Update 2021JUL21.md

2021JUL21.md

@@ -18,12 +18,14 @@ The marginal distribution of $`\mathbf{x}_{n}^{L}, \mathbf{x}_{n}^{H}`$ is
 In summary, in addition to finding the the hyper-parameters $`\pi, \mu, \Sigma_{k}^{H}, \Sigma^{L}_{k}`$, we want to estimate a transformation matrix $`\mathbf{U}`$ such that $`\mathbf{UX}^{H}`$ is as close to $`\mathbf{X}^{L}`$ as possible (or vice versa).
 
 ### Simulation results
-#### Methods
-##### Low-quality data noisier than the high-quality data
+#### We considered three scenarios
+##### I. Low-quality data noisier than the high-quality data
 We simulate the case where the features of low-quality data are noiser than those of the high-quality data. The number of informative features remains the same, however.
 ```julia
 noise_level = 10
+d = 3
 # the high- and low-quality share the same cluster centroid
+# there are two clusters, and d features
 XHmean = hcat(randn(Float32, d), randn(Float32, d))
 XLmean = copy(XHmean)
 n_samples = 1000
@@ -37,11 +39,11 @@ for c ∈ [1, 2]
     XLtrain[:, findall(x -> x==c, class)] .= rand(MvNormal(XLmean[:, c], 0.05f0 * noise_level * I), count(x -> x==c, class))
 end
 ```
-##### Low-quality data noisier than the high-quality data with less informative features
+##### II. Low-quality data noisier than the high-quality data with less informative features
 In this scenario, low-quality data has less informative features
 ```julia
-noise_level = 10
 # the high- and low-quality share the same cluster centroid
+# there are two clusters, and d features
 XHmean = hcat(randn(Float32, d), randn(Float32, d))
 XLmean = copy(XHmean)
 # 50% of the original features are non-informative
@@ -57,10 +59,10 @@ for c ∈ [1, 2]
     XLtrain[:, findall(x -> x==c, class)] .= rand(MvNormal(XLmean[:, c], 0.05f0 * noise_level * I), count(x -> x==c, class))
 end
 ```
-##### Low-quality data noiser than the high-quality data with 10% outliers
+##### III. Low-quality data noiser than the high-quality data with 10% outliers
 ```julia
-noise_level = 10
 # the high- and low-quality share the same cluster centroid
+# there are two clusters, and d features
 XHmean = hcat(randn(Float32, d), randn(Float32, d))
 XLmean = copy(XHmean)
 n_samples = 1000
@@ -77,5 +79,9 @@ end
 XLtrain[:, rand(1:n_samples, Int(round(n_samples / 10)))] .= randn(d, Int(round(n_samples / 10))) .* 2
 ```
 #### Results
+ - d = 3
+![res1](/figs/2021JUL21/d3.svg)
 
+ - d = 10
+![res2](/figs/2021JUL21/d10.svg)