The Iris data set
xxxxxxxxxxxxxxxxxxxx[1] Data set description and possible applications
xxxxxxxxxxThis data set contains 150 samples iris flower. The features in each sample are the length and width of both the iris petal and sepal, and also the species of iris. data = 150×5
Each feature is recorded as a floating point value except for the species (string). The species identifier acts as the labels for this data set (if used for supervised learning).There are no missing values. The data and header is seperated into two different files.
This data could be used for iris classification. This could be useful in an automation task involving these flowers or as a tool for researchers to assist in quick identification. Other, less "real world" applications include use as a data set for ML systems such as supervised learning (NN) and unsupervised learning (K-NN).
xxxxxxxxxx[2] Data summary and visualizations
xxxxxxxxxxImports
xxxxxxxxxxbegin    import Pkg;    packages = ["CSV","DataFrames","PlutoUI","Plots","Combinatorics"]       Pkg.add(packages)        using CSV, DataFrames, PlutoUI, Plots, Combinatorics    plotly()    theme(:solarized_light)endEnter cell code...
xxxxxxxxxxLoading, cleaning, and manipulating the data
xxxxxxxxxxColumn names: sepal_len, sepal_wid, petal_len, petal_wid, class
4 rows × 8 columns
| variable | mean | min | median | max | nunique | nmissing | eltype | |
|---|---|---|---|---|---|---|---|---|
| Symbol | Float64 | Float64 | Float64 | Float64 | Nothing | Nothing | DataType | |
| 1 | sepal_len | 5.84333 | 4.3 | 5.8 | 7.9 | Float64 | ||
| 2 | sepal_wid | 3.054 | 2.0 | 3.0 | 4.4 | Float64 | ||
| 3 | petal_len | 3.75867 | 1.0 | 4.35 | 6.9 | Float64 | ||
| 4 | petal_wid | 1.19867 | 0.1 | 1.3 | 2.5 | Float64 | 
xxxxxxxxxxbegin    path = "iris/iris.data"    csv_data = CSV.File(path, header=false)        iris_names = ["sepal_len", "sepal_wid", "petal_len", "petal_wid", "class"]    df = DataFrame(csv_data.columns, Symbol.(iris_names))    dropmissing!(df)        md"""    **Column names:** $(join(iris_names, ", "))    $(describe(df, cols=1:4))    """endEnter cell code...
xxxxxxxxxxSplitting the data into three iris classes
As you can see, there is a equal representation of each class:
xxxxxxxxxxClass sizes: (50, 5), (50, 5) (50, 5)
xxxxxxxxxxbegin    df_species = groupby(df, :class)    md"""**Class sizes:** $(size(df_species[1])), $(size(df_species[2])) $(size(df_species[3]))"""endEnter cell code...
xxxxxxxxxxVisualizations
xxxxxxxxxxComparing length vs width of the sepal and petal
xxxxxxxxxxxxxxxxxxxxbegin    scatter(title="len vs wid", xlabel = "length", ylabel="width",             df.sepal_len, df.sepal_wid, color="blue", label="sepal")    scatter!(df.petal_len, df.petal_wid, color="red", label="petal")endEnter cell code...
xxxxxxxxxxComparing all combinations of variables
Column pairs per chart: [sepal_len, sepal_wid, petal_len, petal_wid, class]
-> [1, 2] , [1, 3] , [1, 4]
-> [2, 3] , [2, 4] , [3, 4]
xxxxxxxxxxxxxxxxxxxxbegin    # Get all combinations of colums    combins = collect(combinations(1:4,2))    combos = [(df[x][1], df[x][2]) for x in combins]    # Plot all combinations in sub-plots    scatter(combos, layout=(2,3))endEnter cell code...
