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making kmeans take AbstractMatrix instead of Matrix #138

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Jan 29, 2019
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making kmeans take AbstractMatrix instead of Matrix #138

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57c172a
making kmeans take AbstractMatrix instead of Matrix, see #136 and #129
tlienart Jan 25, 2019
4c7f218
PR update based on feedback + cosmetics
tlienart Jan 26, 2019
2e95afb
Update src/kmeans.jl
alyst Jan 28, 2019
be3575d
Update src/kmeans.jl
alyst Jan 28, 2019
d3f167a
Update src/kmeans.jl
alyst Jan 28, 2019
a8ea8c7
Update src/kmeans.jl
alyst Jan 28, 2019
c5bda5b
Update src/kmeans.jl
alyst Jan 28, 2019
3f8b15b
Update src/kmeans.jl
alyst Jan 28, 2019
0d272e9
applying the changes following PR reviews
tlienart Jan 28, 2019
9cb02f7
reverting a few changes that seemed to cause spurious allocations
tlienart Jan 28, 2019
16ae803
type changes, tying costs and centers to the type of X, similar to wh…
tlienart Jan 28, 2019
192694a
Update src/kmeans.jl
alyst Jan 29, 2019
603422d
reverting the rounding of maxiter as per requested change
tlienart Jan 29, 2019
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197 changes: 95 additions & 102 deletions src/kmeans.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@

#### Interface

mutable struct KmeansResult{T<:AbstractFloat} <: ClusteringResult
mutable struct KmeansResult{T<:Real} <: ClusteringResult
centers::Matrix{T} # cluster centers (d x k)
assignments::Vector{Int} # assignments (n)
costs::Vector{T} # costs of the resultant assignments (n)
Expand All @@ -18,35 +18,34 @@ const _kmeans_default_maxiter = 100
const _kmeans_default_tol = 1.0e-6
const _kmeans_default_display = :none

function kmeans!(X::Matrix{T}, centers::Matrix{T};
weights=nothing,
function kmeans!(X::AbstractMatrix{T}, centers::AbstractMatrix{T};
weights::Union{Nothing, AbstractVector{<:Real}}=nothing,
maxiter::Integer=_kmeans_default_maxiter,
tol::Real=_kmeans_default_tol,
display::Symbol=_kmeans_default_display,
distance::SemiMetric=SqEuclidean()) where T<:AbstractFloat
distance::SemiMetric=SqEuclidean()) where T<:Real

m, n = size(X)
m2, k = size(centers)
m == m2 || throw(DimensionMismatch("Inconsistent array dimensions."))
(2 <= k < n) || error("k must have 2 <= k < n.")

assignments = zeros(Int, n)
costs = zeros(T, n)
assignments = Vector{Int}(undef, n)
costs = Vector{T}(undef, n)
counts = Vector{Int}(undef, k)
cweights = Vector{Float64}(undef, k)

_kmeans!(X, conv_weights(T, n, weights), centers,
assignments, costs, counts, cweights,
round(Int, maxiter), tol, display_level(display), distance)
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assignments, costs, counts, cweights, maxiter, tol,
display_level(display), distance)
end

function kmeans(X::Matrix{T}, k::Int;
weights=nothing,
init=_kmeans_default_init,
function kmeans(X::AbstractMatrix{<:Real}, k::Int;
weights=nothing, init=_kmeans_default_init,
maxiter::Integer=_kmeans_default_maxiter,
tol::Real=_kmeans_default_tol,
display::Symbol=_kmeans_default_display,
distance::SemiMetric=SqEuclidean()) where T<:AbstractFloat
distance::SemiMetric=SqEuclidean())

m, n = size(X)
(2 <= k < n) || error("k must have 2 <= k < n.")
Expand All @@ -64,27 +63,27 @@ end

