Clustering Results with Large Errors on Low-Dimension Vectors

Open ToKliar opened this issue 2 years ago • 2 comments

Summary

When I use the Clustering class in faiss to cluster a number of low-dimension vectors with very distinct categories several times, I find that a certain number of clusters in the clustering results are very different from the actual clustering centers occasionally. The results are shown below. The absolute value of each dimension of the clustering centers should be in the range of [110, 120].

This error is episodic, occurring once in thousands of iterations。

The test file is attached.

Clustering Config

Dimension：8 Number of Vectors：256 Number of Clustering Centers：4

Platform

OS: Ubuntu 20.04

Faiss version: git commit, 4bfdd4324f89d62ae5c494f8b14170d073f259fc

Installed from: compiled by myself

Faiss compilation options: using MKL with compile flags

Running on:

Interface:

Error Output

Preprocessing in 0.00 s Iteration 24 (3.57 s search 2.14 s): objective-6.53359e+06 imbalance=1.318 nsplit-0 centroids: [0] :117.000999, 118.111115, 117.055557, 117.277779, 115.833336, 117.555557, 116.722221, 120.000000 [1] :116.391891, 115.581085, 117.445946, 116.554054, 117.770271, 116.878380, 116.594597, 114.729729 [2] :-116.936981, 3.138656, -116.609253, 2.735294, -116.634460, 3.163866, -117.025215, 2.420168 [3] :117.390411, 117.082191, 116.547943, -117.472603, 117.061646, -117.143837, 117.513695, -116.691789

Test File

#include <random>
#include "faiss/Clustering.h"
#include "faiss/IndexFlat.h"
using namespace faiss;

ClusteringParameters DefaultParams() {
    ClusteringParameters params;
    params.niter = 25;
    params.nredo = 1;
    params.verbose = true;
    return params;
}

template <typename VT>
std::string VectorStr(VT vec, const std::string& name) {
    std::string str;
    str += name + ":";
    if (vec.empty()) {
        str += "empty\n";
        return str;
    }
    str += "[";
    for (const auto& v : vec) {
        str += std::to_string(v) + " ";
    }
    str += "]\n";
    return str;
}

std::string FMatrixToStr(
        const float* mtx,
        int row,
        int col,
        int rowlimit = -1,
        int collimit = -1) {
    std::string str;
    int printRows = rowlimit > 0 ? std::min(row, rowlimit) - 1 : row;
    int printCols = collimit > 0 ? std::min(col, collimit) - 1 : col;
    for (int i = 0; i < printRows; ++i) {
        str += "[" + std::to_string(i) + "] :";
        for (int j = 0; j < printCols; ++j) {
            str += std::to_string(mtx[i * col + j]);
            if (j < printCols - 1)
                str += ", ";
        }
        if (printCols < col) {
            str += ", ..., " + std::to_string(mtx[i * col + col - 1]);
        }
        str += "\n";
    }
    if (printRows < row) {
        str += "...\n";
        str += "[" + std::to_string(row - 1) + "] :";
        for (int j = 0; j < printCols; ++j) {
            str += std::to_string(mtx[(row - 1) * col + j]);
            if (j < printCols - 1)
                str += ", ";
        }
        if (printCols < col) {
            str += "..., " + std::to_string(mtx[(row - 1) * col + col - 1]);
        }
        str += "\n";
    }
    return str;
}

Clustering* GetClustering(
        int d,
        int nx,
        int nlist,
        Index** quantizer,
        const ClusteringParameters& cp = DefaultParams()) {
    if (!*quantizer)
        *quantizer = new IndexFlatL2(d);
    Clustering* cluster = new Clustering(d, nlist, cp);
    return cluster;
}

int main() {
    int nRun = 10000;
    for (int i = 0; i < nRun; ++i) {
        const int d = 8;
        int nx = 256;
        int nlist = 4;
        float mean = 117;
        float std = 1.5;
        std::default_random_engine gen;
        std::uniform_int_distribution<int> dist(-3, 3);
        int groups[4][2] = {{1, 1}, {-1, 1}, {-1, -1}, {1, -1}};
        std::vector<float> vecs(nx * d);

        for (int i = 0; i < nx; ++i) {
            int idx = rand();
            for (int j = 0; j < d; ++j) {
                float group_mean;
                group_mean = mean * groups[idx % 4][j % 2];
                int std_num = dist(gen);
                vecs[i * d + j] = group_mean + std_num * std;
            }
        }

