Online Non-negative Matrix Factorization
OnlineNMF.jl performs some online-NMF functions for extreamly large scale matrix.
Note: The input matrix is supposed to be a non-negative matrix.
- Multiplicative Update (MU)
- Alpha-divergence: Cichocki, A. et al., 2008
- Alpha=2 : Pearson divergence-based NMF
- Alpha=0 or 1 : Kullback–Leibler (KL) divergence-based NMF
- Alpha=0.5 : Hellinger divergence-based NMF
- Beta-divergence: Févotte, C. et al., 2011, Nakano, M. et al., 2010
- Beta=2 : Euclidean distance-based NMF with Gaussian distribution
- Beta=1 : Kullback–Leibler divergence-based NMF with Poisson distribution
- Beta=0 : Itakura-Saito divergence-based NMF with Gamma distribution
- Alpha-divergence: Cichocki, A. et al., 2008
- Discretized Non-negative Matrix Factorization (DNMF): Koki Tsuyuzaki, 2023
# push the key "]" and type the following command.
(@julia) pkg> add https://github.com/rikenbit/OnlineNMF.jl
(@julia) pkg> add PlotlyJS
# After that, push Ctrl + C to leave from Pkg REPL modeusing OnlinePCA
using OnlinePCA: write_csv
using OnlineNMF
using Distributions
using DelimitedFiles
using SparseArrays
using MatrixMarket
# CSV（Input data is supposed to be non-negative Integer）
tmp = mktempdir()
data = rand(Binomial(10, 0.05), 300, 99)
data[1:50, 1:33] .= 100*data[1:50, 1:33]
data[51:100, 34:66] .= 100*data[51:100, 34:66]
data[101:150, 67:99] .= 100*data[101:150, 67:99]
write_csv(joinpath(tmp, "Data.csv"), data)
# Matrix Market (MM)
mmwrite(joinpath(tmp, "Data.mtx"), sparse(data))
# Binary COO (BinCOO)
data2 = zeros(Int, 300, 99)
data2[1:50, 1:33] .= 1
data2[51:100, 34:66] .= 1
data2[101:150, 67:99] .= 1
data2[151:300, :] .= 1
bincoofile = joinpath(tmp, "Data.bincoo")
open(bincoofile, "w") do io
for i in 1:size(data2, 1)
for j in 1:size(data2, 2)
if data2[i, j] != 0
println(io, "$i $j")
end
end
end
end
# Binarization (Zstandard)
csv2bin(csvfile=joinpath(tmp, "Data.csv"), binfile=joinpath(tmp, "Data.zst"))
# Sparsification (Zstandard + MM format)
mm2bin(mmfile=joinpath(tmp, "Data.mtx"), binfile=joinpath(tmp, "Data.mtx.zst"))
# Binarziation (BinCOO + Zstandard)
bincoo2bin(bincoofile=bincoofile, binfile=joinpath(tmp, "Data.bincoo.zst"))using DataFrames
using PlotlyJS
function subplots(out_nmf, group)
# data frame
data_left = DataFrame(nmf1=out_nmf[1][:,1], nmf2=out_nmf[1][:,2], group=group)
data_right = DataFrame(nmf2=out_nmf[1][:,2], nmf3=out_nmf[1][:,3], group=group)
# plot
p_left = Plot(data_left, x=:nmf1, y=:nmf2, mode="markers", marker_size=10, group=:group)
p_right = Plot(data_right, x=:nmf2, y=:nmf3, mode="markers", marker_size=10,
group=:group, showlegend=false)
p_left.data[1]["marker_color"] = "red"
p_left.data[2]["marker_color"] = "blue"
p_left.data[3]["marker_color"] = "green"
p_right.data[1]["marker_color"] = "red"
p_right.data[2]["marker_color"] = "blue"
p_right.data[3]["marker_color"] = "green"
p_left.data[1]["name"] = "group1"
p_left.data[2]["name"] = "group2"
p_left.data[3]["name"] = "group3"
p_left.layout["title"] = "Component 1 vs Component 2"
p_right.layout["title"] = "Component 2 vs Component 3"
p_left.layout["xaxis_title"] = "nmf-1"
p_left.layout["yaxis_title"] = "nmf-2"
p_right.layout["xaxis_title"] = "nmf-2"
p_right.layout["yaxis_title"] = "nmf-3"
plot([p_left p_right])
end
group=vcat(repeat(["group1"],inner=100), repeat(["group2"],inner=100), repeat(["group3"],inner=100))out_nmf_alpha = nmf(input=joinpath(tmp, "Data.zst"), dim=3, alpha=2, numepoch=30, algorithm="alpha")
