使用Pyhon+Flux+Julia實(shí)現(xiàn)手寫數(shù)字識(shí)別

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為什么使用Flux和Julia?

機(jī)器學(xué)習(xí)概論

• 線性代數(shù)的核心思想。（https://medium.com/@Jernfrost/the-core-idea-of-linear-algebra-7405863d8c1d）
• 線性代數(shù)基本上是關(guān)于向量和矩陣的，這是你在機(jī)器學(xué)習(xí)中經(jīng)常用到的東西。
• 使用引用。（https://medium.com/@Jernfrost/working-with-and-emulating-references-in-julia-e02c1cae5826）
• 它看起來有點(diǎn)不太好理解，但是如果你想理解像Flux這樣的ML庫，那么理解Julia中的引用是很重要的。
• Flux的實(shí)現(xiàn)。（https://medium.com/@Jernfrost/implementation-of-a-modern-machine-learning-library-3596badf3be）
• 如何實(shí)現(xiàn)Flux-ML庫的初學(xué)者指南。
• 機(jī)器學(xué)習(xí)簡介。（https://medium.com/@Jernfrost/machine-learning-for-dummies-in-julia-6cd4d2e71a46） 機(jī)器學(xué)習(xí)概論。

簡單多層感知機(jī)

using?Flux,?Flux.Data.MNIST,?Statistics
using?Flux:?onehotbatch,?onecold,?crossentropy,?throttle
using?Base.Iterators:?repeated

#?Load?training?data.?28x28?grayscale?images?of?digits
imgs?=?MNIST.images()

#?Reorder?the?layout?of?the?data?for?the?ANN
imagestrip(image::Matrix{<:Gray})?=?Float32.(reshape(image,?:))
X?=?hcat(imagestrip.(imgs)...)

#?Target?output.?What?digit?each?image?represents.
labels?=?MNIST.labels()
Y?=?onehotbatch(labels,?0:9)

#?Defining?the?model?(a?neural?network)
m?=?Chain(
?Dense(28*28,?32,?relu),
?Dense(32,?10),
?softmax)
?
loss(x,?y)?=?crossentropy(m(x),?y)
dataset?=?repeated((X,?Y),?200)
opt?=?ADAM()

evalcb?=?()?->?@show(loss(X,?Y))

#?Perform?training?on?data
Flux.train!(loss,?params(m),?dataset,?opt,?cb?=?throttle(evalcb,?10))

探索輸入數(shù)據(jù)

imgs?=?MNIST.images()

julia>?size(imgs)
(60000,)

julia>?eltype(imgs)
Array{Gray{FixedPointNumbers.Normed{UInt8,8}},2}

julia>?eltype(imgs)?<:?Matrix{T}?where?T?<:?Gray
true

help?>?Gray
??Gray?is?a?grayscale?object.?You?can?extract?its?value?with?gray(c).

julia>?size(imgs[1])
(28,?28)

julia>?size(imgs[2])
(28,?28)

julia>?using?Plots
julia>?plot(imgs[2])

imgplots?=?plot.(imgs[1:9])
plot(imgplots...)

準(zhǔn)備輸入數(shù)據(jù)

julia>?A?=?collect(1:4)
4-element?Array{Int64,1}:
?1
?2
?3
?4

julia>?B?=?reshape(A,?(2,?2))
2×2?Array{Int64,2}:
?1??3
?2??4

julia>?reshape(B,?4)
4-element?Array{Int64,1}:
?1
?2
?3
?4

julia>?reshape(B,?:)
4-element?Array{Int64,1}:
?1
?2
?3
?4

imagestrip(image::Matrix{<:Gray})?=?Float32.(reshape(image,?:))

X?=?hcat(imagestrip.(imgs)...)

X?=?hcat(X?,?X?,?X?,?...,?X?)

labels?=?MNIST.labels()

imgplots?=?plot.(imgs[1:9])
plot(imgplots...)
labels[1:9]

獨(dú)熱編碼

julia>?Flux.onehot('B',?['A',?'B',?'C'])
3-element?Flux.OneHotVector:
0
1
0

julia>?Flux.onehot("foo",?["foo",?"bar",?"baz"])
3-element?Flux.OneHotVector:
1
0
0

Y?=?onehotbatch(labels,?0:9)

構(gòu)造神經(jīng)網(wǎng)絡(luò)模型

m?=?Chain(
??Dense(28^2,?32,?relu),
??Dense(32,?10),
??softmax)

Softmax函數(shù)

julia>?ys?=?rand(1:10,?10)
10-element?Array{Int64,1}:
??9
??6
?10
??5
?10
??2
??6
??6
??7
??9

julia>?softmax(ys)
10-element?Array{Float64,1}:
?0.12919082661651196???
?0.006432032517257137??
?0.3511770763952676????
?0.002366212528045101??
?0.3511770763952676????
?0.00011780678490667763
?0.006432032517257137??
?0.006432032517257137??
?0.017484077111717768??
?0.12919082661651196

julia>?sum(softmax(ys))
0.9999999999999999

julia>?using?LinearAlgebra

julia>?normalize(ys)
10-element?Array{Float64,1}:
0.38446094597254243
0.25630729731502827
0.4271788288583805?
0.21358941442919024
0.4271788288583805?
0.0854357657716761?
0.25630729731502827
0.25630729731502827
0.2990251802008663?
0.38446094597254243

julia>?sum(normalize(ys))
2.9902518020086633

julia>?norm(normalize(ys))
1.0

julia>?norm(softmax(ys))
0.52959100847191

定義損失函數(shù)

loss(x,?y)?=?crossentropy(m(x),?y)

指定Epoch

dataset?=?repeated((X,?Y),?200)

dataset?=?[(X1,?Y1),?(X2,?Y2),?...,?(X200,?Y200)]

優(yōu)化器

opt?=?ADAM()

進(jìn)行訓(xùn)練

evalcb?=?()?->?@show(loss(X,?Y))

Flux.train!(loss,?params(m),?dataset,?opt,?cb?=?throttle(evalcb,?10))

評(píng)價(jià)模型預(yù)測(cè)精度

accuracy(x,?y)?=?mean(onecold((m(x)))?.==?onecold(y))

@show?accuracy(X,?Y)

julia>?onecold([0.1,?0.7,?0.2])
2

julia>?onecold([0.9,?0.05,?0.05])
1

用測(cè)試數(shù)據(jù)驗(yàn)證模型

tX?=?hcat(float.(reshape.(MNIST.images(:test),?:))...)
tY?=?onehotbatch(MNIST.labels(:test),?0:9)

@show?accuracy(tX,?tY)

最后