xxxxxxxxxxComparing the sepal length vs sepal width vs petal length of all three classes of iris
Restricted to three variables to plot in 3d
xxxxxxxxxxxxxxxxxxxxbegin    setosa, versicolor, virginica = df_species        scatter(setosa[1], setosa[2], setosa[3], label="Setosa", xlabel="d")    scatter!(versicolor[1], versicolor[2], versicolor[3], label="versicolor")    scatter!(virginica[1], virginica[2], virginica[3], label="virginica")endEnter cell code...
xxxxxxxxxx[3] Deep Learning
xxxxxxxxxxImports
xxxxxxxxxx0x0000007b
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1073116007
222134151
1073120226
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1072956456
-580276323
1073476387
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1073715449
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2119209372
1073158224
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1073708804
760591513
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-1999907543
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32947490
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0
xxxxxxxxxxbegin    Pkg.add("Flux")    Pkg.add("CUDA")    Pkg.add("IterTools")        using Flux    using Flux: Data.DataLoader    using Flux:     using CUDA    using Random    using IterTools: ncycle        Random.seed!(123);#   CUDA.allowscalar(false)endEnter cell code...
xxxxxxxxxxThe Data
xxxxxxxxxxFormating data for training (including onehot conversion and (NOT) moving to gpu)
xxxxxxxxxxbegin       # Convert df to array    data = convert(Array, df)        # Shuffle    data = data[shuffle(1:end), :]    # train/test split    train_test_ratio = .7    idx = Int(floor(size(df, 1) * train_test_ratio))    data_train = data[1:idx,:]    data_test = data[idx+1:end, :]    # Get feature vectors    get_feat(d) = transpose(convert(Array{Float32},d[:, 1:end-1]))    x_train = get_feat(data_train)    x_test = get_feat(data_test)        # One hot labels    #   onehot(d) = [Flux.onehot(v, unique(df.class)) for v in d[:,end]]    onehot(d) = Flux.onehotbatch(d[:,end], unique(df.class))    y_train = onehot(data_train)    y_test = onehot(data_test)    # Push data onto the GPU    #   x_train = cu(x_train)#   x_test = cu(x_test)#   y_train = cu(y_train)#   y_test = cu(y_test)        md"""    Formating data for training (including onehot conversion and (NOT) moving to gpu)    """endEnter cell code...
xxxxxxxxxxCreating DataLoaders for batches
xxxxxxxxxxbegin    batch_size= 1    train_dl = DataLoader((x_train, y_train), batchsize=batch_size, shuffle=true)    test_dl = DataLoader((x_test, y_test), batchsize=batch_size)        md"""#### Creating DataLoaders for batches"""endEnter cell code...
xxxxxxxxxxThe model
I am going to implement a fully connected neural network to classify by species.
Layers: Chain(Dense(4, 8, relu), Dense(8, 3), softmax)
Loss: logit binary crossentropy
Optimizer: Flux.Optimise.ADAM
Learning rate: 0.001
Epochs: 30
Batch size: 1
xxxxxxxxxxTraining!
Train
acc: 0.9619047619047619
loss: 0.6096755f0
Test
acc: 1.0
loss: 0.6018428f0
xxxxxxxxxxbegin    ### Model ------------------------------    function get_model()        c = Chain(            Dense(4,8,relu),            Dense(8,3),            softmax        )#       c = cu(c)    end        model = get_model()    ### Loss ------------------------------    loss(x,y) = Flux.Losses.logitbinarycrossentropy(model(x), y)        train_losses = []    test_losses = []    train_acces = []    test_acces = []        ### Optimiser ------------------------------    lr = 0.001    opt = ADAM(lr, (0.9, 0.999))    ### Callbacks ------------------------------    function loss_all(data_loader)        sum([loss(x, y) for (x,y) in data_loader]) / length(data_loader)     end        function acc(data_loader)        f(x) = Flux.onecold(cpu(x))        acces = [sum(f(model(x)) .== f(y)) / size(x,2)  for (x,y) in data_loader]        sum(acces) / length(data_loader)    end        callbacks = [        () -> push!(train_losses, loss_all(train_dl)),        () -> push!(test_losses, loss_all(test_dl)),        () -> push!(train_acces, acc(train_dl)),        () -> push!(test_acces, acc(test_dl)),    ]    # Training ------------------------------    epochs = 30    ps = Flux.params(model)         epochs Flux.train!(loss, ps, train_dl, opt, cb = callbacks)         train_loss = loss_all(train_dl)     test_loss = loss_all(test_dl)     train_acc = acc(train_dl)     test_acc = acc(test_dl)        md"""    ### Training!    **Train**               acc: $(train_acc)            loss: $(train_loss)        **Test**          acc: $(test_acc)            loss: $(test_loss)    """endEnter cell code...
