RFM Clustering — Recency × Frequency × Monetary

RFM analysis is a 30-year-old segmentation framework, originally for direct marketing. Each subject (customer or, here, product) is summarized by three numbers:

Recency — how long ago was it last purchased? (lower = better)
Frequency — how often was it purchased? (higher = better)
Monetary — how much revenue did it generate? (higher = better)

The classic application is customer scoring; we apply the same logic at the article level — which products in the catalog are healthy, which are dying, which need attention?

Code

library(readr)
library(dplyr)
library(ggplot2)
library(plotly)
library(rpart)
library(rpart.plot)

set.seed(42)

Compute R, F, M per article

Reference date is the last day of the data window. Recency is measured in months since the article’s last sale.

Code

.data_path <- if (file.exists("data/raw/transactions.csv")) "data/raw/transactions.csv" else "data/synthetic/transactions.csv"
raw <- read_delim(.data_path, delim = ";", show_col_types = FALSE)

REF_DATE <- max(raw$date)

rfm <- raw |>
  group_by(article_name) |>
  summarise(
    frequency = n(),
    value     = sum(gross_price),
    recency   = as.numeric(REF_DATE - max(date)) / 30.4375,  # months
    .groups   = "drop"
  )

cat(sprintf("Reference date: %s | %d articles, recency range [%.1f, %.1f] months, value range [%.0f, %.0f] EUR\n",
            format(REF_DATE), nrow(rfm), min(rfm$recency), max(rfm$recency),
            min(rfm$value), max(rfm$value)))

Reference date: 2017-06-30 | 40 articles, recency range [0.0, 3.7] months, value range [1828, 413866] EUR

A quick look at the marginal distributions:

Code

library(patchwork)
p1 <- ggplot(rfm, aes(recency))   + geom_histogram(bins = 15, fill = "steelblue") + labs(x = "recency (months)")
p2 <- ggplot(rfm, aes(frequency)) + geom_histogram(bins = 15, fill = "darkorange") + labs(x = "frequency")
p3 <- ggplot(rfm, aes(value))     + geom_histogram(bins = 15, fill = "seagreen") + labs(x = "value (EUR)")
p1 + p2 + p3

Figure 1: Marginal distributions of recency (months since last sale), frequency (line-item count), and monetary value (EUR).

Most articles have very recent last sales — the data window ends at the reference date and most products are still selling. A small tail of articles last sold months ago — on synthetic data these are the declining products engineered into the synthesis (filing_cabinet, dvd_player); on real data they are end-of-life SKUs.

How many clusters?

Code

features <- scale(rfm[, c("frequency", "recency", "value")])

inertias <- sapply(1:10, function(k) {
  kmeans(features, centers = k, nstart = 10)$tot.withinss
})

ggplot(data.frame(k = 1:10, ss = inertias), aes(k, ss)) +
  geom_line() + geom_point(size = 2) +
  scale_x_continuous(breaks = 1:10) +
  labs(x = "Number of clusters", y = "Within-cluster SS")

Figure 2: Elbow plot: the within-cluster sum of squares drops sharply through k=4, flattening after.

The bend lands around k = 4 — same as the BCG analysis, suggesting the catalog naturally falls into roughly four product archetypes.

Fit and rank clusters

Code

K <- 4
fit <- kmeans(features, centers = K, nstart = 25)
rfm$cluster <- fit$cluster

# Rank clusters: higher value & frequency, lower recency = better
centers <- as.data.frame(fit$centers) |>
  tibble::rowid_to_column("cluster") |>
  mutate(weight = (frequency + value - recency) / 3) |>
  arrange(desc(weight)) |>
  mutate(rank = row_number())

rfm <- rfm |>
  left_join(centers |> select(cluster, rank), by = "cluster")

centers |> select(cluster, rank, recency, frequency, value, weight) |> round(3)

  cluster rank recency frequency  value weight
1       4    1  -0.382     1.418  2.714  1.505
2       3    2  -0.350     1.168  0.026  0.514
3       1    3  -0.142    -0.496 -0.379 -0.245
4       2    4   4.007    -1.056 -0.599 -1.887

The 3D view

Plotly gives us a rotatable, zoomable 3D scatter — much more useful than a static projection when three axes matter.