        Index* quantizer = nullptr;
        Clustering* cluster = GetClustering(d, nx, nlist, &quantizer);

        cluster->train(nx, vecs.data(), *quantizer);
        const std::vector<float>& centroids = cluster->centroids;
        auto precisionEqual = [&](float a, float b) {
            return fabs(fabs(a) - fabs(b)) <= std * 2.;
        };

        for (const float& a : centroids) {
            if (!precisionEqual(a, mean)) {
                std::fprintf(
                        stdout,
                        "%s\n",
                        FMatrixToStr(vecs.data(), nx, d).data());
                std::fprintf(
                        stdout,
                        "centroids: \n%s",
                        FMatrixToStr(centroids.data(), nlist, d).c_str());
                delete cluster;
                delete quantizer;
                return -1;
            }
        }
        delete cluster;
        delete quantizer;
    }
    return 0;
}

Sep 20 '23 08:09 ToKliar

Do you have the log of the kmeans run (with verbose=true) ?

Sep 27 '23 14:09 mdouze

Do you have the log of the kmeans run (with verbose=true) ?

Clustering 256 points in 8D to 4 clusters, redo 1 times, 25 iterations
  Preprocessing in 0.00 s
  Iteration 0 (0.00 s, search 0.00 s): objective=1.25164e+07 imbalance=1.178 nsplit=0       
  Iteration 1 (0.00 s, search 0.00 s): objective=6.60736e+06 imbalance=1.440 nsplit=1       
  Iteration 2 (0.00 s, search 0.00 s): objective=6.53412e+06 imbalance=1.315 nsplit=0       
  Iteration 3 (0.00 s, search 0.00 s): objective=6.53367e+06 imbalance=1.316 nsplit=0       
  Iteration 4 (0.00 s, search 0.00 s): objective=6.53363e+06 imbalance=1.318 nsplit=0       
  Iteration 5 (0.00 s, search 0.00 s): objective=6.53361e+06 imbalance=1.318 nsplit=0       
  Iteration 6 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 7 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 8 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 9 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 10 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 11 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 12 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 13 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 14 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 15 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 16 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 17 (0.00 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 18 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 19 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 20 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 21 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 22 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 23 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
  Iteration 24 (0.01 s, search 0.00 s): objective=6.53359e+06 imbalance=1.318 nsplit=0       
[0] :112.500000, 112.500000, 120.000000, 117.000000, 117.000000, 114.000000, 112.500000, 118.500000
[1] :118.500000, -112.500000, 115.500000, -117.000000, 120.000000, -121.500000, 112.500000, -117.000000
[2] :-115.500000, 112.500000, -118.500000, 112.500000, -118.500000, 118.500000, -115.500000, 121.500000
[3] :-114.000000, 117.000000, -121.500000, 118.500000, -118.500000, 118.500000, -112.500000, 120.000000
[4] :114.000000, -121.500000, 120.000000, -118.500000, 118.500000, -114.000000, 121.500000, -118.500000
[5] :114.000000, 121.500000, 120.000000, 120.000000, 118.500000, 112.500000, 118.500000, 121.500000
[6] :114.000000, 117.000000, 120.000000, 117.000000, 114.000000, 114.000000, 115.500000, 114.000000
[7] :-117.000000, 121.500000, -112.500000, 112.500000, -112.500000, 117.000000, -117.000000, 115.500000
[8] :-112.500000, -117.000000, -120.000000, -121.500000, -112.500000, -121.500000, -117.000000, -118.500000
[9] :-120.000000, 121.500000, -117.000000, 117.000000, -112.500000, 112.500000, -114.000000, 120.000000
