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Scatter plot - how to do it

I would like to reproduce this plot in Python: (https://i.stack.imgur.com/6CRfn.png)
Any idea how to do this?
I tried to do a normal plt.scatter() but I can't draw this axes on the zero, for example.

That's a very general question... Using plt.scatter() is certainly a good option. Then just add the two lines to the plot (e.g. using axhline and axvline).
Slightly adapting this example:
import numpy as np
import matplotlib.pyplot as plt
# don't show right and top axis[![enter image description here][1]][1]
import matplotlib as mpl
mpl.rcParams['axes.spines.right'] = False
mpl.rcParams['axes.spines.top'] = False
# some random data
N = 50
x = np.random.randint(-10, high=11, size=N, dtype=int)
y = np.random.randint(-10, high=11, size=N, dtype=int)
colors = np.random.rand(N)
area = (30 * np.random.rand(N))**2 # 0 to 15 point radii
# creating a vertical and a horizontal line
plt.axvline(x=0, color='grey', alpha=0.75, linestyle='-')
plt.axhline(y=0, color='grey', alpha=0.75, linestyle='-')
# scatter plot
plt.scatter(x, y, s=area, c=colors, alpha=0.5)
plt.show()

how to get color from a line plot

I want to plot several normal distributions, and add labels to each one in its line color. However the color does not seem to update.
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import scipy.stats as stats
def single_plot(mu, sigma, ax, label=None):
x = np.linspace(mu - 4*sigma, mu + 4*sigma, 1000)
ax = sns.lineplot(x, stats.norm.pdf(x, mu, sigma), ax=ax, label=label, zorder=2)
#my code to get color
color = ax.get_lines()[0].get_c() #fetch color of line
ax.text(mu, max(stats.norm.pdf(x, mu, sigma)), label, fontsize=16, color=color)
When put to use, however, this does not update the color with each line. If I try:
fig, ax = plt.subplots()
ax = single_plot(mu=1000, sigma=100, ax=ax, label='test1')
ax = single_plot(mu=1500, sigma=200, ax=ax, label='test2')
fig.show()
I am getting this figure. The label for "test2" was not updated.
I am wondering where I was wrong and how to fix this problem.

How to set fontsize of axis label with LaTex symbol on matplotlib/seaborn?

In matplotlib, how can I change the font size of a latex symbol?
I have the following code:
import matplotlib.pyplot as plt
import seaborn as sns
# get x and y from file
plt.plot(x, y, linestyle='--', marker='o', color='b')
plt.xlabel(r'$\alpha$ (distance weighted)', fontsize='large')
plt.ylabel('AUC')
plt.show()
But I get the following graph:
Notice that the $\alpha$ is still small.

To increase the size of the fonts set the desired value to fontsize. One way to mitigate the difference between the "normal" font and the "latex" one is by using \mathrm. The example below shows the behaviour of doing this:
import matplotlib.pyplot as plt
import seaborn as sns
x = np.arange(10)
y = np.random.rand(10)
fig = plt.figure(1, figsize=(10,10))
for i, j in zip(np.arange(4), [10,15,20,30]):
ax = fig.add_subplot(2,2,i+1)
ax.plot(x, y, linestyle='--', marker='o', color='b')
ax.set_xlabel(r'$\mathrm{\alpha \ (distance \ weighted)}$', fontsize=j)
ax.set_ylabel('AUC')
plt.show()

Add minor gridlines to matplotlib plot using seaborn

I'm a fan of the Seaborn package for making nice-looking plots using Matplotlib. But I can't seem to figure out how to show minor gridlines in my plots.
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sbn
x = np.linspace(0, 2 * np.pi, 100)
y = np.sin(x)
fig, ax = plt.subplots(1, 1)
ax.scatter(x, y)
ax.grid(b=True, which='major')
ax.grid(b=True, which='minor')
gives:
Any thoughts here? Also any thoughts on how to adjust the style of the Seaborn gridlines that do show up...in particular, I'd love to make them narrower.

Wound up combining CT Zhu's answer with tcaswell's hint:
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sbn
x = np.linspace(0, 2 * np.pi, 100)
y = np.sin(x)
fig, ax = plt.subplots(1, 1)
ax.scatter(x, y)
ax.get_xaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.get_yaxis().set_minor_locator(mpl.ticker.AutoMinorLocator())
ax.grid(b=True, which='major', color='w', linewidth=1.0)
ax.grid(b=True, which='minor', color='w', linewidth=0.5)

That's because the minor ticks are not yet defined, so we need to add for example:
ax.set_xticks(np.arange(0,8)-0.5, minor=True)
ax.set_yticks([-1.25, -0.75, -0.25,0.24,0.75,1.25], minor=True)

python: scatter plot logarithmic scale

In my code, I take the logarithm of two data series and plot them. I would like to change each tick value of the x-axis by raising it to the power of e (anti-log of natural logarithm).
In other words. I want to graph the logarithms of both series but have x-axis in levels.
Here is the code that I'm using.
from pylab import scatter
import pylab
import matplotlib.pyplot as plt
import pandas as pd
from pandas import Series, DataFrame
import numpy as np
file_name = '/Users/joedanger/Desktop/Python/scatter_python.csv'
data = DataFrame(pd.read_csv(file_name))
y = np.log(data['o_value'], dtype='float64')
x = np.log(data['time_diff_day'], dtype='float64')
fig = plt.figure()
plt.scatter(x, y, c='blue', alpha=0.05, edgecolors='none')
fig.suptitle('test title', fontsize=20)
plt.xlabel('time_diff_day', fontsize=18)
plt.ylabel('o_value', fontsize=16)
plt.xticks([-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4])
plt.grid(True)
pylab.show()

let matplotlib take the log for you:
fig = plt.figure()
ax = plt.gca()
ax.scatter(data['o_value'] ,data['time_diff_day'] , c='blue', alpha=0.05, edgecolors='none')
ax.set_yscale('log')
ax.set_xscale('log')
If you are using all the same size and color markers, it is faster to use plot
fig = plt.figure()
ax = plt.gca()
ax.plot(data['o_value'] ,data['time_diff_day'], 'o', c='blue', alpha=0.05, markeredgecolor='none')
ax.set_yscale('log')
ax.set_xscale('log')

The accepted answer is a bit out of date. At least pandas 0.25 natively supports log axes:
# logarithmic X
df.plot.scatter(..., logx=True)
# logarithmic Y
df.plot.scatter(..., logy=True)
# both
df.plot.scatter(..., loglog=True)