Code

# Density-aware marker styling: small dataset (synth, ~40 items) keeps the
# original look; large dataset (real, ~2,100 items) needs smaller faded
# markers to keep the cluster colours readable through overlap.
.marker_size    <- if (nrow(rfm) < 100) 6 else 3
.marker_opacity <- if (nrow(rfm) < 100) 0.85 else 0.45

plot_ly(
  rfm,
  x = ~recency, y = ~frequency, z = ~value,
  color = ~factor(rank),
  colors = c("#27ae60", "#3498db", "#f39c12", "#c0392b"),
  text = ~article_name,
  hovertemplate = paste0(
    "<b>%{text}</b><br>",
    "recency: %{x:.1f} mo<br>",
    "frequency: %{y}<br>",
    "value: €%{z:,.0f}<extra></extra>"
  ),
  type = "scatter3d", mode = "markers",
  marker = list(size = .marker_size, opacity = .marker_opacity)
) |>
  layout(
    scene = list(
      xaxis = list(title = "Recency (months)"),
      yaxis = list(title = "Frequency"),
      zaxis = list(title = "Monetary value (EUR)")
    ),
    legend = list(title = list(text = "<b>Rank</b>"))
  )

Figure 3: Interactive 3D RFM space. Drag to rotate, scroll to zoom, hover for product names. Cluster numbers are ranked: 1 = top performers (frequent, valuable, recent). On real data (~2,100 products) markers shrink and fade automatically so the cluster colours stay readable through overlap.

Cluster narrative

Code

rfm |>
  group_by(rank) |>
  summarise(
    n_products = n(),
    mean_recency   = round(mean(recency),   2),
    mean_frequency = round(mean(frequency), 0),
    mean_value     = round(mean(value),     0),
    examples = paste(head(article_name[order(-value)], 4), collapse = ", "),
    .groups = "drop"
  )

# A tibble: 4 × 6
   rank n_products mean_recency mean_frequency mean_value examples              
  <int>      <int>        <dbl>          <dbl>      <dbl> <chr>                 
1     1          4         0.04            323     316320 sofa, bed, mattress, …
2     2          8         0.07            294      65841 armchair, coffee_tabl…
3     3         26         0.22            103      28128 tv, wardrobe, sideboa…
4     4          2         3.4              38       7619 filing_cabinet, dvd_p…

Reading the table:

Rank 1 — recent, frequently sold, high revenue. The flagship products (sofas, beds, dining tables and their high-frequency partners). Marketing should protect these.
Rank 2 / 3 — middle of the pack. Either decent volume but lower revenue (smaller-ticket items like chairs and decor), or solid revenue but lower volume.
Rank 4 — high recency (i.e. not recent — last sold months ago), low frequency, low value. The end-of-life products. Candidates for delisting or replacement.

A simple rule from the clusters

The decision tree reduces the 4-cluster structure to a few interpretable splits:

Code

tree <- rpart(rank ~ recency + frequency + value, data = rfm,
              method = "class", control = rpart.control(maxdepth = 4))
rpart.plot(tree, type = 2, extra = 100, fallen.leaves = TRUE,
           box.palette = "BuOr", main = "")

Figure 4: Decision tree predicting cluster rank from raw R/F/M values. The thresholds are the boundaries the k-means actually picked, made readable.

Codified as a few if-thresholds, this is a deployable scoring rule that needs no clustering library at runtime.

Coarse view — RFM at Department level

The Family-level scatter is detailed enough for catalog operations. For executive reporting the more digestible aggregation is Department — six store-floor sections instead of dozens of products. With six points clustering becomes pointless; we just compute R/F/M per department and read the result directly.

Code

raw_dept <- raw |>
  filter(!is.na(department), department != "") |>
  group_by(department) |>
  summarise(
    frequency = n(),
    value     = sum(gross_price),
    recency   = as.numeric(REF_DATE - max(date)) / 30.4375,
    .groups   = "drop"
  ) |>
  arrange(desc(value))

raw_dept

# A tibble: 6 × 4
  department frequency   value recency
  <chr>          <int>   <dbl>   <dbl>
1 Living          2447 956087.  0     
2 Bedroom         1190 769246.  0     
3 Dining          1689 540159.  0.0329
4 Office           567 158775.  0     
5 Storage          203  68596.  0.0657
6 Outdoor          296  45717.  0.164

Code

ggplot(raw_dept, aes(recency, value, size = frequency, label = department)) +
  geom_point(color = "#3498db", alpha = 0.7) +
  geom_text(size = 4, fontface = "bold", vjust = -1.4) +
  scale_size(range = c(8, 20), guide = "none") +
  labs(x = "Recency (months since last sale)", y = "Total revenue (EUR)") +
  theme_minimal()

Department-level readings are coarser by design — you lose the per-product detail but gain a cleaner narrative for stakeholders who don’t want to parse a 40-point 3D scatter.

