When a Recommender System Starts Revealing Its Shape: Exploring Latent Space Through User Clusters and Behavioral Chains of Items

Recommender systems often behave like black boxes. Of course, how they do it depends on the model used. With matrix factorization, you feed it an interactions table, train a matrix factorization model, and it returns a rich world of latent structures. This includes user vectors, item vectors, distances, angles, and similarities. Somewhere in these spaces, you will see the reasons why customers have certain preferences.

When faced with real situations, it gradually becomes apparent that you need more than sterile responses and formal numbers. You start to ask: can we see how the model perceives users and items?

This leads you to really wanting to understand what the model “sees”.

This doesn’t just mean how well it optimizes metrics, but also what internal structure it forms and whether that structure matches real behavioral patterns. In this early stage, even before caring about whether the metrics look promising, there is a natural inclination to inspect whether the model’s internal world somehow resembles the real one.

This curiosity eventually became the starting point of a longer investigation that we didn’t initially expect: a way to look inside an implicit matrix factorization model and derive an interpretable structure from it. This article is about our attempts to do exactly that, across several production cases in retail, food service, and other domains.

Our version to achieve these objectives uses a proprietary multi-step clustering procedure. The internal recommender engine on top of which we build our constructions is based on the benfred/implicit library and its matrix factorization.

Why Standard Tools Weren’t Enough

Using the “benfred/implicit” recommender engine as the foundation, the initial system provides several convenient analytical tools, including item–item similarity. On its own, this similarity mechanism is quite reasonable: when the model is well-trained, the nearest neighbors of any item often give the first, coarse (but meaningful) glimpse into how the system perceives the structure of user interests.

This is valuable. In the majority of real-world datasets, items have recognizable names, and domain experts who know the assortment can sanity-check the model’s intuition: Does this item really look like the most similar ones? Is this set of neighbors plausible? Do these associations reflect actual purchasing patterns? Even if the picture is still rough, the similarity tool enables the first “alignment check” between the internal geometry of latent factors and the real market structure.

Crucially, this similarity distance is not arbitrary. By construction, it is consistent with the geometry of latent factors, and therefore with the behavioral patterns extracted from the interaction data. This is important for the next steps. Everything we build later inherits these properties. Our extended geometry does not break the link with user behavior; it reinforces it. We take the meaningful part of the latent-space structure and develop it further.

Despite these advantages and the fact that item similarity gives a useful initial window into the model, the insights obtainable from raw similarity alone were too limited. Standard item–item proximity was a good beginning, but similarity-based insights were too simplistic.

Once applied to real-world datasets (from minimal assortments to massive, sparse product catalogs), the approach surfaced several structural weaknesses of similarity-based inspection.

Before turning to more general observations, it helps to look at some immediate, straightforward situations where the limitations of similarity-based inspection reveal themselves almost instantly.

• Small assortments provide only a thin layer of information. Even with a few dozen items, similarity yields a limited and often already-obvious structure, offering little beyond what is known beforehand. Even standard item clustering would not have enriched the picture significantly.

• Extremely large catalogs are very difficult to inspect manually. Similarity chains become unmanageable, and even experts cannot interpret endless neighbor lists. This creates a structural bottleneck that invites more compact representations.

• Popular items distort nearest neighbors. High-frequency products flood neighborhoods, suppressing expected fine-grained patterns.

• Niche items vanish into sparsity. Groups of items that are relevant for small user segments become invisible when everything is reduced to a single similarity surface.

• Items play different functional roles. Substitutes, complements, variants, and seasonal alternates mean similarity cannot separate these relationships within one homogeneous score.

• User segments collapse into one geometry. Similarity mixes fundamentally different behavioral patterns, losing structure that clearly exists in the data.

When metrics remain inconclusive and similarity patterns look muddled, there is a natural desire to find additional ways to probe the latent space. Without alternative structural perspectives, it becomes difficult to tell whether the model is undertrained, inherently limited, or simply not yet interpretable.

These practical issues, although simple, consistently signal a deeper structural misalignment between global similarity and the true organization of user-item interactions. This becomes clearer when we look at broader, more conceptual observations. Here they are:

The system captures only pairwise proximity, not internal structure

Even when the recommendation system is well-trained and its nearest-neighbor relations look plausible, item similarity remains a fundamentally local signal. It tells us that item A is close to item B (and perhaps to item C), but it does not explain why this proximity exists, nor how these items relate to one another as a group. The geometry around a point can be meaningful, but similarity alone gives no way for understanding the internal organization of a connected region in latent space.

In practice, real product domains almost always contain branches, chains, and various micro-families of items. These are groups that share not just a vague affinity, but a common purchasing logic. Some items form tight, homogeneous “cores”; others appear as peripheral neighbors that are similar for fundamentally different reasons (e.g., universal best-sellers, near-duplicate variants, complementary add-ons, globally popular substitutes, multipack or bundled versions, seasonal or limited-run items, or deeply niche products that become relevant only in a specific user context). Pairwise, similarity cannot distinguish these roles. It flattens nuanced structure into a uniform list of neighbors.

As a result, examining item-to-item proximity one pair at a time does not reveal the shape of the underlying region in latent space. We cannot see whether a neighborhood is internally consistent, whether it splits into subfamilies, or whether it includes accidental intruders whose similarity is driven by global popularity rather than genuine thematic coherence. To make sense of these patterns, we need tools that can reason about groups of items as geometric and semantic units, not just isolated pairs. Taken together, the above limitations implicitly point toward the need for some form of higher-order organization.