[10] :120.000000, -121.500000, 112.500000, -115.500000, 121.500000, -115.500000, 120.000000, -114.000000
[11] :121.500000, -112.500000, 114.000000, -118.500000, 115.500000, -117.000000, 118.500000, -114.000000
[12] :-118.500000, 120.000000, -120.000000, 115.500000, -117.000000, 117.000000, -118.500000, 114.000000
[13] :114.000000, 118.500000, 120.000000, 112.500000, 117.000000, 117.000000, 121.500000, 120.000000
[14] :-117.000000, -112.500000, -115.500000, -114.000000, -120.000000, -120.000000, -114.000000, -121.500000
[15] :112.500000, -120.000000, 112.500000, -118.500000, 112.500000, -115.500000, 121.500000, -120.000000
[16] :114.000000, 115.500000, 121.500000, 118.500000, 114.000000, 118.500000, 115.500000, 115.500000
[17] :-117.000000, 114.000000, -115.500000, 120.000000, -115.500000, 121.500000, -117.000000, 114.000000
[18] :-112.500000, -118.500000, -121.500000, -117.000000, -120.000000, -117.000000, -117.000000, -112.500000
[19] :112.500000, -120.000000, 115.500000, -115.500000, 112.500000, -115.500000, 118.500000, -114.000000
[20] :114.000000, -117.000000, 115.500000, -120.000000, 112.500000, -112.500000, 115.500000, -121.500000
[21] :121.500000, -118.500000, 112.500000, -112.500000, 112.500000, -120.000000, 112.500000, -118.500000
[22] :-120.000000, 112.500000, -114.000000, 117.000000, -118.500000, 117.000000, -114.000000, 121.500000
[23] :-115.500000, -120.000000, -115.500000, -112.500000, -120.000000, -112.500000, -117.000000, -117.000000
[24] :-115.500000, 120.000000, -114.000000, 117.000000, -112.500000, 118.500000, -117.000000, 120.000000
[25] :-115.500000, -115.500000, -112.500000, -112.500000, -114.000000, -118.500000, -117.000000, -117.000000
[26] :112.500000, 115.500000, 118.500000, 121.500000, 117.000000, 120.000000, 121.500000, 120.000000
[27] :-114.000000, -115.500000, -114.000000, -121.500000, -112.500000, -117.000000, -117.000000, -121.500000
[28] :118.500000, 117.000000, 118.500000, 118.500000, 114.000000, 121.500000, 121.500000, 121.500000
[29] :-117.000000, -121.500000, -117.000000, -112.500000, -120.000000, -117.000000, -118.500000, -117.000000
[30] :121.500000, -117.000000, 117.000000, -114.000000, 115.500000, -120.000000, 121.500000, -120.000000
[31] :118.500000, 118.500000, 112.500000, 112.500000, 120.000000, 120.000000, 115.500000, 115.500000
[32] :-115.500000, 118.500000, -120.000000, 120.000000, -115.500000, 120.000000, -121.500000, 112.500000
[33] :120.000000, 118.500000, 114.000000, 114.000000, 112.500000, 115.500000, 121.500000, 121.500000
[34] :-118.500000, 114.000000, -115.500000, 114.000000, -114.000000, 120.000000, -118.500000, 114.000000
[35] :114.000000, 112.500000, 114.000000, 121.500000, 114.000000, 120.000000, 112.500000, 115.500000
[36] :118.500000, 114.000000, 120.000000, 114.000000, 121.500000, 114.000000, 114.000000, 112.500000
[37] :-120.000000, -115.500000, -115.500000, -114.000000, -115.500000, -114.000000, -115.500000, -115.500000
[38] :-121.500000, -115.500000, -120.000000, -118.500000, -115.500000, -121.500000, -114.000000, -117.000000
[39] :-117.000000, -115.500000, -118.500000, -115.500000, -120.000000, -120.000000, -117.000000, -112.500000
[40] :120.000000, -117.000000, 120.000000, -118.500000, 112.500000, -117.000000, 115.500000, -115.500000
[41] :-117.000000, 117.000000, -120.000000, 115.500000, -118.500000, 117.000000, -117.000000, 115.500000
[42] :-120.000000, 112.500000, -118.500000, 114.000000, -115.500000, 118.500000, -117.000000, 120.000000
[43] :120.000000, 121.500000, 117.000000, 121.500000, 115.500000, 117.000000, 117.000000, 118.500000
[44] :-118.500000, 118.500000, -112.500000, 114.000000, -115.500000, 115.500000, -117.000000, 117.000000
[45] :120.000000, 112.500000, 114.000000, 118.500000, 117.000000, 121.500000, 114.000000, 121.500000
[46] :114.000000, -114.000000, 118.500000, -117.000000, 120.000000, -121.500000, 114.000000, -115.500000
[47] :-115.500000, 117.000000, -115.500000, 120.000000, -112.500000, 118.500000, -120.000000, 120.000000