Takeaway

The k=4 RFM segmentation cleanly separates the catalog into a healthy core, a long middle, and a tail of dying products. The framework was originally designed for customers but transfers directly to articles — and the same techniques work for any entity you can summarize as (recency, frequency, monetary).

For the standalone Python version of this same analysis with a more interactive 3D experience, see notebooks/rfm_clustering.ipynb.

--- title: "RFM Clustering — Recency × Frequency × Monetary" --- [RFM analysis](https://en.wikipedia.org/wiki/RFM_(market_research)) is a 30-year-old segmentation framework, originally for direct marketing. Each subject (customer or, here, *product*) is summarized by three numbers: - **Recency** — how long ago was it last purchased? (lower = better) - **Frequency** — how often was it purchased? (higher = better) - **Monetary** — how much revenue did it generate? (higher = better) The classic application is customer scoring; we apply the same logic at the article level — *which products in the catalog are healthy, which are dying, which need attention?* ```{r} #| label: setup #| message: false library(readr) library(dplyr) library(ggplot2) library(plotly) library(rpart) library(rpart.plot) set.seed(42) ``` ## Compute R, F, M per article Reference date is the last day of the data window. Recency is measured in months since the article's last sale. ```{r} #| label: rfm-features .data_path <- if (file.exists("data/raw/transactions.csv")) "data/raw/transactions.csv" else "data/synthetic/transactions.csv" raw <- read_delim(.data_path, delim = ";", show_col_types = FALSE) REF_DATE <- max(raw$date) rfm <- raw |> group_by(article_name) |> summarise( frequency = n(), value = sum(gross_price), recency = as.numeric(REF_DATE - max(date)) / 30.4375, # months .groups = "drop" ) cat(sprintf("Reference date: %s | %d articles, recency range [%.1f, %.1f] months, value range [%.0f, %.0f] EUR\n", format(REF_DATE), nrow(rfm), min(rfm$recency), max(rfm$recency), min(rfm$value), max(rfm$value))) ``` A quick look at the marginal distributions: ```{r} #| label: fig-rfm-distributions #| fig-cap: "Marginal distributions of recency (months since last sale), frequency (line-item count), and monetary value (EUR)." #| fig-width: 11 #| fig-height: 3.2 library(patchwork) p1 <- ggplot(rfm, aes(recency)) + geom_histogram(bins = 15, fill = "steelblue") + labs(x = "recency (months)") p2 <- ggplot(rfm, aes(frequency)) + geom_histogram(bins = 15, fill = "darkorange") + labs(x = "frequency") p3 <- ggplot(rfm, aes(value)) + geom_histogram(bins = 15, fill = "seagreen") + labs(x = "value (EUR)") p1 + p2 + p3 ``` Most articles have very recent last sales — the data window ends at the reference date and most products are still selling. A small tail of articles last sold months ago — on synthetic data these are the declining products engineered into the synthesis (`filing_cabinet`, `dvd_player`); on real data they are end-of-life SKUs. ## How many clusters? ```{r} #| label: fig-elbow #| fig-cap: "Elbow plot: the within-cluster sum of squares drops sharply through k=4, flattening after." features <- scale(rfm[, c("frequency", "recency", "value")]) inertias <- sapply(1:10, function(k) { kmeans(features, centers = k, nstart = 10)$tot.withinss }) ggplot(data.frame(k = 1:10, ss = inertias), aes(k, ss)) + geom_line() + geom_point(size = 2) + scale_x_continuous(breaks = 1:10) + labs(x = "Number of clusters", y = "Within-cluster SS") ``` The bend lands around **k = 4** — same as the BCG analysis, suggesting the catalog naturally falls into roughly four product archetypes. ## Fit and rank clusters ```{r} #| label: fit-kmeans K <- 4 fit <- kmeans(features, centers = K, nstart = 25) rfm$cluster <- fit$cluster # Rank clusters: higher value & frequency, lower recency = better centers <- as.data.frame(fit$centers) |> tibble::rowid_to_column("cluster") |> mutate(weight = (frequency + value - recency) / 3) |> arrange(desc(weight)) |> mutate(rank = row_number()) rfm <- rfm |> left_join(centers |> select(cluster, rank), by = "cluster") centers |> select(cluster, rank, recency, frequency, value, weight) |> round(3) ``` ## The 3D view Plotly gives us a rotatable, zoomable 3D scatter — much more useful than a static projection when three axes matter. ```{r} #| label: fig-3d-rfm #| fig-cap: "Interactive 3D RFM space. Drag to