subplots(out_nmf_alpha, group)
out_nmf_beta = nmf(input=joinpath(tmp, "Data.zst"), dim=3, beta=2, numepoch=30, algorithm="beta")
subplots(out_nmf_beta, group)
out_dnmf_beta = dnmf(input=joinpath(tmp, "Data.zst"), dim=3, beta=2, numepoch=30, binu=10^4)
minimum(out_dnmf_beta[1])
maximum(out_dnmf_beta[1])
subplots(out_dnmf_beta, group)
out_sparse_nmf_alpha = sparse_nmf(input=joinpath(tmp, "Data.mtx.zst"), dim=3, alpha=2, numepoch=30, algorithm="alpha")
subplots(out_sparse_nmf_alpha, group)
out_sparse_nmf_beta = sparse_nmf(input=joinpath(tmp, "Data.mtx.zst"), dim=3, beta=1, numepoch=30, algorithm="beta")
subplots(out_sparse_nmf_beta, group)
out_sparse_dnmf_beta = sparse_dnmf(input=joinpath(tmp, "Data.mtx.zst"), dim=3, beta=2, numepoch=30, binu=10^2)
minimum(out_sparse_dnmf_beta[1])
maximum(out_sparse_dnmf_beta[1])
subplots(out_sparse_dnmf_beta, group)
out_bincoo_nmf_alpha = bincoo_nmf(input=joinpath(tmp, "Data.bincoo.zst"), dim=3, alpha=2, numepoch=10, algorithm="alpha")
subplots(out_bincoo_nmf_alpha, group)
out_bincoo_nmf_beta = bincoo_nmf(input=joinpath(tmp, "Data.bincoo.zst"), dim=3, beta=2, numepoch=5, algorithm="beta")
subplots(out_bincoo_nmf_beta, group)
out_bincoo_dnmf_beta = bincoo_dnmf(input=joinpath(tmp, "Data.bincoo.zst"), dim=3, beta=2, numepoch=5, binu=10^1)
minimum(out_bincoo_dnmf_beta[1])
maximum(out_bincoo_dnmf_beta[1])
subplots(out_bincoo_dnmf_beta, group)
The type of input file is assumed to be CSV or MM formats, and then be processed by csv2bin or mm2bin in OnlinePCA package. The binary file is specified as the input of NMF functions in OnlineNMF package. The NMF functions also can be performed as command line tools with same parameter names like below.
# CSV → Julia Binary
julia YOUR_HOME_DIR/.julia/v0.x/OnlinePCA/bin/csv2bin \
--csvfile Data.csv --binfile Data.zst
# MM → Julia Binary
julia YOUR_HOME_DIR/.julia/v0.x/OnlinePCA/bin/mm2bin \
--mmfile Data.mtx --binfile Data.mtx.zst
# BinCOO → Julia Binary
julia YOUR_HOME_DIR/.julia/v0.x/OnlinePCA/bin/bincoo2bin \
--mmfile Data.bincoo --binfile Data.bincoo.zst
# NMF based on Alpha-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/nmf \
--input Data.zst --dim 3 \
--numepoch 10 --alpha 1
# NMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/nmf \
--input Data.zst --dim 3 \
--numepoch 10 --beta 2
# DNMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/dnmf \
--input Data.zst --dim 3 \
--numepoch 10 --beta 2
# Sparse-NMF based on Alpha-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/sparse_nmf \
--input Data.mtx.zst --dim 3 \
--numepoch 10 --alpha 1
# Sparse-NMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/sparse_nmf \
--input Data.mtx.zst --dim 3 \
--numepoch 10 --beta 2
# Sparse-DNMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/sparse_dnmf \
--input Data.mtx.zst --dim 3 \
--numepoch 10 --beta 2
# BinCOO-NMF based on Alpha-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/bincoo_nmf \
--input Data.bincoo.zst --dim 3 \
--numepoch 10 --alpha 1
# BinCOO-NMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/bincoo_nmf \
--input Data.bincoo.zst --dim 3 \
--numepoch 10 --beta 2
# BinCOO-DNMF based on Beta-Divergence
julia YOUR_HOME_DIR/.julia/v0.x/OnlineNMF/bin/bincoo_dnmf \
--input Data.bincoo.zst --dim 3 \
--numepoch 10 --beta 2If you have suggestions for how OnlineNMF.jl could be improved, or want to report a bug, open an issue! We'd love all and any contributions.
For more, check out the Contributing Guide.
- Koki Tsuyuzaki