5.0-1025-azure #26~22.04.1-Ubuntu SMP Thu Jul 11 22:33:04 UTC 2024 x86_64 x86_64 CPU: AMD EPYC 7763 64-Core Processor: speed user nice sys idle irq #1 3243 MHz 823 s 0 s 87 s 3284 s 0 s #2 3248 MHz 787 s 0 s 102 s 3303 s 0 s #3 2680 MHz 755 s 0 s 95 s 3346 s 0 s #4 3241 MHz 555 s 0 s 92 s 3546 s 0 s Memory: 15.606491088867188 GB (12482.78515625 MB free) Uptime: 422.06 sec Load Avg: 1.01 0.73 0.34 WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-11.0.1 (ORCJIT, generic) ``` --- # Target result # Benchmark Report for */home/runner/work/ParallelKMeans.jl/ParallelKMeans.jl* ## Job Properties * Time of benchmark: 21 Oct 2024 - 18:21 * Package commit: 16881e * Julia commit: 3b76b2 * Julia command flags: None * Environment variables: None ## Results Below is a table of this job's results, obtained by running the benchmarks. The values listed in the `ID` column have the structure `[parent_group, child_group, ..., key]`, and can be used to index into the BaseBenchmarks suite to retrieve the corresponding benchmarks. The percentages accompanying time and memory values in the below table are noise tolerances. The "true" time/memory value for a given benchmark is expected to fall within this percentage of the reported value. An empty cell means that the value was zero. | ID | time | GC time | memory | allocations | |------------------------------------------|----------------:|--------:|----------------:|------------:| | `["distance", "100kx10"]` | 682.004 μs (5%) | | | | | `["distance", "100kx3"]` | 248.033 μs (5%) | | | | | `["kmeans", "10x100_000x10x1 Lloyd"]` | 1.046 s (5%) | | 785.55 KiB (1%) | 18 | | `["kmeans", "10x100_000x10x1 Hammerly"]` | 472.588 ms (5%) | | 2.29 MiB (1%) | 21 | | `["kmeans", "10x100_000x10x2 Lloyd"]` | 1.047 s (5%) | | 929.20 KiB (1%) | 1569 | | `["kmeans", "10x100_000x10x2 Hammerly"]` | 557.046 ms (5%) | | 2.59 MiB (1%) | 2904 | | `["kmeans", "10x100_000x3x1 Lloyd"]` | 126.322 ms (5%) | | 783.72 KiB (1%) | 18 | | `["kmeans", "10x100_000x3x1 Hammerly"]` | 141.633 ms (5%) | | 2.29 MiB (1%) | 21 | | `["kmeans", "10x100_000x3x2 Lloyd"]` | 126.390 ms (5%) | | 819.08 KiB (1%) | 399 | | `["kmeans", "10x100_000x3x2 Hammerly"]` | 142.277 ms (5%) | | 2.41 MiB (1%) | 1224 | ## Benchmark Group List Here's a list of all the benchmark groups executed by this job: - `["distance"]` - `["kmeans"]` ## Julia versioninfo ``` Julia Version 1.6.7 Commit 3b76b25b64 (2022-07-19 15:11 UTC) Platform Info: OS: Linux (x86_64-pc-linux-gnu) Ubuntu 22.04.5 LTS uname: Linux 6.5.0-1025-azure #26~22.04.1-Ubuntu SMP Thu Jul 11 22:33:04 UTC 2024 x86_64 x86_64 CPU: AMD EPYC 7763 64-Core Processor: speed user nice sys idle irq #1 2591 MHz 670 s 0 s 82 s 2700 s 0 s #2 2445 MHz 688 s 0 s 93 s 2666 s 0 s #3 3243 MHz 584 s 0 s 89 s 2780 s 0 s #4 2445 MHz 231 s 0 s 86 s 3130 s 0 s Memory: 15.606491088867188 GB (12445.23828125 MB free) Uptime: 347.47 sec Load Avg: 1.03 0.65 0.28 WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-11.0.1 (ORCJIT, generic) ``` --- # Baseline result # Benchmark Report for */home/runner/work/ParallelKMeans.jl/ParallelKMeans.jl* ## Job Properties * Time of benchmark: 21 Oct 2024 - 18:22 * Package commit: 500f7a * Julia commit: 3b76b2 * Julia command flags: None * Environment variables: None ## Results Below is a table of this job's results, obtained by running the benchmarks. The values listed in the `ID` column have the structure `[parent_group, child_group, ..., key]`, and can be used to index into the BaseBenchmarks suite to retrieve the corresponding benchmarks. The percentages accompanying time and memory values in the below table are noise tolerances. The "true" time/memory value for a given benchmark is expected to fall within this percentage of the reported value. An empty cell means that the value was zero. | ID | time | GC time | memory | allocations | |------------------------------------------|----------------:|--------:|----------------:|------------:| | `["distance", "100kx10"]` | 