pierrelouisbescond

# Let's see how the correlation coefficient evolves as the shift number increases
# and record the successive values into a DataFrame
shift_corr_results = pd.DataFrame(columns=["x1_shifted","x2_shifted","x3_shifted"], dtype=float)

for feature in shift_corr_results.columns:

  # We define a shift range from 0 to 50 but it should be adapted to every use-case
  for shift_value in range(0,50):

    # The correlation coefficient is calculated

pierrelouisbescond

for feature in ["x1","x2","x3"]:
  
  # We create a shifted feature matching the original one
  feature_new_name = feature + "_shifted"
  
  # The shift is determined randomly
  random_shift = np.random.randint(10,50)
  
  df[feature_new_name] = df[feature].shift(-random_shift)
  

pierrelouisbescond

import pandas as pd
import numpy as np
import plotly.graph_objects as go

# Let's start by creating our index 
dataset_size = 1000
idx = np.linspace(0,20, dataset_size)

# x1, x2 have a cyclical behavior, quite close from each other
x1 = np.cos(idx) + 0.2 * np.random.random(dataset_size)

pierrelouisbescond

pierrelouisbescond

df_selected = df[["cos_x","sin_x"]].sample(15).sort_index()
display(df_selected)

fig = go.Figure()

fig.add_trace(go.Scatter(x=df_selected.cos_x, y=df_selected.sin_x, mode="markers"))

fig.update_layout(xaxis = dict(title="cos_x"),
                  yaxis = dict(title="sin_x", scaleanchor = "x", scaleratio = 1))

pierrelouisbescond

fig = go.Figure()

# We use [::24] to extract only 60 rows from the 1440
fig.add_trace(go.Scatter(x=df.cos_x[::24], y=df.sin_x[::24], mode="markers"))

fig.update_layout(xaxis = dict(title="cos_x"),
                  yaxis = dict(title="sin_x", scaleanchor = "x", scaleratio = 1))

fig.show()

pierrelouisbescond

df["sin_x"] = np.sin(df["x_norm"])

import plotly.graph_objects as go

fig = go.Figure()

fig.add_trace(go.Scatter(x=df.x_norm, y=df.cos_x, name='cos_x'))
fig.add_trace(go.Scatter(x=df.x_norm, y=df.sin_x, name='sin_x'))

fig.update_layout(yaxis = dict(scaleanchor = "x", scaleratio = 1))

pierrelouisbescond

# We normalize x values to match with the 0-2π cycle
df["x_norm"] = 2 * math.pi * df["x"] / df["x"].max()

df["cos_x"] = np.cos(df["x_norm"])

display(df)

import plotly.graph_objects as go

fig = go.Figure()

pierrelouisbescond

import pandas as pd
import numpy as np
import math

# We create the DataFrame as a date range between 6/1/2020 (US format) and 6/2/2020 -1
df = pd.DataFrame(index=pd.date_range(start='6/1/2020', end='6/2/2020', freq='min')[:-1])

# We create an integer array from 0 to 1439 (= 24 hours x 60 minutes) 
df["x"]=np.linspace(0, 24 * 60 - 1, 24 * 60, dtype=int)
df

pierrelouisbescond

from sklearn.decomposition import PCA

# The number of dimensions targeted here is 2, 1 less than  the original dataset
pca = PCA(n_components=2)
# we run the dimensions reduction on df
pca.fit(df)

# pca.explained_variance_ratio_ outputs the amount of variance explained by each vector
print("The variance from the original dataset explained thanks to the first vector is: {}%".format(round(100*pca.explained_variance_ratio_[0],1)))
print("The variance from the original dataset explained thanks to the second vector is: {}%".format(round(100*pca.explained_variance_ratio_[1],1)))