[48] :-120.000000, 112.500000, -117.000000, 112.500000, -120.000000, 121.500000, -114.000000, 120.000000
[49] :-117.000000, 112.500000, -115.500000, 117.000000, -121.500000, 117.000000, -118.500000, 114.000000
[50] :115.500000, 118.500000, 118.500000, 118.500000, 117.000000, 114.000000, 120.000000, 115.500000
[51] :118.500000, 115.500000, 112.500000, 112.500000, 117.000000, 120.000000, 114.000000, 112.500000
[52] :-121.500000, 114.000000, -114.000000, 115.500000, -121.500000, 117.000000, -117.000000, 117.000000
[53] :-117.000000, 114.000000, -118.500000, 120.000000, -115.500000, 118.500000, -115.500000, 115.500000
[54] :112.500000, -112.500000, 117.000000, -121.500000, 120.000000, -121.500000, 115.500000, -117.000000
[55] :-115.500000, -114.000000, -115.500000, -117.000000, -121.500000, -121.500000, -112.500000, -120.000000
[56] :115.500000, -115.500000, 118.500000, -121.500000, 117.000000, -112.500000, 115.500000, -114.000000
[57] :121.500000, -120.000000, 114.000000, -118.500000, 120.000000, -112.500000, 114.000000, -114.000000
[58] :-115.500000, 117.000000, -120.000000, 118.500000, -121.500000, 114.000000, -121.500000, 117.000000
[59] :112.500000, -120.000000, 118.500000, -117.000000, 112.500000, -115.500000, 115.500000, -114.000000
[60] :-121.500000, 121.500000, -121.500000, 112.500000, -117.000000, 120.000000, -112.500000, 114.000000
[61] :115.500000, 120.000000, 117.000000, 120.000000, 118.500000, 118.500000, 120.000000, 112.500000
[62] :114.000000, 114.000000, 117.000000, 118.500000, 118.500000, 115.500000, 114.000000, 114.000000
[63] :118.500000, -120.000000, 120.000000, -120.000000, 112.500000, -115.500000, 112.500000, -112.500000
[64] :117.000000, 118.500000, 121.500000, 112.500000, 118.500000, 120.000000, 117.000000, 112.500000
[65] :-117.000000, 117.000000, -114.000000, 112.500000, -117.000000, 121.500000, -117.000000, 115.500000
[66] :117.000000, -114.000000, 114.000000, -120.000000, 115.500000, -112.500000, 121.500000, -120.000000
[67] :112.500000, 112.500000, 117.000000, 114.000000, 117.000000, 112.500000, 120.000000, 115.500000
[68] :115.500000, -118.500000, 118.500000, -115.500000, 121.500000, -114.000000, 120.000000, -115.500000
[69] :-118.500000, 121.500000, -115.500000, 115.500000, -117.000000, 117.000000, -118.500000, 114.000000
[70] :112.500000, -118.500000, 117.000000, -118.500000, 112.500000, -120.000000, 120.000000, -117.000000
[71] :-115.500000, -112.500000, -120.000000, -115.500000, -120.000000, -118.500000, -121.500000, -117.000000
[72] :-120.000000, -114.000000, -117.000000, -121.500000, -120.000000, -115.500000, -118.500000, -120.000000
[73] :121.500000, 112.500000, 120.000000, 121.500000, 114.000000, 118.500000, 112.500000, 115.500000
[74] :-118.500000, -117.000000, -114.000000, -114.000000, -114.000000, -118.500000, -114.000000, -115.500000
[75] :112.500000, 112.500000, 114.000000, 120.000000, 112.500000, 117.000000, 121.500000, 114.000000
[76] :114.000000, 112.500000, 118.500000, 118.500000, 117.000000, 114.000000, 118.500000, 115.500000
[77] :-120.000000, 114.000000, -117.000000, 117.000000, -112.500000, 121.500000, -117.000000, 112.500000
[78] :-117.000000, 112.500000, -114.000000, 118.500000, -114.000000, 115.500000, -120.000000, 117.000000
[79] :-117.000000, -118.500000, -112.500000, -112.500000, -114.000000, -112.500000, -118.500000, -120.000000
[80] :121.500000, -115.500000, 117.000000, -112.500000, 118.500000, -114.000000, 117.000000, -115.500000
[81] :-120.000000, -112.500000, -114.000000, -120.000000, -121.500000, -118.500000, -121.500000, -121.500000
[82] :-117.000000, -121.500000, -117.000000, -114.000000, -117.000000, -115.500000, -114.000000, -115.500000
[83] :112.500000, 114.000000, 118.500000, 115.500000, 112.500000, 112.500000, 121.500000, 114.000000
[84] :115.500000, -115.500000, 114.000000, -121.500000, 118.500000, -114.000000, 118.500000, -121.500000
