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Clustering is an important part of time series analysis that allows us to organize time series into groups by combining “tsfeatures” (summary matricies) with unsupervised techniques such as K-Means Clustering. In this short tutorial, we will cover the tk_tsfeatures() functions that computes a time series feature matrix of summarized information on one or more time series.

Libraries

To get started, load the following libraries.

Data

This tutorial will use the walmart_sales_weekly dataset:

  • Weekly
  • Sales spikes at various events
walmart_sales_weekly
## # A tibble: 1,001 × 17
##    id    Store  Dept Date       Weekly_Sales IsHoliday Type    Size Temperature
##    <fct> <dbl> <dbl> <date>            <dbl> <lgl>     <chr>  <dbl>       <dbl>
##  1 1_1       1     1 2010-02-05       24924. FALSE     A     151315        42.3
##  2 1_1       1     1 2010-02-12       46039. TRUE      A     151315        38.5
##  3 1_1       1     1 2010-02-19       41596. FALSE     A     151315        39.9
##  4 1_1       1     1 2010-02-26       19404. FALSE     A     151315        46.6
##  5 1_1       1     1 2010-03-05       21828. FALSE     A     151315        46.5
##  6 1_1       1     1 2010-03-12       21043. FALSE     A     151315        57.8
##  7 1_1       1     1 2010-03-19       22137. FALSE     A     151315        54.6
##  8 1_1       1     1 2010-03-26       26229. FALSE     A     151315        51.4
##  9 1_1       1     1 2010-04-02       57258. FALSE     A     151315        62.3
## 10 1_1       1     1 2010-04-09       42961. FALSE     A     151315        65.9
## # … with 991 more rows, and 8 more variables: Fuel_Price <dbl>,
## #   MarkDown1 <dbl>, MarkDown2 <dbl>, MarkDown3 <dbl>, MarkDown4 <dbl>,
## #   MarkDown5 <dbl>, CPI <dbl>, Unemployment <dbl>

TS Features

Using the tk_tsfeatures() function, we can quickly get the “tsfeatures” for each of the time series. A few important points:

  • The features parameter come from the tsfeatures R package. Use one of the function names from tsfeatures R package e.g.(“lumpiness”, “stl_features”).

  • We can supply any function that returns an aggregation (e.g. “mean” will apply the base::mean() function).

  • You can supply custom functions by creating a function and providing it (e.g. my_mean() defined below)

# Custom Function
my_mean <- function(x, na.rm=TRUE) {
  mean(x, na.rm = na.rm)
}

tsfeature_tbl <- walmart_sales_weekly %>%
    group_by(id) %>%
    tk_tsfeatures(
      .date_var = Date,
      .value    = Weekly_Sales,
      .period   = 52,
      .features = c("frequency", "stl_features", "entropy", "acf_features", "my_mean"),
      .scale    = TRUE,
      .prefix   = "ts_"
    ) %>%
    ungroup()

tsfeature_tbl
## # A tibble: 7 × 22
##   id    ts_frequency ts_nperiods ts_seasonal_per… ts_trend ts_spike ts_linearity
##   <fct>        <dbl>       <dbl>            <dbl>    <dbl>    <dbl>        <dbl>
## 1 1_1             52           1               52 0.000670  2.80e-5      -0.0581
## 2 1_3             52           1               52 0.0614    9.87e-6       0.511 
## 3 1_8             52           1               52 0.756     1.95e-6       6.41  
## 4 1_13            52           1               52 0.354     4.75e-6       2.74  
## 5 1_38            52           1               52 0.425     1.79e-5      -4.07  
## 6 1_93            52           1               52 0.791     7.54e-7       6.22  
## 7 1_95            52           1               52 0.639     5.67e-7       3.94  
## # … with 15 more variables: ts_curvature <dbl>, ts_e_acf1 <dbl>,
## #   ts_e_acf10 <dbl>, ts_seasonal_strength <dbl>, ts_peak <dbl>,
## #   ts_trough <dbl>, ts_entropy <dbl>, ts_x_acf1 <dbl>, ts_x_acf10 <dbl>,
## #   ts_diff1_acf1 <dbl>, ts_diff1_acf10 <dbl>, ts_diff2_acf1 <dbl>,
## #   ts_diff2_acf10 <dbl>, ts_seas_acf1 <dbl>, ts_my_mean <dbl>

Clustering with K-Means

We can quickly add cluster assignments with the kmeans() function and some tidyverse data wrangling.

set.seed(123)


cluster_tbl <- tibble(
    cluster = tsfeature_tbl %>% 
        select(-id) %>%
        as.matrix() %>%
        kmeans(centers = 3, nstart = 100) %>%
        pluck("cluster")
) %>%
    bind_cols(
        tsfeature_tbl
    )

cluster_tbl
## # A tibble: 7 × 23
##   cluster id    ts_frequency ts_nperiods ts_seasonal_period ts_trend    ts_spike
##     <int> <fct>        <dbl>       <dbl>              <dbl>    <dbl>       <dbl>
## 1       2 1_1             52           1                 52 0.000670 0.0000280  
## 2       2 1_3             52           1                 52 0.0614   0.00000987 
## 3       2 1_8             52           1                 52 0.756    0.00000195 
## 4       1 1_13            52           1                 52 0.354    0.00000475 
## 5       3 1_38            52           1                 52 0.425    0.0000179  
## 6       3 1_93            52           1                 52 0.791    0.000000754
## 7       1 1_95            52           1                 52 0.639    0.000000567
## # … with 16 more variables: ts_linearity <dbl>, ts_curvature <dbl>,
## #   ts_e_acf1 <dbl>, ts_e_acf10 <dbl>, ts_seasonal_strength <dbl>,
## #   ts_peak <dbl>, ts_trough <dbl>, ts_entropy <dbl>, ts_x_acf1 <dbl>,
## #   ts_x_acf10 <dbl>, ts_diff1_acf1 <dbl>, ts_diff1_acf10 <dbl>,
## #   ts_diff2_acf1 <dbl>, ts_diff2_acf10 <dbl>, ts_seas_acf1 <dbl>,
## #   ts_my_mean <dbl>

Visualize the Cluster Assignments

Finally, we can visualize the cluster assignments by joining the cluster_tbl with the original walmart_sales_weekly and then plotting with plot_time_series().

cluster_tbl %>%
    select(cluster, id) %>%
    right_join(walmart_sales_weekly, by = "id") %>%
    group_by(id) %>%
    plot_time_series(
      Date, Weekly_Sales, 
      .color_var   = cluster, 
      .facet_ncol  = 2, 
      .interactive = FALSE
    )

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