# core k-means skeleton
function _kmeans!(
x::Matrix{T}, # in: sample matrix (d x n)
w::Union{Nothing, Vector{T}}, # in: sample weights (n)
centers::Matrix{T}, # in/out: matrix of centers (d x k)
assignments::Vector{Int}, # out: vector of assignments (n)
costs::Vector{T}, # out: costs of the resultant assignments (n)
counts::Vector{Int}, # out: the number of samples assigned to each cluster (k)
cweights::Vector{Float64}, # out: the weights of each cluster
maxiter::Int, # in: maximum number of iterations
tol::Real, # in: tolerance of change at convergence
displevel::Int, # in: the level of display
distance::SemiMetric) where T<:AbstractFloat # in: function to calculate the distance with
X::AbstractMatrix{T}, # in: sample matrix (d x n)
w::Union{Nothing, AbstractVector{<:Real}}, # in: sample weights (n)
centers::AbstractMatrix{T}, # in/out: matrix of centers (d x k)
assignments::Vector{Int}, # out: vector of assignments (n)
costs::Vector{T}, # out: costs of the resultant assignments (n)
counts::Vector{Int}, # out: # samples assigned to each cluster (k)
cweights::Vector{Float64}, # out: weights of each cluster
maxiter::Integer, # in: maximum number of iterations
tol::Real, # in: tolerance of change at convergence
displevel::Int, # in: the level of display
distance::SemiMetric # in: function to calculate the distance with
) where T<:Real
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The pre-PR code contained both indented and unindented examples of a stray closing bracket + type constraints declaration.
I like unindented version more as it helps to separate the function arguments from its body. @nalimilan What is the recommended convention?

Suggested change
) where T<:Real
) where T<:Real

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@tlienart tlienart Jan 29, 2019 •
edited
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to be honest it's not really like the current code (now and before) is super consistent in terms of style... but can we work on this in another PR potentially with broadcasting and type fix?
I'm considering rewriting the whole backbone of this kmeans.jl file so that it can use more than one algorithm, is clearer on the Type promotion front, uses broadcasting and can take a Table instead of just matrices... style questions and better docstrings could go in there too.

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I don't think there's a convention about this. In general the Julia code base doesn't use that style, but instead puts the first argument on the same line as the function name.


# initialize

k = size(centers, 2)
to_update = Vector{Bool}(undef, k) # indicators of whether a center needs to be updated
unused = Int[]
unused = Vector{Int}()
num_affected::Int = k # number of centers, to which the distances need to be recomputed

dmat = pairwise(distance, centers, x)
dmat = convert(Array{T}, dmat) #Can be removed if one day Distance.result_type(SqEuclidean(), T, T) == T
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dmat = pairwise(distance, centers, X)
dmat = convert(Array{T}, dmat) # Can be removed if one day Distance.result_type(SqEuclidean(), T, T) == T
update_assignments!(dmat, true, assignments, costs, counts, to_update, unused)
objv = w === nothing ? sum(costs) : dot(w, costs)

Expand All @@ -101,35 +100,33 @@ function _kmeans!(
t = t + 1

# update (affected) centers

update_centers!(x, w, assignments, to_update, centers, cweights)
update_centers!(X, w, assignments, to_update, centers, cweights)

if !isempty(unused)
repick_unused_centers(x, costs, centers, unused)
repick_unused_centers(X, costs, centers, unused)
end

# update pairwise distance matrix

if !isempty(unused)
to_update[unused] .= true
end

if t == 1 || num_affected > 0.75 * k
pairwise!(dmat, distance, centers, x)
pairwise!(dmat, distance, centers, X)
else
# if only a small subset is affected, only compute for that subset
affected_inds = findall(to_update)
dmat_p = pairwise(distance, centers[:, affected_inds], x)
dmat_p = pairwise(distance, centers[:, affected_inds], X)
dmat[affected_inds, :] .= dmat_p
end

# update assignments

update_assignments!(dmat, false, assignments, costs, counts, to_update, unused)

num_affected = sum(to_update) + length(unused)

# compute change of objective and determine convergence

prev_objv = objv
objv = w === nothing ? sum(costs) : dot(w, costs)
objv_change = objv - prev_objv
Expand Down Expand Up @@ -157,8 +154,8 @@ function _kmeans!(
end
end

return KmeansResult(centers, assignments, costs, counts, cweights,
Float64(objv), t, converged)
return KmeansResult(convert(Matrix, centers), assignments, costs, counts,
cweights, Float64(objv), t, converged)
end


