Towards an Ideal Store

Searching for Consumer-Inspired Structures in Product Networks

Kate Li, ISOM, Sawyer Business SchoolZhen Zhu, Marketing, Sawyer Business School

Dmitry Zinoviev, Mathematics and Computer Science, College of Arts and Sciences

Suffolk University, Boston MA

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”

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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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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)

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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

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● 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 storeDepartments per basket (absolute)

1.42 1.41

Departments per basket (relative)

0.04 (4%) 0.08 (8%)

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”

05/29/2015 19

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

05/29/2015 21

Correlation between Projects

0 7 14 21 28 35 42 490.22

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

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Smallest correlation

area

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0 7 14 21 28 35 42 49 56 63 70 77 84 91 9810

100

1000

10000

100000

Project length for the gap=15, days

Nu

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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.