What are Data Lakes?
Along with all the activity and marketing hype around Big Data, there are still troubling loose ends to contend with: how do we associate disparate but overlapping data to each other if we’re simply to “pour” data together? Using the lake paradigm, how is one to fish out the specific data that match some form of criterion, as well as anything else associated to it? Some explanations point to adding some type information, but this limits how data from different collections (related but not exactly equal types) can be cross-linked when necessary. We can choose to link entities across types using constrained rules or semantics. However, if we are to rely on some form of data semantics to associate related things, how is this data semantics to be established, added to the lake, and then managed? The metaphor for the lake quickly begins to get murky…
But what happened to semantic data aka linked data, to the ability to link data from multiple sources across an organization or even the Internet? What of all the promises of truly interlinked data independent of where they arise? Is the data lake the replacement paradigm? One notable shift has been to the localization of data to within an organization’s auspices, rather than relying on outbound links, as championed by semantic web standards. But is the lake terminology right for this? In the sciences, there are always external resources that need to be updated and merged with the internal sets. If not properly using linked data identifier (URI) semantics, what then? What is really offered here?
To many, the lake analogy affords a serene image of lazy afternoons of sailing and fishing; but it is deceptive nonetheless. Are things best discovered by using simple tags, are these controlled? Are unique relations the key in identifying special objects? Is it a particular tangle of linked things that help fish out a prize catch? Do large assemblages of multiple facts come out whole in a meaningful way, or is it a jumble of stringy facts? It is not a far stretch to conjure up the thought of an Edmund Fitzgerald-size data wreck if one does not take the time to structure the inserted data. Some things dumped into the lake may never see the light of day again. Is data depth now become a good thing or a bad thing? In this article, we will take a deeper dive into the challenges facing data aggregation and struxturing, and some new ideas of how to better organize growing and evolving data resources.
A concept that was introduced in a previous article, is the Yoneda lemma (abstract algebras), which formally ties all records of entities (including keys) from any table to each other to create one large network of composite relations. It makes it possible to define a query algebra (e.g., SQL, SPARQL) that works with any schema for a dataset. In the case of data lakes, this foundation is missing or at least has not been formally introduced, so a large uncertainty exists on what the formal basis will be to ensure data integrity for insertions, updates and queries. Currently data lakes appear to be a convenient option for handling large influx of datasets, coming in varied, disjoint structural forms. Sean Martin of Cambridge Semantics said of current efforts : “We see customers creating big data graveyards, dumping everything into HDFS [Hadoop Distributed File System] and hoping to do something with it down the road. But then they just lose track of what’s there”.
An alternative generalized model is the concept of what I call a Datacomb, which relies on both efficiency and logic (ala geometric algebras) for storage, structure, and discoverability. Here any typed real-world entity (RWE) or conjunction of RWEs, can be mapped using single or multiple keys. The latter is usually associated with JOIN results (Patient + Primary Physician), but which can be automatically typed as a Cartesian Product (CP) using existing atomic entities:
Such a relation instance materializes if a fact exists about a patient having a primary physician, as in any join, but now a compound typed-object exists as well. This compound object may uniquely contain data on when the patient first began going to this doctor, and what was the circumstance of the first visit. The actual visits are also compositionally typed (and linked) as VISIT ≝ PATIENT×PPHYSICIAN×DATE, which would include the location, any tests performed, and what was the diagnosis. Cartesian products have the basic ability to be decomposed (projected) into the set of atomic entities ((PATIENT, PPHYSICIAN), DATE), with their original associated (row) data. If we wish to include prescribed drug therapies, we can organize this by extending the previous objects thusly: PATIENT×PPHYSICIAN×DATE×THERAPY_START. For every a ∊ PATIENT, b ∊ PPHYSICIAN, c ∊ DATE, and d ∊ THERAPY_START, a 3-simplex (4 vertices) is created, where each combination from 1-4 conjunctions (total of 15) has compositional semantic meaning:
The ability to compose and decompose objects is very useful and mathematically sound, and enables databases to be quite flexible. In fact, any set of k-joined entities can be (if one needs to) decomposed generally into k subsets of k-1 CP entities, which then can be decomposed into k(k-1)/2 subsets of k-2 CP entities, etc, until we arrive at the k atomic entities. This structure is commonly known as a Simplex and the data instance constructs are known as Simplicial Sets, and was first described by David Spivak as having many uses in data storage . One application of them is in statistical inference when computing/analyzing joint and marginal frequencies or probabilities of mixed combinations of similar events or attributes. For example, if a patient has a tumor containing somatic mutations [EGFR amp, P53, PTEN], a mutation simplex is defined that may be part of a larger mutation pattern [EGFR amp, CDK4, P53, PTEN] that some patients have, as well as subsuming smaller patterns of others: [EGFR amp, PTEN] and [EGFR amp, P53]. The entities are different subsets of mutations that are co-occurring, and may each contain the incidence counts for each combination found in patients, or an identified molecular interaction between the co-occurring mutations. This is a numeric example, which can be further combined with other data.
