## styles in designs

Product design (or the form of a product) is an important aspect of new product development. This portion is where I (in collaboration with Jürgen Mihm, and Manuel Sosa) post results, data, and materials for our ongoing research on product design.

The styles dataset (found here) came out of this paper: using design patent data granted from 1977-2010, we categorized over 350,000 designs into over 9,000 styles (or categories of designs that are perceived to be visually similar).

The same dataset is also used in a collaboration with Yonghoon Lee (currently a working paper). If you use the data or would propose improvements / alternatives to our approach, please also let us know and we are happy to improve the approach over time, and acknowledge your work.

Attached is the pseudocode if you wish to identify styles on a dataset of designs (first you need a measure of similarity between them).

The approach in turn relies on the Ng-Jordan-Weiss (2002) algorithm (NJW), which approximately partitions a group of objects into two groups by minimizing conductance (a graph measure of heterogeneity). The evaluate step stops the algorithm corresponding to a post-hoc identified Δ value of about 0.002, at which point a sharp increase in conductance is observed. (The NJW algorithm is popular and you can find ready implementations online, e.g., from MATLAB central).

Given a similarity matrix between designs S

- Select the group with the lowest conductance ϕ: Calculate e
_{2}from the second step of NJW (below) for each group of designs. Label the group with the smallest e_{2}as G_{T}. Label the corresponding e_{2}as ϕ_{T}. (Note that there is only one group in first iteration, so G_{T}=G_{1}). - Partition G
_{T}into two groups: Partition G_{T}into two groups G_{T1}and G_{T2}using NJW. - Evaluate if partitioning is to continue: measure conductance ϕ over all the groups that created thus far, and label the lowest value identified ϕ
_{TNext}. Stop if ϕ_{TNext}>Δ+ϕ_{T}. Else, repeat Steps 1-3.

NJW:

- Compute the normalized graph Laplacian matrix L=I-D
^{1/2}SD^{1/2}where I is the identity matrix and D is a diagonal matrix with each entry the degree of the vertex. - Compute the two smallest eigenvalues {e
_{1},e_{2}} and their associated eigenvectors {u_{1},u_{2}} - Let U∈R
^{n×2}be the matrix containing {u_{1},u_{2}} as columns. - Normalize the rows of U to unit lengths (i.e., length = 1).
- Treat every row as a point in space, and use K-means (two groups) to group the n data points.

## measuring “decomposability” of a (utility) patent

Patent claims are written in such a strict way that the *subject matter* of the claim - that is, the thing that the idea the claim protects - can be fairly easily identified. This in turn allows to measure the degree to which a patent is **decomposable**. We say an invention is more decomposable (or modular) if it has more subject matters identified in this way. Conversely, it is less decomposable (or integral) if it has less subject matters identified in this way. (The intuition is that the more subject matters identified in an invention, the more one can apply ideas to individual parts of the invention without changing the rest).

I use this approach to show that an inventor is more likely to create breakthroughs when working alone (compared to working with others) especially when working on integral inventions. (see paper)

I have another working paper (with Steffen Keck, Haibo Liu, and Wenjie Tang) showing that teams with women members also outperform all-men teams when working on integral inventions (Invention Integrality and Team Gender Composition).

Check out the pseudocode below. I use CoreNLP to identify the noun phrase.

- For each claim, identify whether it is independent or dependent by using a regular-expression search for the term “claim #”, where # signifies any number.
- If the claim is independent:
- Break down the claim into individual words.
- Tag each word in the claim with its type: noun, adjective, verb, etc.
- Identify the root for each word (e.g., reduce the word “surfaces” to “surface”).
- Identify the subject matter for the claim based on first-occurring noun phrase with adjectives (e.g., “outer free end”, “elastic strip”, “bioprosthetic mitral valve replacement”).

- If the claim is dependent:
- Take the sentence starting after “claim #”—for example, from the text “A mitral valve replacement as in claim 1, wherein the base is…” use only “wherein the base is…”.
- Return to the substeps of Step 2.

- Count the number of distinct subject matter in the patent.