Expand All @@ -167,15 +164,16 @@ end
# an updated (squared) distance matrix
#
function update_assignments!(
dmat::Matrix{T}, # in: distance matrix (k x n)
is_init::Bool, # in: whether it is the initial run
assignments::Vector{Int}, # out: assignment vector (n)
costs::Vector{T}, # out: costs of the resultant assignment (n)
counts::Vector{Int}, # out: number of samples assigned to each cluster (k)
to_update::Vector{Bool}, # out: whether a center needs update (k)
unused::Vector{Int}) where T<:AbstractFloat # out: the list of centers get no samples assigned to it
dmat::Matrix{T}, # in: distance matrix (k x n)
is_init::Bool, # in: whether it is the initial run
assignments::Vector{Int}, # out: assignment vector (n)
costs::Vector{T}, # out: costs of the resultant assignment (n)
counts::Vector{Int}, # out: # samples assigned to each cluster (k)
to_update::Vector{Bool}, # out: whether a center needs update (k)
unused::Vector{Int} # out: list of centers with no samples
) where T<:Real

k::Int, n::Int = size(dmat)
k, n = size(dmat)

# re-initialize the counting vector
fill!(counts, 0)
Expand All @@ -190,12 +188,12 @@ function update_assignments!(
end

# process each sample
@inbounds for j = 1 : n
@inbounds for j = 1:n

# find the closest cluster to the i-th sample
a::Int = 1
c::T = dmat[1, j]
for i = 2 : k
a = 1
c = dmat[1, j]
for i = 2:k
ci = dmat[i, j]
if ci < c
a = i
Expand Down Expand Up @@ -224,7 +222,7 @@ function update_assignments!(

# look for centers that have no associated samples

for i = 1 : k
for i = 1:k
if counts[i] == 0
push!(unused, i)
to_update[i] = false # this is handled using different mechanism
Expand All @@ -238,49 +236,43 @@ end
# (specific to the case where samples are not weighted)
#
function update_centers!(
x::Matrix{T}, # in: sample matrix (d x n)
w::Nothing, # in: sample weights
assignments::Vector{Int}, # in: assignments (n)
to_update::Vector{Bool}, # in: whether a center needs update (k)
centers::Matrix{T}, # out: updated centers (d x k)
cweights::Vector) where T<:AbstractFloat # out: updated cluster weights (k)

d::Int = size(x, 1)
n::Int = size(x, 2)
k::Int = size(centers, 2)
X::AbstractMatrix{T}, # in: sample matrix (d x n)
w::Nothing, # in: sample weights
assignments::Vector{Int}, # in: assignments (n)
to_update::Vector{Bool}, # in: whether a center needs update (k)
centers::AbstractMatrix{T}, # out: updated centers (d x k)
cweights::Vector{Float64} # out: updated cluster weights (k)
) where T<:Real

d, n = size(X)
k = size(centers, 2)

# initialize center weights
for i = 1 : k
if to_update[i]
cweights[i] = 0.
end
end
cweights[to_update] .= 0.0

# accumulate columns
@inbounds for j = 1 : n
@inbounds for j = 1:n
cj = assignments[j]
1 <= cj <= k || error("assignment out of boundary.")
if to_update[cj]
if cweights[cj] > 0
for i = 1:d
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centers[i, cj] += x[i, j]
centers[i, cj] += X[i, j]
end
else
for i = 1:d
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centers[i, cj] = x[i, j]
centers[i, cj] = X[i, j]
end
end
cweights[cj] += 1
end
end

