Week 9 Wednesday

Comment: The attached file mnist.csv contains 42,000 of the usual 70,000 handwritten digits. I decreased the number of rows just to make it a smaller size for uploading to Deepnote; even this smaller version is 73 megabytes. (I wouldn’t have done this if I were working locally on my own computer.)

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import altair as alt
alt.data_transformers.enable('default', max_rows = 10000)

from sklearn.datasets import make_regression

Part 1 - PCA with simulated data

X, y, m = make_regression(n_samples=4000, n_features=1, noise=20, coef=True, random_state=529)
df = pd.DataFrame(X, columns=["x"])
df["y"] = y

alt.Chart(df).mark_circle().encode(
    x="x",
    y="y"
)

from sklearn.decomposition import PCA

pca_model = PCA()

# Just input, no target, since unsupervised
pca_model.fit(df)

PCA()

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arr = pca_model.transform(df)

type(arr)

numpy.ndarray

arr[:3]

array([[-11.9795057 ,   0.41887263],
       [  2.54206288,  -0.20554913],
       [-32.28415112,  -0.39903818]])

df_transform = pd.DataFrame(arr, columns=["PC1", "PC2"])

alt.Chart(df_transform).mark_circle().encode(
    x="PC1",
    y="PC2"
)

alt.Chart(df_transform).mark_circle().encode(
    x="PC1",
    y=alt.Y("PC2", scale=alt.Scale(domain=(-150, 150)))
)

pca_model.explained_variance_ratio_

array([9.99780409e-01, 2.19591117e-04])

Part 2 - PCA with MNIST

df = pd.read_csv("mnist.csv")

df[:3]

	label	pixel0	pixel1	pixel2	pixel3	pixel4	pixel5	pixel6	pixel7	pixel8	...	pixel774	pixel775	pixel776	pixel777	pixel778	pixel779	pixel780	pixel781	pixel782	pixel783
0	1	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
1	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
2	1	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0

3 rows × 785 columns

df_label = df["label"]

df_X = df.loc[:, "pixel0":]

df_X.shape

(42000, 784)

fig, ax = plt.subplots()
ax.imshow(df_X.iloc[178].to_numpy().reshape((28,28)), cmap="binary");

df_label.iloc[178]

2

Restrict the dataset to only images of 0 and 8.

bool_ser = df_label.isin([0,8])
bool_ser

0        False
1         True
2        False
3        False
4         True
         ...  
41995     True
41996    False
41997    False
41998    False
41999    False
Name: label, Length: 42000, dtype: bool

X_sub = df_X[bool_ser]
y_sub = df_label[bool_ser]

y_sub.value_counts()

label
0    4132
8    4063
Name: count, dtype: int64

X_sub.shape

(8195, 784)

pca = PCA(n_components=2)

pca.fit(X_sub)

PCA(n_components=2)

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X_transform = pca.transform(X_sub)

df_transform = pd.DataFrame(X_transform, columns=["PC1", "PC2"])

df_transform[:3]

	PC1	PC2
0	1160.227253	-1048.161600
1	1514.001737	-1096.474230
2	-45.408654	-45.805242

alt.Chart(df_transform).mark_circle().encode(
    x="PC1",
    y="PC2"
)

df_transform[:3]

	PC1	PC2
0	1160.227253	-1048.161600
1	1514.001737	-1096.474230
2	-45.408654	-45.805242

y_sub[:3]

1    0
4    0
5    0
Name: label, dtype: int64

y_sub.reset_index(drop=True)

0       0
1       0
2       0
3       8
4       0
       ..
8190    0
8191    8
8192    0
8193    0
8194    0
Name: label, Length: 8195, dtype: int64

df_transform["label"] = y_sub.reset_index(drop=True)

df_transform[:3]

	PC1	PC2	label
0	1160.227253	-1048.161600	0
1	1514.001737	-1096.474230	0
2	-45.408654	-45.805242	0

alt.Chart(df_transform).mark_circle().encode(
    x="PC1",
    y="PC2",
    color="label:N"
)

df_reset = df_transform.reset_index()
df_reset

	index	PC1	PC2	label
0	0	1160.227253	-1048.161600	0
1	1	1514.001737	-1096.474230	0
2	2	-45.408654	-45.805242	0
3	3	-553.621756	785.414302	8
4	4	779.665844	1178.590268	0
...	...	...	...	...
8190	8190	1446.677423	529.649470	0
8191	8191	-764.906679	-595.978439	8
8192	8192	905.435172	381.444734	0
8193	8193	919.788642	-495.668776	0
8194	8194	744.664272	-520.716016	0

8195 rows × 4 columns

alt.Chart(df_reset).mark_circle().encode(
    x="PC1",
    y="PC2",
    color="label:N",
    tooltip="index"
)

arr_outlier = X_sub.iloc[7663].to_numpy().reshape((28,28))

fig, ax = plt.subplots()
ax.imshow(arr_outlier, cmap="binary")

<matplotlib.image.AxesImage at 0x7ff02a20ecd0>

Created in Deepnote