It is worthwhile considering that the actual physical storage implementation of a Simplicial database  does not have to allocate every mutation combination possible, nor every combination that exists within sets of patients. The logical constraints are complete, so the model may need to only allocate those for which useful data can be associated (e.g., therapies). This can be considered a form of storage caching and compression, for faster look-ups and associations. Nonetheless, a simple analysis of real genomic data from ~1000 cancer patients required only a few million unique simplicial entities to be allocated and linked, which makes this highly tractable in today’s large-scale storage systems. Moreover, in some data spaces where events are strongly mutually associated, the combinatorics is not unbounded, and often simplicial sets become saturated (relatively sparse) at intermediate and lower levels.
Note the hierarchy of entities from large mutation combinations to smaller subsets form a “sieve”. Each patient’s pattern is linked to the top (complete) entity, and then filters down to all the subsets contained within that pattern, providing information of which patients share a particular sub-pattern. If these mutation distributions are not statistically independent, it provides evidence there is an underlying mechanism at work [see Fichtenholtz, 2016]. The simplicial database makes it very efficient to find all cases of shared patterns, compared to a query filter (for each) in a relational DB or an edge traversal in a data graph. The mutation simplex is formed directly from calculating and indexing the patterns from a list of mutations for each patient’s analysis, and is cost efficient after most patterns are captured.
Returning to our original PATIENT×PHYSICIAN×DATE example, one can build a simplicial model around the PATIENT×PHYSICIAN pair (edge) linked to a sequence of dates (vertices) to create an implicit series visits (=PATIENT×PHYSICIAN×DATE), i.e., triangular faces. This structure includes a PHYSICIAN×DATE edge, which maps to all the patients that doctor has seen on the same day. A clear advantage of this form of database, is that all key combinations are pre-computed (aka pre-joined), so a simple canonical n-way hash of the values can find the full set of data in a single lookup; this is very well-suited for fast analytics, where multiple lookups are equivalent to query caching. Another advantage is that the CP entities have clear automatic types and can be handled exactly by type-dependent downstream processes, specifically by descriptive algebras supporting CP entities (e.g., MUTATION_SIMPLEX⊗DISEASE⊗THERAPY à DISEASE⊗RESPONSE). The combined simplicial set naturally lends itself to analytics for effective treatments based on genomics and disease types.
The basis for the ideas presented here arise from Category Theory (CT), which ensures logical consistency within data model schema. The interconnected set of simplicial entities is described as a simplicial complex (partial overlaps of different simplicial elements) and is a well-defined object in CT, and is at the heart of the formal definition of what we call a Datacomb. The complex possesses a formal query algebra for any subset of simplicial entities, and can be used to extract any geometric (connected) subset of data, including measurable things like frequencies. Note also that any graph data-model is automatically a subset of a datacomb since it is just the 1-D skeleton (vertices and edges) of the complex. The datacomb model can be implemented on top of a few different storage technologies, such as multi-array DBs, RDBs, key-valued NOSQL DBs, graph DBs, and (materialized) column-stores (relational systems may not be practical since they require explicit types and type-specific keying). The simplicial logic that is required to interface with them can be layered on top of the existing technologies, so that a common API can be installed on different storage technologies. In fact, RDF could actually be used as a universal description for internal structures in any data system (not only triplestores). All in all, the datacomb approach is a more rigorously defined solution for complex data sets than offered by the data lake meme, one with real definable specifications and multiple analytic and mining applications.
