What is a similarity matrix?

If you're looking to determine the similarity between two different data points, it's helpful to use a similarity matrix. This quantitative tool is used in many fields, such as mathematics and science. However, several common applications in product development and market research make similarity matrices extremely useful for evaluating data.

A similarity matrix is a matrix whose elements measure how similar a pair is to each other. The higher the value of the measure, the greater the similarity between the two. The smaller the value of the measure, the more dissimilar they are. 

The similarity measure you use depends on the object type you're evaluating. For example, you may evaluate data points, strings, probability distributions, or sets. The similarity measurement formulas vary with the different objects being measured.

Often, researchers seek to understand the similarity between two data points. To do so, they'll engage in cluster analysis, a way to separate sets of data points into small groups (clusters) according to their similarities. 

The appropriate approach to clustering depends on the data on hand and which kinds of similarities you’re evaluating. For example, if you're working with continuous data, you'll use a similarity measurement formula known as Euclidean distance. A measurement approach known as the Jaccard index is more appropriate for binary data.

You can also find similarity matrices used in sequence alignment, with dissimilar sequences earning lower scores and similar ones earning higher scores. As with cluster analysis, there are different similarity measurement approaches depending on the type of sequences you’re comparing.

The first time many product designers and market researchers see a similarity matrix is in a usability testing tool—a software application designed for quantitative and qualitative product testing. 

Many leading usability tools incorporate card sorting into their suite of available research tools. Accordingly, these tools commonly include a similarity matrix as a built-in data analysis tool. Rather than numerical calculations, a usability tool's similarity matrix is typically treated as a graphical representation of card pairs.

What is card sorting?

Card sorting is a common and useful way to gather insights about the information architecture of a website. The research method involves participants grouping labels on notecards in the order that makes sense to them. By evaluating these arrangements, you can better understand how to build and structure your website in a user-friendly and intuitive manner.

However, the more cards you include and the more participants you have, the more complex the card sort becomes. Many researchers looking to gauge user feedback from many locations will conduct card sorting virtually, which is an effective approach to gathering a lot of data. It's considered a best practice to limit the number of cards you include to 30–40 at most, while participants should be limited to no more than 15–30.

With these upper ranges, you can generate a robust data set while mitigating the risk of participant fatigue. But when you want to hone in on a specific subset of cards or identify trends in specific paired groupings, you'll need data analysis tools like similarity matrices to delve into specific subsets of cards or responses.

In a usability tool, you'll frequently find a similarity matrix option for card sorts that displays the results visually and numerically. Usually, the darker the shade denoting pairs, the higher the similarity between pairs. A simpler formula is often used to test similarity in these similarity matrices. 

The formula is: Pairing count * 100 / tester count total

This formula helps generate an easy-to-understand representation of pair similarities by percentage. Usability tools shade similar and dissimilar pairs accordingly.

Recommender systems

Similarity matrices are often used to develop recommender systems—the kind that powers some of our most widely used services like Netflix and Amazon. 

The algorithms of their platforms create similarity matrices for different pairs of items in their inventory and then compare their values to data generated by a consumer's preferences, likes, and clicks. With huge amounts of consumer data at their disposal, they can generate surprisingly accurate recommendations about what we may like and not like.

Data visualization

Similarity matrices also undergird several other types of common data visualization tools. For example, the software algorithms that produce heatmaps and dendrograms rely on similarity matrices to produce results. These tools are also commonly used to evaluate card sorts, among other market research study results.

A heatmap is a graphic representation of data with data of different magnitudes and frequencies depicted in different colors. Heatmaps are frequently used to analyze user behavior on a website. Dendrograms are visual representations of hierarchical relationships found in data subjected to hierarchical cluster analysis. The representations illustrate both the distinct clusters and the relationship between them.

Similarity matrices are great tools to determine what your users expect regarding design. They're especially useful when designing or evaluating the information architecture of a website and can help you make your site easy to use. 

Though usability tools like these exist, many web developers still rely on internal brainstorming, external sites, and other sources of information to guide their website construction efforts. However, doing so often results in hard-to-find content, overloaded menus, and high bounce rates.

If you're building a website or another product that relies on hierarchical order for UX, card sorting during the development process is essential. Using a similarity matrix to evaluate the results will help you capture the insight that can make the difference between a great user experience and a terrible one.

A similarity matrix may refer to a mathematical method for evaluating the difference between two types of data sets. Within the context of UX, it often refers to a data analysis tool found within usability testing software applications for evaluating card sorts.

A similarity matrix measures the similarities between two pairs. Within a mathematical context, it uses one of several similarity measurement formulas to measure the similarities between two pairs of objects. The higher the measure's value, the greater the similarity between the two pairs. 

Within a UX design context, similarity matrices are incorporated into usability tools and generate graphic representations of card sorts with pairs shaded according to their similarity.

Similarity matrices are used to evaluate multiple data types in fields ranging from biology to business. They’re frequently used in product development and marketing research to evaluate the information architecture of websites.