This document discusses research on modeling consumer purchasing behavior to better organize retail stores. It analyzes product purchase data to identify: 1) Short-term "product sets" representing items frequently bought together. These are used to construct an "ideal store" layout based on consumer behavior. 2) Long-term "consumer projects" representing extended purchase patterns over time. Preliminary analysis finds most projects are single shopping trips, but some contain multiple connected purchases. 3) The ideal store based on product sets performs nearly twice as well as the original store layout in reducing the number of departments visited per purchase basket. The research aims to further analyze and classify the identified consumer projects.

1. Towards an Ideal Store
Searching for Consumer-Inspired
Structures in Product Networks
Kate Li, ISOM, Sawyer Business School
Zhen Zhu, Marketing, Sawyer Business School
Dmitry Zinoviev, Mathematics and Computer Science,
College of Arts and Sciences
Suffolk University, Boston MA

2. 05/29/2015 2
Directions of Research
● “Product Sets”
– Identify product sets*—short-term consumer-
inspired purchase patterns
● “Ideal Store”
– Rearrange store departments based on the
consumer purchasing behavior
● “Consumer Projects”
– Identify consumer projects—long-term consumer-
inspired purchase patterns
*Formerly known as “tiles”

3. 05/29/2015 3
Directions of Research
● “Product Sets”
– Identify product sets*—short-term consumer-
inspired purchase patterns
● “Ideal Store”
– Rearrange store departments based on the
consumer purchasing behavior
● “Consumer Projects”
– Identify consumer projects—long-term consumer-
inspired purchase patterns
*Formerly known as “tiles”

4. 05/29/2015 4
Product Network
● Pairs of products frequently purchased together
– “Together”—within a 4-week window
– “Frequently”—statistically more often than by
pure chance
● Arrange the products in a product network
– 16,000 products (1.4% of all Store products)
– 142,412 connections

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Core Products
● Core Products: Products that are frequently
purchased together with too many other, seemingly
unrelated, products
● Such as: sodas, buckets, wood studs, paint trays,
top soil
● Core products are also staples: they are the most
frequently purchased products
● The core products pollute the network
– Remove the products with 210 connections or
more from the network!

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Product Sets
● Identify retailing-related geometric patterns in the
product network—product sets
● The product sets are represented as new nodes
in the product network—the synthetic nodes
(synodes)
● Synthetic nodes represent consumers'
purchasing choices!

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Cliques
● Complete Clique:
Each product is
connected to each
product; buy at least
two products
together

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Stars
● Star: The hub is connected to each leaf; all leaves
disconnected; buy the hub and exactly one leaf
● Substitutable products!

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Pendants and Chains
● Pendant/Chain: Products connected pairwise in a
chain-like fashion; one or both ends may also be
connected to other products; buy any two connected
products (a “link”)

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Wheels
● Wheel: A more
complex structure (a
special collection of 3-
cliques)
● A chain of at least three
products, wrapped
around a star; buy:
– any “chain link,”
– the hub and any
leaf or
– all three products
together

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Hierarchical Synodes
● Replace the original products with the product sets
(synodes) and repeat the discovery process until no
more synodes are found
● Get wheels of chains, chains of cliques, stars of
stars, etc.
● New product network:
– 9,765 products (was: 16,000)
– 27,698 connections (was: 142,412)
● Inspired by consumer purchasing behavior
● Easier to analyze (smaller, more modular)

12. 05/29/2015 12
Directions of Research
● “Product Sets”
– Identify product sets*—short-term consumer-
inspired purchase patterns
● “Ideal Store”
– Rearrange store departments based on the
consumer purchasing behavior
● “Consumer Projects”
– Identify consumer projects—long-term consumer-
inspired purchase patterns
*Formerly known as “tiles”

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Consumer-Inspired Departments
● In an ideal store, the products are organized by the
consumers' purchasing patterns

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Ideal Store Construction
● Start with the product network
● Replace frequently purchased products with product
sets (synodes)
● Detect communities in the new product network
– If two products belong to the same product set,
they are represented by one synode and are
guaranteed to be in the same community
● Rearrange products based on the community
structure

15. 05/29/2015 15
● Nodes =
departments
● Arcs = co-
purchases
● Node labels =
references to the
original store
departments (in
the order of
decreasing
contribution)
● Only the 15
largest and
connected
departments
shown

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How Ideal Is “Ideal”?
● Compare the performance of
the “ideal” store and the brick-
and-mortar (B&M) store:
― Use purchasing data
― Count the number of
visited departments,
based on the products
(real or synthetic) in
each of the 491,511
baskets that has at least
one item sold in the
“ideal” store

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“Real” ≠ “Ideal”!
● The “ideal” store performs almost twice better than
the B&M store!
– The average basket contains the products
from the same number of department
– However, an “ideal” department is smaller
than a B&M department
“Ideal” store B&M store
Departments per
basket (absolute)
1.42 1.41
Departments per
basket (relative)
0.04 (4%) 0.08 (8%)

18. 05/29/2015 18
Directions of Research
● “Product Sets”
– Identify product sets*—short-term consumer-
inspired purchase patterns
● “Ideal Store”
– Rearrange store departments based on the
consumer purchasing behavior
● “Consumer Projects”
– Identify consumer projects—long-term consumer-
inspired purchase patterns
*Formerly known as “tiles”

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This part is exploratory so far!

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How Long Is a Project?
● Look at the gaps between the store visits in the
same household: long* gaps probably separate one
project (or project stage) from another
● *What is a long gap? The products purchased
before the gap shall differ from the products
purchased after the gap
● Operational definition: the inter-project gap
minimizes the correlation between the departments
from which the products have been purchased
before and after the gap

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Correlation between Projects
0 7 14 21 28 35 42 49
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
Real store “Ideal” store
Minimal gap between projects, days
Correlationbetweenprojects
Smallest
correlation
area

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0 7 14 21 28 35 42 49 56 63 70 77 84 91 98
10
100
1000
10000
100000
Project length for the gap=15, days
Numberofprojects
How Long Is a Project?
61% of projects are
single-trip projects

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Project as a Subgraph
All projects Non-trivial projects
Min Avg Max Min Avg Max
Number of products 1 4.68 233 2 8.56 233
Number of
components
1 3.38 103 1 5.2 103
Average degree 0 0.38 13.8 0.06 0.98 13.8
Clustering coefficient 0 0.047 1 0 0.12 1
Density 0 0.105 1 0.002 0.271 1
249,741 projects (96,497 non-trivial projects—i.e., the projects with at
least one network connection,—39%).

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An Average Project

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We just started working on this. Next stage:
Unification and Classification of the extracted
projects.