[85] :-115.500000, 121.500000, -112.500000, 117.000000, -117.000000, 120.000000, -112.500000, 118.500000
[86] :-114.000000, -117.000000, -117.000000, -120.000000, -112.500000, -115.500000, -120.000000, -117.000000
[87] :118.500000, -115.500000, 112.500000, -117.000000, 118.500000, -115.500000, 117.000000, -115.500000
[88] :-115.500000, 117.000000, -120.000000, 117.000000, -114.000000, 112.500000, -121.500000, 117.000000
[89] :115.500000, -121.500000, 114.000000, -121.500000, 115.500000, -117.000000, 118.500000, -115.500000
[90] :-112.500000, -114.000000, -117.000000, -117.000000, -115.500000, -115.500000, -118.500000, -117.000000
[91] :-117.000000, -115.500000, -117.000000, -120.000000, -115.500000, -120.000000, -115.500000, -117.000000
[92] :121.500000, -120.000000, 115.500000, -115.500000, 120.000000, -112.500000, 118.500000, -114.000000
[93] :-117.000000, -120.000000, -120.000000, -112.500000, -120.000000, -115.500000, -121.500000, -112.500000
[94] :-120.000000, 121.500000, -120.000000, 121.500000, -117.000000, 112.500000, -118.500000, 118.500000
[95] :117.000000, -121.500000, 120.000000, -121.500000, 117.000000, -118.500000, 115.500000, -114.000000
[96] :115.500000, 115.500000, 112.500000, 118.500000, 117.000000, 114.000000, 112.500000, 121.500000
[97] :-112.500000, 117.000000, -118.500000, 120.000000, -120.000000, 114.000000, -121.500000, 114.000000
[98] :117.000000, 115.500000, 121.500000, 115.500000, 115.500000, 118.500000, 115.500000, 112.500000
[99] :120.000000, -112.500000, 121.500000, -112.500000, 120.000000, -120.000000, 118.500000, -121.500000
[100] :-114.000000, -117.000000, -112.500000, -120.000000, -112.500000, -115.500000, -118.500000, -114.000000
[101] :117.000000, -112.500000, 115.500000, -115.500000, 120.000000, -112.500000, 115.500000, -120.000000
[102] :-114.000000, -114.000000, -112.500000, -121.500000, -115.500000, -112.500000, -118.500000, -121.500000
[103] :-120.000000, 115.500000, -121.500000, 118.500000, -117.000000, 120.000000, -112.500000, 120.000000
[104] :118.500000, -112.500000, 121.500000, -117.000000, 112.500000, -118.500000, 115.500000, -115.500000
[105] :112.500000, 112.500000, 114.000000, 117.000000, 118.500000, 114.000000, 115.500000, 121.500000
[106] :-115.500000, 118.500000, -112.500000, 115.500000, -112.500000, 120.000000, -117.000000, 112.500000
[107] :117.000000, 117.000000, 117.000000, 117.000000, 120.000000, 121.500000, 115.500000, 114.000000
[108] :-121.500000, -121.500000, -112.500000, -118.500000, -120.000000, -112.500000, -114.000000, -120.000000
[109] :-121.500000, -120.000000, -118.500000, -115.500000, -117.000000, -115.500000, -117.000000, -118.500000
[110] :-118.500000, -115.500000, -117.000000, -120.000000, -115.500000, -112.500000, -115.500000, -118.500000
[111] :-114.000000, 120.000000, -114.000000, 115.500000, -121.500000, 117.000000, -115.500000, 118.500000
[112] :118.500000, 120.000000, 115.500000, 115.500000, 115.500000, 115.500000, 118.500000, 114.000000
[113] :115.500000, 118.500000, 120.000000, 115.500000, 114.000000, 118.500000, 112.500000, 121.500000
[114] :-118.500000, 117.000000, -118.500000, 114.000000, -118.500000, 120.000000, -121.500000, 118.500000
[115] :112.500000, 117.000000, 115.500000, 114.000000, 120.000000, 118.500000, 112.500000, 120.000000
[116] :-117.000000, -118.500000, -118.500000, -118.500000, -117.000000, -114.000000, -114.000000, -120.000000
[117] :117.000000, -118.500000, 112.500000, -121.500000, 114.000000, -117.000000, 120.000000, -118.500000
[118] :120.000000, -118.500000, 114.000000, -118.500000, 121.500000, -115.500000, 115.500000, -117.000000
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[1] :116.391891, 115.581085, 117.445946, 116.554054, 117.770271, 116.878380, 116.594597, 114.729729
[2] :-116.936981, 3.138656, -116.609253, 2.735294, -116.634460, 3.163866, -117.025215, 2.420168
[3] :117.390411, -117.082191, 116.547943, -117.472603, 117.061646, -117.143837, 117.513695, -116.691780

Sep 28 '23 02:09 ToKliar