The datacomb can be applied to several different settings: most naturally, it can be mapped to any existing data-array storage systems already in place, with the extension to more flexibly and automatically handle complex-typed objects, useful for precomputing data for use in downstream analytics. In relational DB instances, frequently materialized joins can be more formally and efficiently captured and accessed using a datacomb framework, making it easier and faster to query on conjoined content, as well as recalling the atomic entities on demand. Datacombs serve as the common superset for both data-arrays and relational data, and therefore form a powerful higher-order framework that covers both data analytics and full sets of non-numeric data. Inasmuch, the datacomb offers a lot of advantages to organize and define datasets for any machine-learning tasks, by flexibly formatting raw data into pre-processed structures required by many ML platforms.
In addition, when dealing with closely related entities (e.g., lists of genes and their coded proteins), instead of ambiguously choosing one or the other identifier (e.g., P204392) for recalling the whole set of related data records, a simplex of the related entities would provide a much more even and efficient way to get all the matches. It would then be keyed by any one entity (vertices), or the hashed-sum of the full set (k-cell). This would go a long way to solving the biomedical disambiguation problem. This is the formal equivalent of earlier attempts like SRS to connect multiple related molecular entities.
Datacombs can also handle non-local data by serving as local caches of all the intra- and inter-relations between data records (e.g., genomic data references), providing something much more substantial in function and structure than existing data lake models, analogous to a universal data switchboard. A cloud-based implementation should be very effective by managing all the relations between simple and complex entities from thousands (or more) of different sources. It would then effectively solve what the semantic web initiative had always alluded to do but never did: explicitly handling of complex entity logic (indexing, typing, and filtering) from data that resides in multiple sources, which are usually thought to be (yet unsupported) in the purview of ontologies.
Many organizations intending to utilize their collections of data more effectively are positioning themselves around big data. Yet most of the data environments are a mixture of different classes of technologies, developed/installed at different times, for different goals, and accessed/managed by different groups. Trying to unify this heterogeneous mix will have a broad range of costs depending on the type of technology used and the urgency for completing it (and of course thoroughness of the solution). This easily can range from $100,000’s to $millions; but the cost of doing this incorrectly within a time limit may be even orders of magnitude greater (over $100 millions) due to the business impact of a non-optimal solution, and the new added cost—and additional time—of doing it right the second time. The looming challenge facing many organizations means they need to properly and confidently choose the best approach, fully considering both the maturity of the technologies, and enhanced paradigms for reducing development and maintenance costs. There is concern that no database product from any traditional company is quite ready for the challenge. The consumer must therefore rely on their own knowledge of their precise needs and determine what level of innovation in which they will be willing to invest. A brave new world is emerging for information technologies.
1 –Stein, Brian; Morrison, Alan (2014). in Data lakes and the promise of unsiloed data (pdf) (Report). Technology Forecast: Rethinking integration. PricewaterhouseCooper.
2 – David I. Spivak. Simplicial Databases, https://arxiv.org/abs/0904.2012, 2009
3 - Fichtenholtz, AM, Camarda, ND, Neumann EK. Knowledge-Based Bioinformatics Predicting Significance of Unknown Variants In Glial Tumors Through Sub-Class Enrichment. pp 297-308, Pacific Symposium on Biocomputing 2016.
 Regularized structures that are semantically flexible, as with honeycombs in beehives
 One could argue that EVENT=DATE×LOCATION should be used rather than DATE, but often it is not needed since location does not change within a day.
 They are at the heart of new methodologies including topological data analysis (TDA)