Similarity is global when real user behavior is local

While point A highlights the structural flatness of pairwise similarity, a second limitation emerges from how real customers make decisions. Similarity, as implemented in latent-factor models, is inherently global: the distance between two items is computed in the full latent space, using information aggregated across the entire population. But user behavior is rarely global. It is local, segmented, and context-driven. This mismatch produces systematic distortions.

In real datasets, the same item can play different semantic roles for different user groups. A craft beer may be a niche preference for one segment, a routine staple for another, and an incidental add-on for a third. Yet global similarity collapses these nuances into a single, population-level notion of closeness. As a result, items that are “similar” in the aggregate may be practically unrelated for any particular subset of users.

Conversely, items that co-occur meaningfully within a specific behavioral niche often fail to appear close under global similarity. Their joint signal is strong within a coherent region of user behavior, but too weak or diluted across the whole dataset to influence the global geometry. This is especially visible in sparse or long-tail assortments, where the interests of small but important user segments are easy to drown out.

The practical consequence is a kind of semantic averaging: globally nearest neighbors tend not to represent any one group well. They often mix together incompatible behavioral contexts, such as the preferences of heavy buyers with those of casual shoppers, the patterns of specialists with those of generalists. For evaluation, debugging, interpretability, or discovering new insights, this makes similarity both unstable and even potentially misleading.

The implication is straightforward: a single global similarity score cannot capture the structure of user interests. It shows which products are close in a broad geometric sense, but it cannot explain how items group into distinct behavioral patterns or why different user segments treat the same product in different ways.

Once these limitations become clear (both the absence of internal structure in item neighborhoods and the lack of any meaningful context-specific differentiation), the need for a more structured representation arises naturally.

Our approach developed along a multi-stage path. We first clustered users, capturing stable segments of demand and revealing the major contexts in which items are actually compared. Then, within these user-defined contexts, we organized items into overlapping clusters, allowing each product to participate in several semantically coherent groups rather than a single undifferentiated neighborhood.

These clusters were designed precisely to turn scattered similarities into more pronounced patterns, which are sharper, more stable, and far easier to interpret. In practice and across real datasets, this layered organization consistently delivered the expected benefits.

From Global Space to Structured Segments

Before moving to the practical construction, it is useful to clarify what the task really becomes once global similarity is no longer sufficient.

Conceptually, our approach decomposes into two coordinated but distinct goals:

• Build a high-quality clustering mechanism for latent factor vectors themselves — a method that respects the geometry induced by the model’s similarity metric and remains stable across both user- and item-factor spaces.

• Use these clusters as the basis for interpretable structural units.

In principle, the first goal is symmetric across users and items: both inhabit the same latent geometry, and any clustering technique that works well in one space should work equally well in the other.

However, standard off-the-shelf clustering algorithms (even those designed for high-dimensional vectors) performed surprisingly poorly once we evaluated their results through the lens of interpretability. They produced clusters that were mathematically tidy yet semantically weak.

This gap led us to adopt a tailored method: a lightweight mathematical trick combined with a custom clustering routine that produced significantly clearer and more stable structures. The technical specifics are not the subject of current discussion here; what matters is that this method became the foundation for the two-stage construction that follows.

With this groundwork in place, the construction naturally unfolds in two steps: we begin by structuring the user side of the latent space, which is where behavioral segmentation provides the necessary context, then project this structure onto items, where overlapping clusters become interpretable and semantically rich.

Starting with Users

The first structural layer is a clustering of users. Here the logic is both natural and practical:

• People form behavioral segments, but not always cleanly, not always sharply, but the underlying tendency is real.

• Some groups consistently prefer premium items, others gravitate toward budget options; some follow seasonal patterns, others remain stable over time.

  These behavioral regularities make user clustering the most direct way to introduce context into an otherwise global latent space.

Important user clusters are not meant to be interpreted on their own. Unlike product clusters, they do not produce human-readable labels, and no domain expert can “recognize” a cluster of people. Their role is different:

• They divide the latent space into context-specific regions.

• They define distinct behavioral viewpoints through which similarity can be re-evaluated.

• They provide the conditioning needed to overcome the limitations of global similarity.

Once such user segments are formed using our custom latent-space clustering method, each cluster becomes a localized behavioral lens.

Instead of asking: “Which items are globally similar?”, we can now ask: “Which items are similar for this particular behavioral segment?”

This shift is the key that enables the next construction stage.

Passing to Items

With behaviorally grounded user clusters in hand, we can now define the second and ultimately more interpretable layer: overlapping item clusters.

Here the logic reverses: unlike people, items are interpretable. They have names, meanings, categories, and relationships that domain experts instantly recognize. And most importantly, a single item often participates in multiple behavioral contexts:

• A best-seller crosses many segments
• Some niche products become central within specific groups
• Substitutes and complements shift depending on who is doing the buying

Thus, item clusters should be overlapping by design. A rigid, non-overlapping clustering would collapse important information: The same product may play a different semantic role in different user segments, and only an overlapping structure can express this.

Operationally, for each user cluster we extract the most characteristic items: the ones that appear consistently in that group's latent preferences.

These items form a local chain (or spectrum) of preferences. This is a narrow, coherent slice of the product space that reflects a specific behavioral mode.

Stacking these segments across all user clusters yields the family of overlapping item clusters. Together they provide:

• Internal structure within item neighborhoods
• Context-specific interpretations of products
• Multiple viewpoints for each item
• Immediate readability for anyone familiar with the domain (thanks to product names)

This is the layer where the system becomes “inspectable”: product chains expose structure that raw latent vectors hide, yet they remain anchored in the geometry of the model.

As practical projects confirm, this two-stage construction indeed transforms scattered global similarities into stable, interpretable patterns that align with real user behavior.