Julia中的内核PCA实现

Question

我正在尝试在Julia笔记本中实施内核主成分分析（kernel PCA）的方法。更具体地说，我正在尝试复制本教程中完成的过程：https://sebastianraschka.com/Articles/2014_kernel_pca.html#References但是本教程使用的是python，因此我在Julia中复制该方法时遇到问题。这是我到目前为止在Julia中使用的代码

using LinearAlgebra, CSV, Plots, DataFrames
function sq_norm(X, rows, cols)

#     X should be MxN matrix, and it will do the square norm between all N-dim vectors
#     rows is the number of rows (INT)
#     cols is the number of columns 

    result = zeros(rows, rows)
    for i in 1:rows
        for j in 1:rows
            sum = 0.0
            for k in 1:cols
                sum = (X[i, k] - X[j, k])^2
            end
#             print("this is the sum at i: ")
#             print(i)
#             print(" and j: ")
#             print(j)
#             print(" sum: ")
#             print(sum)
#             print("\n")
            result[i, j] = sum
        end
    end

    return result
end

function kernel_mat_maker(gamma, data, rows)
    #data must be a square symmetric matrix

    result = zeros(rows, rows)
    for i in 1:rows
        for j in 1:rows
            result[i, j] = exp( (-gamma) * data[i, j])
        end
    end
    return result
end

function center_k(K, rows)
    one_N = ones(rows, rows)
    one_N = (1/rows) * one_N

    return K - one_N*K - K*one_N + one_N*K*one_N
end

function data_splitter(data, filter, key)

    # data should be Nx2 matrix
    # filter will be a Nx1 matrix composed of 1's and 0's

#     sum = 0
#     siz = size(filter)
#     for i in 1:100
#         sum += filter[i]
#     end

    output1 = DataFrame(A = 1:50, B = 0)
    output2 = DataFrame(A = 1:50, B = 0)

    print("everything fine where expected\n")

    for i in 1:size(data, 1)
        if filter[i] == 1
            output1 = data[i, :]
            print("saved to output1 fine\n")

        end
    end

    return output1
end

# data1 = CSV.read("C:\\Users\\JP-27\\Desktop\\X1data.csv", header=false)
# data2 = CSV.read("C:\\Users\\JP-27\\Desktop\\X2data.csv", header=false)
data = CSV.read("C:\\Users\\JP-27\\Desktop\\data.csv", header=true)

gdf = groupby(data, :a)

plot(gdf[1].x, gdf[1].y, seriestype=:scatter, legend=nothing)

plot!(gdf[2].x, gdf[2].y, seriestype=:scatter)

# select(data, 2:3)
# filter = select(data, :1)    

newData = select(data, 2:3)
# print("this is newData:\n")
# print(newData)
# print("\n")
nddf = DataFrame(newData)
# print("this is nddf:\n")
# print(nddf)
# print("\n")

# CSV.write("C:\\Users\\JP-27\\Desktop\\ju_data_preprocessing.csv", nddf)

step1 = sq_norm(data, 100, 2)
# df1 = DataFrame(step1)
# CSV.write("C:\\Users\\JP-27\\Desktop\\ju_sq_dists.csv", df1)

step2 = kernel_mat_maker(15,step1,100)
# df2 = DataFrame(step2)
# CSV.write("C:\\Users\\JP-27\\Desktop\\ju_mat_sq_dists.csv", df2)

step3 = center_k(step2, 100)

# df3 = DataFrame(step3)
# CSV.write("C:\\Users\\JP-27\\Desktop\\juliaK.csv", df3)


e_vals = eigvals(step3)
e_vcts = eigvecs(step3)
e_vcts = real(e_vcts)

# print("this is e_vcts\n")
# print(e_vcts)
# print("\n")

# e_vects = DataFrame(e_vcts)

# CSV.write("C:\\Users\\JP-27\\Desktop\\juliaE_vcts.csv", e_vects)

result = DataFrame(e_vcts[:, 99:100])




# step11 = sq_norm(data1, 50, 2)
# step12 = kernel_mat_maker(15,step11,50)
# step13 = center_k(step12, 50)

# step21 = sq_norm(data2, 50, 2)
# step22 = kernel_mat_maker(15,step21,50)
# step23 = center_k(step22, 50)

# vals1 = eigvals(step13)
# vals2 = eigvals(step23)

# evects1 = eigvecs(step13)
# evects2 = eigvecs(step23)

# evects1 = real(evects1)
# evects2 = real(evects2)


# dataevect1 = DataFrame(evects1[:, 49:50])
# dataevect2 = DataFrame(evects2[:, 49:50])


#now we extract the last two columns of our two processed 50x50 matrices

# plot(dataevect1[1], dataevect1[2], seriestype = :scatter, title = "My Scatter Plot")
# plot!(dataevect2[1], dataevect2[2], seriestype = :scatter, title = "My Scatter Plot")

有人可以帮助我更正上面的实现吗？如果您知道一种更简单的方法来执行该过程，而该方法不涉及使用将执行该过程的内核pca函数，那么这也将非常有用。

Answer 1

供您参考，内核PCA方法在MultivariateStats（https://multivariatestatsjl.readthedocs.io/en/stable/kpca.html）中实现。

如果您对详细信息感兴趣，这里是从头开始的实现：

https://github.com/Alexander-Barth/MachineLearningNotebooks/blob/master/kernel-pca.ipynb