rotate, scroll to zoom, hover for product names. Cluster numbers are ranked: 1 = top performers (frequent, valuable, recent). On real data (~2,100 products) markers shrink and fade automatically so the cluster colours stay readable through overlap." # Density-aware marker styling: small dataset (synth, ~40 items) keeps the # original look; large dataset (real, ~2,100 items) needs smaller faded # markers to keep the cluster colours readable through overlap. .marker_size <- if (nrow(rfm) < 100) 6 else 3 .marker_opacity <- if (nrow(rfm) < 100) 0.85 else 0.45 plot_ly( rfm, x = ~recency, y = ~frequency, z = ~value, color = ~factor(rank), colors = c("#27ae60", "#3498db", "#f39c12", "#c0392b"), text = ~article_name, hovertemplate = paste0( "%{text} ", "recency: %{x:.1f} mo ", "frequency: %{y} ", "value: €%{z:,.0f}<extra></extra>" ), type = "scatter3d", mode = "markers", marker = list(size = .marker_size, opacity = .marker_opacity) ) |> layout( scene = list( xaxis = list(title = "Recency (months)"), yaxis = list(title = "Frequency"), zaxis = list(title = "Monetary value (EUR)") ), legend = list(title = list(text = "Rank")) ) ``` ## Cluster narrative ```{r} #| label: cluster-summary rfm |> group_by(rank) |> summarise( n_products = n(), mean_recency = round(mean(recency), 2), mean_frequency = round(mean(frequency), 0), mean_value = round(mean(value), 0), examples = paste(head(article_name[order(-value)], 4), collapse = ", "), .groups = "drop" ) ``` Reading the table: - **Rank 1** — recent, frequently sold, high revenue. The flagship products (sofas, beds, dining tables and their high-frequency partners). Marketing should protect these. - **Rank 2 / 3** — middle of the pack. Either decent volume but lower revenue (smaller-ticket items like chairs and decor), or solid revenue but lower volume. - **Rank 4** — high recency (i.e. *not* recent — last sold months ago), low frequency, low value. The end-of-life products. Candidates for delisting or replacement. ## A simple rule from the clusters The decision tree reduces the 4-cluster structure to a few interpretable splits: ```{r} #| label: fig-tree #| fig-cap: "Decision tree predicting cluster rank from raw R/F/M values. The thresholds are the boundaries the k-means actually picked, made readable." tree <- rpart(rank ~ recency + frequency + value, data = rfm, method = "class", control = rpart.control(maxdepth = 4)) rpart.plot(tree, type = 2, extra = 100, fallen.leaves = TRUE, box.palette = "BuOr", main = "") ``` Codified as a few `if`-thresholds, this is a deployable scoring rule that needs no clustering library at runtime. ## Coarse view — RFM at Department level The Family-level scatter is detailed enough for catalog operations. For executive reporting the more digestible aggregation is **Department** — six store-floor sections instead of dozens of products. With six points clustering becomes pointless; we just compute R/F/M per department and read the result directly. ```{r} #| label: rfm-dept raw_dept <- raw |> filter(!is.na(department), department != "") |> group_by(department) |> summarise( frequency = n(), value = sum(gross_price), recency = as.numeric(REF_DATE - max(date)) / 30.4375, .groups = "drop" ) |> arrange(desc(value)) raw_dept ``` ```{r} #| label: fig-rfm-dept #| fig-cap: "Department-level RFM. Bubble size encodes frequency; positions encode recency × monetary value. Useful for budget conversations." ggplot(raw_dept, aes(recency, value, size = frequency, label = department)) + geom_point(color = "#3498db", alpha = 0.7) + geom_text(size = 4, fontface = "bold", vjust = -1.4) + scale_size(range = c(8, 20), guide = "none") + labs(x = "Recency (months since last sale)", y = "Total revenue (EUR)") + theme_minimal() ``` Department-level readings are coarser by design — you lose the per-product detail but gain a cleaner narrative for stakeholders who don't want to parse a 40-point 3D scatter. ## Takeaway The k=4 RFM segmentation cleanly separates the catalog into a healthy core, a long middle, and a tail of dying products. The framework was originally designed for customers but transfers directly to articles — and the same techniques work for *any* entity you can summarize as (recency, frequency, monetary). For the standalone Python version of this same analysis with a more interactive 3D experience, see [`notebooks/rfm_clustering.ipynb`](notebooks/rfm_clustering.ipynb).