xxxxxxxxxxResults
xxxxxxxxxxxxxxxxxxxxbegin    x_axis = 1:epochs * size(y_train,2)    plot(x_axis, train_losses, label="Training loss",        title="Loss", xaxis="epochs * data size")    plot!(x_axis, test_losses, label="Testing loss")endxxxxxxxxxxbegin    plot(x_axis, train_acces, label="Training acc",        title="Accuracy", xaxis="epochs * data size")    plot!(x_axis, test_acces, label="Testing acc")endOne example prediction:
Prediction: 0.0074335323 , 0.8525481 , 0.14001828
Truth: 0 , 1 , 0
error: 0.2949037f0
xxxxxxxxxxConfusion matrix
xxxxxxxxxxxxxxxxxxxxbegin    preds = round.(model(x_test))    truths = y_test        un_onehot(v) = v[1] == true ? 1 : v[2] == true ? 2 : 3    preds = [un_onehot(v) for v in eachcol(preds)]    truths = [un_onehot(v) for v in eachcol(truths)]        conf_mat = zeros(3,3)    for (y′, y) in zip(preds, truths)           if y == 1            if y′ == 1                conf_mat[1,1] += 1            elseif y′ == 2                conf_mat[1,2] += 1            else                conf_mat[1,3] += 1            end        elseif y == 2            if y′ == 1                conf_mat[2,1] += 1            elseif y′ == 2                conf_mat[2,2] += 1            else                conf_mat[2,3] += 1            end        else            if y′ == 1                conf_mat[3,1] += 1            elseif y′ == 2                conf_mat[3,2] += 1            else                conf_mat[3,3] += 1            end        end    end#   conf_mat = conf_mat ./ sum(conf_mat) # normalize    label = "setosa \t:\t versicolor \t:\t virginica"    heatmap(conf_mat, color=:plasma, aspect_ratio=1, xaxis=label, axis = nothing)    endEnter cell code...
xxxxxxxxxx[4] Conclusion
Platform/Tools
I chose to implement a basic feed forward neural network because of the scale of the problem. With the data set containing so few samples with very little features a small network would fit better. Again, because of the size of the problem, shallow ML approaches would have been sufficient. Something to expand on in this research is to compare to such methods.
I wanted to challenge myself and learn an entirely new language and platform for this project. The Julia Programming Language is a high level, dynamically typed language. It comes with its own web-based editor that is much like Python's Jupter notebooks. Because Julia is newer and the community is smaller than Python, the documentation and support were not even close in magnitude. This slowed me down considerably. Despite the setbacks, I learned a lot in this research and I am glad I decided to use Julia.
Results
My model's test accuracy was 95.55%. This is satisfactory for me due to the simplicity of the data set and the model. While one species was linearly seperable, the other two were not. These later species are the main problem for the model to tackle.
As I stated in the beginning of this paper, this model could be used for classification tasks such as automation or as a tool for bio researchers to aid in identification. Furthermore, this model could be used as a pre-trained model for more specific tasks; I understand this statement is a bit of a stretch but I want to account for as many applications as possible.
xxxxxxxxxx[5] Related work
Related research: Kaggle
One thing they did, that I didn't do, is compare their deep learning model to more classical approaches.
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