Multivariate and time series¶

Principal components and clustering (via scikit-learn), and the series, its autocorrelation and a seasonal decomposition (via statsmodels), all redrawn in the depictr theme.

import numpy as np
import pandas as pd

import depictr as dp

wb = dp.wellbeing_survey()

PCA biplot¶

A PCA biplot, coloured by group, with the variable loadings.

p = dp.pca_plot(wb, group="region")
print(show(p, width=8, height=6))

Clustering¶

k-means clusters of the standardised data, drawn on the first two principal components. They are the clusters the silhouette plot below measures.

p = dp.cluster_plot(wb, k=3)
print(show(p))

Scree plot¶

The variance each principal component explains, with the running cumulative line.

p = dp.scree_plot(wb)
print(show(p))

Dendrogram¶

A hierarchical-clustering tree over the regional profiles.

p = dp.dendrogram_plot(wb.groupby("region", observed=True).mean(numeric_only=True))
print(show(p))

Silhouette¶

Each observation's silhouette width, grouped and ordered by cluster. Wide positive bars are well-placed observations, and a negative bar may belong to a neighbouring cluster.

p = dp.silhouette_plot(wb, k=3)
print(show(p))

Seasonal decomposition¶

A monthly series with a trend, a 12-period season and noise, and its decomposition into observed, trend, seasonal and residual components.

rng = np.random.default_rng(0)
t = np.arange(120)
series = pd.Series(
    50 + 0.3 * t + 10 * np.sin(2 * np.pi * t / 12) + rng.normal(0, 3, 120),
    index=pd.period_range("2016-01", periods=120, freq="M"),
)

p = dp.decompose_plot(series, period=12)
print(show(p, width=8, height=8))

The series with a rolling mean¶

The same series as a line, with a centred twelve-month moving average over it. Twelve is an even window, so the average is the 2×12 one, a twelve-month average followed by a two-month one, which centres it on each month.

p = dp.timeseries_plot(series, rolling=12)
print(show(p))

Autocorrelation¶

The autocorrelation function, with an approximate 95% band. The trend keeps the correlations high at short lags, and the season rides on their slow decay as a wave. It dips near lag six, where the series is half a cycle out of step with itself. It peaks again at lag twelve, the only multiple of the period within the default range of lags.

p = dp.acf_plot(series)
print(show(p))

The partial autocorrelation function, which leaves out what the shorter lags already explain. Lag one carries most of the dependence, and the value at lag twelve lies well inside the band.

p = dp.acf_plot(series, kind="pacf")
print(show(p))

The seasonal pattern¶

One line per year across the months, so the repeating shape and any drift between years are easy to read.

p = dp.seasonal_plot(series, period=12)
print(show(p))