NaN-Pattern Pre-partitioning in Data Segmentation

• NaN-pattern pre-partitioning is a technique that groups records with identical missing value indicators to form homogeneous data subsets for improved processing.
• It enhances downstream tasks—including anonymization and neural network modeling—by ensuring uniformity in the available features within each partition.
• Empirical results show reduced information loss and faster execution, optimizing scalability in privacy-preserving and parallel processing environments.

NaN-pattern pre-partitioning is a data segmentation technique in contemporary partition-based algorithms, most notably integrated into privacy-preserving frameworks and fast neural network constructions. It systematically divides records or features based on the pattern of missing values (NaNs) prior to the application of downstream partitioning or generalization methodologies. This upfront discretization of missingness enhances the homogeneity of partitioned subsets and can be leveraged for improved utility, efficiency, and scalability in anonymization engines and local model fitting regimes.

1. Foundational Concept

NaN-pattern pre-partitioning refers to the pre-processing step where records sharing identical patterns of missing values (NaNs) across selected quasi-identifier (QID) attributes are grouped. Each record is mapped to a binary pattern—‘1’ for NaN, ‘0’ for present—spanning all QIDs. Partitions form by aggregating records whose NaN indicator vectors are identical. For example, a table with QID_A and QID_B yields up to four partitions, reflecting the set $$\{(\mathsf{QID}_A \text{ NaN}, \mathsf{QID}_B \text{ NaN}), (\mathsf{QID}_A \text{ NaN}, \mathsf{QID}_B \text{ present}), (\mathsf{QID}_A \text{ present}, \mathsf{QID}_B \text{ NaN}), (\mathsf{QID}_A \text{ present}, \mathsf{QID}_B \text{ present})\}$$ (Bloomston et al., 7 Oct 2025). Partitioning by NaN patterns is orthogonal to classical domain-driven partitioning based on value ranges, and may precede any further multidimensional partitioning, regression, or anonymization process.

2. Methodological Implementation

The implementation in Core Mondrian (Bloomston et al., 7 Oct 2025) adopts a grouping algorithm that is concisely illustrated by the following pseudocode:

def NaNPatternPartition(dataset, QID_list): partitions = {} for record in dataset: pattern = [] for qid in QID_list: pattern.append(1 if record[qid] is NaN else 0) key = tuple(pattern) if key not in partitions: partitions[key] = [] partitions[key].append(record) return partitions

This routine scans each record, forms a "NaN-mask," and assigns the record to its respective partition. In the actual system, these partitions are instantiated as nodes within a partition tree (e.g., Node_DeferredCutData__PartitionRoot). Each homogeneous partition is subsequently processed as an independent sub-anonymization or modeling task. The segmentation serves to isolate the effects of missingness, preventing cross-contamination of NaN patterns in subsequent cut-score-driven splits.

3. Impact on Partition Quality and Utility Metrics

Grouping records by NaN-pattern prior to anonymization or modeling significantly improves utility preservation. All records within a partition share the same set of available attributes, enabling generalization or predictive modeling steps to operate on data of uniform completeness. In privacy frameworks such as Core Mondrian, this results in smoother generalization hierarchies and mitigates the risk of excessive suppression or degraded utility due to intermingling heterogeneous missing patterns. Experimental results indicate lower Discernibility Metric (DM) scores and higher Revised Information Loss Metric (RILM) scores for numeric quasi-identifier sets compared to algorithms that do not incorporate NaN-pattern pre-partitioning (Bloomston et al., 7 Oct 2025).

4. Scalability and Performance in Parallel Frameworks

The upfront partitioning by NaN-patterns generates smaller, more uniform partitions, which are well-suited for parallel execution engines. Core Mondrian leverages this structure by distributing partitions independently across available cores, integrating with a hybrid recursive/queue execution model. Empirical evidence demonstrates up to 4x speedup in anonymization runtime over sequential execution, attributed to both partition uniformity and parallel scheduling efficiency (Bloomston et al., 7 Oct 2025). The modular segmentation obviates the need for expensive backtracking during recursive partitioning and allows deterministic output by processing homogeneous blocks.

5. Relevance to Reactive NaN Repair and Memory Partitioning

Reactive NaN repair, as described in numerical applications on approximate memory (Hamada et al., 2018), shares methodological parallels with NaN-pattern pre-partitioning. Both strategies operate under the principle of targeted intervention—repairing or partitioning only those records or memory regions with critical NaN patterns, while tolerating non-fatal errors. For example, in high-bit-error-rate memory, the location back-tracing mechanism for NaN repair can be extended to preemptively segment memory into “critical” vs. “non-critical” regions based on their observed NaN manifestation rates. This focused approach minimizes resource overhead and preserves computational integrity in environments where ECC is impractical (Hamada et al., 2018). A plausible implication is that future memory partitioning designs could leverage hardware signals to trigger pre-partitioning routines analogous to those in Core Mondrian.

6. Application in Partitioned Subspace Neural Networks

NaN-pattern pre-partitioning also underlies the construction of localized subspace models in machine learning architectures, notably in the PairNet framework (Zhang, 2020). The n-dimensional input space is divided into M subspaces based on partitioning intervals of each feature, effectively segmenting the data into regions with shared patterns of feature values (and potentially missingness). Within each subspace, a fast, analytically optimized PairNet model is trained using multivariate least squares, without the need for iterative backpropagation. This facilitates rapid, parallelizable model fitting and is conducive to big data mining and real-time learning scenarios. While the PairNet paper focuses on numeric range-based partitioning, the general notion is congruent—partitioning by structural patterns (including NaN masks) yields homogeneous modeling domains (Zhang, 2020).

7. Experimental Outcomes and Practical Significance

In Core Mondrian, experimental benchmarks on the UCI ADULT dataset and scaled synthetic datasets up to 1 million records establish that the integration of NaN-pattern pre-partitioning demonstrably reduces information loss and improves processing speed. Utility metrics (DM and RILM) are consistently improved relative to the Original Mondrian algorithm, which does not handle missingness at the partitioning stage. The modular, parallelizable nature of pre-partitioned datasets contributes to enhanced scalability and supports production-level privacy-compliant analytics (Bloomston et al., 7 Oct 2025). In PairNet architectures, partitioned modeling enables lower testing mean squared errors and dramatically reduced training times compared to traditional ANNs (Zhang, 2020).

Conclusion

NaN-pattern pre-partitioning is a utility- and performance optimizing pre-processing step in anonymization and machine learning frameworks. By segmenting records based on missing value patterns before downstream partitioning, the technique ensures the homogeneity of partitions, enables tailored generalization or modeling, and supports scalable parallel execution. Empirical evidence confirms its beneficial impact on information loss metrics and runtime efficiency. As demonstrated in Core Mondrian and PairNet, and informed by reactive NaN repair logic, this strategy is integral to modern high-performance, utility-preserving data analytics pipelines (Bloomston et al., 7 Oct 2025, Zhang, 2020, Hamada et al., 2018).