# sum ==> mean
for j = 1:k
@inbounds for j = 1:k
if to_update[j]
@inbounds cj::T = 1 / cweights[j]
vj = view(centers,:,j)
for i = 1:d
@inbounds vj[i] *= cj
centers[i, j] /= cweights[j]
end
end
end
Expand All @@ -292,47 +284,47 @@ end
# (specific to the case where samples are weighted)
#
function update_centers!(
x::Matrix{T}, # in: sample matrix (d x n)
weights::Vector{T}, # in: sample weights (n)
assignments::Vector{Int}, # in: assignments (n)
to_update::Vector{Bool}, # in: whether a center needs update (k)
centers::Matrix{T}, # out: updated centers (d x k)
cweights::Vector # out: updated cluster weights (k)
) where T<:AbstractFloat

d::Int = size(x, 1)
n::Int = size(x, 2)
k::Int = size(centers, 2)
X::AbstractMatrix{T}, # in: sample matrix (d x n)
weights::AbstractVector{<:Real}, # in: sample weights (n)
assignments::Vector{Int}, # in: assignments (n)
to_update::Vector{Bool}, # in: whether a center needs update (k)
centers::AbstractMatrix{T}, # out: updated centers (d x k)
cweights::Vector{Float64} # out: updated cluster weights (k)
) where T<:Real

d, n = size(X)
k = size(centers, 2)

# initialize center weights
cweights[to_update] .= 0.0

# accumulate columns
# accumulate_cols_u!(centers, cweights, x, assignments, weights, to_update)
for j = 1 : n
@inbounds wj = weights[j]

@inbounds for j = 1:n
wj = weights[j]
if wj > 0
@inbounds cj = assignments[j]
cj = assignments[j]
1 <= cj <= k || error("assignment out of boundary.")

if to_update[cj]
rj = view(centers, :, cj)
xj = view(x, :, j)
if cweights[cj] > 0
@inbounds rj .+= xj * wj
for i = 1:d
centers[i, cj] += X[i, j] * wj
end
else
@inbounds rj .= xj * wj
for i = 1:d
centers[i, cj] = X[i, j] * wj
end
end
cweights[cj] += wj
end
end
end

# sum ==> mean
for j = 1:k
@inbounds for j = 1:k
if to_update[j]
@inbounds centers[:, j] .*= 1 / cweights[j]
for i = 1:d
centers[i, j] /= cweights[j]
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I'm not 100% sure, but back in the days / was more expensive than *.

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with /= --> 132.276ms; 76.272ms
with *= 1 / ... --> 132.628ms; 77.268ms

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Note that the current code computes 1/cweights[j] only once, and then does the multiplication for each i. IIUC the timings for *= 1 / recompute the division it for each i, which isn't faster.

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Actually, I think LLVM is smart enough to calculate 1/wj only once (at least that's what I see in @code_llvm for a toy example). But I still prefer the broadcast version (cej = view(centers, :, j); cej .*= 1/cweights[j]), where this would be definitely done once. :)

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I agree, the broadcasted version was nicer. Better use view. Same above, where view was used but you removed it: use xj .* wj and everything should be OK.

end
end
end
end
Expand All @@ -342,23 +334,24 @@ end
# Re-picks centers that get no samples assigned to them.
#
function repick_unused_centers(
x::Matrix{T}, # in: the sample set (d x n)
costs::Vector{T}, # in: the current assignment costs (n)
centers::Matrix{T}, # to be updated: the centers (d x k)
unused::Vector{Int}) where T<:AbstractFloat # in: the set of indices of centers to be updated
X::AbstractMatrix{T}, # in: the sample set (d x n)
costs::Vector{T}, # in: the current assignment costs (n)
centers::AbstractMatrix{T}, # to be updated: the centers (d x k)
unused::Vector{Int} # in: set of indices of centers to be updated
) where T<:Real

# pick new centers using a scheme like kmeans++
ds = similar(costs)
tcosts = copy(costs)
n = size(x, 2)
n = size(X, 2)

for i in unused
j = wsample(1:n, tcosts)
tcosts[j] = 0
v = x[:,j]
centers[:,i] = v
v = view(X, :, j)
centers[:, i] = v

colwise!(ds, SqEuclidean(), v, x)
colwise!(ds, SqEuclidean(), v, X)
tcosts = min(tcosts, ds)
end
end
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