412.200 μs (5%) | | | | | `["distance", "100kx3"]` | 164.378 μs (5%) | | | | | `["kmeans", "10x100_000x10x1 Lloyd"]` | 1.050 s (5%) | | 785.55 KiB (1%) | 18 | | `["kmeans", "10x100_000x10x1 Hammerly"]` | 529.350 ms (5%) | | 2.29 MiB (1%) | 21 | | `["kmeans", "10x100_000x10x2 Lloyd"]` | 1.054 s (5%) | | 929.20 KiB (1%) | 1569 | | `["kmeans", "10x100_000x10x2 Hammerly"]` | 540.309 ms (5%) | | 2.59 MiB (1%) | 2904 | | `["kmeans", "10x100_000x3x1 Lloyd"]` | 126.180 ms (5%) | | 783.72 KiB (1%) | 18 | | `["kmeans", "10x100_000x3x1 Hammerly"]` | 149.985 ms (5%) | | 2.29 MiB (1%) | 21 | | `["kmeans", "10x100_000x3x2 Lloyd"]` | 126.461 ms (5%) | | 819.08 KiB (1%) | 399 | | `["kmeans", "10x100_000x3x2 Hammerly"]` | 159.252 ms (5%) | | 2.41 MiB (1%) | 1224 | ## Benchmark Group List Here's a list of all the benchmark groups executed by this job: - `["distance"]` - `["kmeans"]` ## Julia versioninfo ``` Julia Version 1.6.7 Commit 3b76b25b64 (2022-07-19 15:11 UTC) Platform Info: OS: Linux (x86_64-pc-linux-gnu) Ubuntu 22.04.5 LTS uname: Linux 6.5.0-1025-azure #26~22.04.1-Ubuntu SMP Thu Jul 11 22:33:04 UTC 2024 x86_64 x86_64 CPU: AMD EPYC 7763 64-Core Processor: speed user nice sys idle irq #1 3243 MHz 823 s 0 s 87 s 3284 s 0 s #2 3248 MHz 787 s 0 s 102 s 3303 s 0 s #3 2680 MHz 755 s 0 s 95 s 3346 s 0 s #4 3241 MHz 555 s 0 s 92 s 3546 s 0 s Memory: 15.606491088867188 GB (12482.78515625 MB free) Uptime: 422.06 sec Load Avg: 1.01 0.73 0.34 WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-11.0.1 (ORCJIT, generic) ``` --- # Runtime information | Runtime Info | | |:--|:--| | BLAS #threads | 4 | | `BLAS.vendor()` | `openblas64` | | `Sys.CPU_THREADS` | 4 | `lscpu` output: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Address sizes: 48 bits physical, 48 bits virtual Byte Order: Little Endian CPU(s): 4 On-line CPU(s) list: 0-3 Vendor ID: AuthenticAMD Model name: AMD EPYC 7763 64-Core Processor CPU family: 25 Model: 1 Thread(s) per core: 2 Core(s) per socket: 2 Socket(s): 1 Stepping: 1 BogoMIPS: 4890.85 Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl tsc_reliable nonstop_tsc cpuid extd_apicid aperfmperf pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 movbe popcnt aes xsave avx f16c rdrand hypervisor lahf_lm cmp_legacy svm cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw topoext invpcid_single vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves clzero xsaveerptr rdpru arat npt nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold v_vmsave_vmload umip vaes vpclmulqdq rdpid fsrm Virtualization: AMD-V Hypervisor vendor: Microsoft Virtualization type: full L1d cache: 64 KiB (2 instances) L1i cache: 64 KiB (2 instances) L2 cache: 1 MiB (2 instances) L3 cache: 32 MiB (1 instance) NUMA node(s): 1 NUMA node0 CPU(s): 0-3 Vulnerability Gather data sampling: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Retbleed: Not affected Vulnerability Spec rstack overflow: Vulnerable: Safe RET, no microcode 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 Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Not affected | Cpu Property | Value | |:------------------ |:---------------------------------------------------------- | | Brand | AMD EPYC 7763 64-Core Processor | | Vendor | :AMD | | Architecture | :Unknown | | Model | Family: 0xaf, Model: 0x01, Stepping: 0x01, Type: 0x00 | | Cores | 16 physical cores, 16 logical cores (on executing CPU) | | | No Hyperthreading hardware capability detected | | Clock Frequencies | Not supported by CPU | | Data Cache | Level 1:3 : (32, 512, 32768) kbytes | | | 64 byte cache line size | | Address Size | 48 bits virtual, 48 bits physical | | SIMD | 256 bit = 32 byte max. SIMD vector size | | Time Stamp Counter | TSC is accessible via `rdtsc` | | | TSC runs at constant rate (invariant from clock frequency) | | Perf. Monitoring | Performance Monitoring Counters (PMC) are not supported | | Hypervisor | Yes, Microsoft |