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Local Reference Geometry Residual Augmentation for Imbalanced Time Series Classification

Chuanhang Qiu, Yanran Xu, Yue Wang, Anthony Bagnall

arXiv:2609.00093v1cs.LG

TL;DR

Imbalanced time series classification leaves open whether minority regions remain locally reliable after support is reduced, even when global feature structure remains useful. The paper introduces LRG, a training-only post-hoc residual augmentation for fixed representations, and reports gains across representation types and intervention settings, with improvements concentrated in locally risky regions.

  • Problem

    The paper asks whether local minority unreliability in an existing time-series representation can be identified and corrected without retraining the encoder.

  • Method

    LRG uses training features and labels to diagnose local exposure and class-mixture risk, then appends signed residual and LDA-projected residual features between a fixed extractor and classifier.

  • Results

    LRG improves learned, pretrained, and fixed representations, with balanced accuracy gains of 1.3-5.0 percentage points and Macro-F1 gains of 2.3-7.7 percentage points.

  • Takeaways & Limitations

    The results support signed local residuals as corrective information that complements imbalance interventions and classifier corrections, especially in high-risk local regions.

  • Takeaways & Limitations

    The evaluation is limited to univariate time series, leaving multivariate archives and channel-interaction effects for future work.

Abstract

from arXiv · show

Imbalanced time series classification is often addressed by changing the training distribution, objective, logits, or final threshold. These interventions address important biases, yet leave a representation-level question unmeasured: after minority support is reduced, does a learned feature space remain locally reliable around minority regions? We identify a training-local geometry failure: under imbalance, minority cases can lie in sparse, rest-dominated, or mixed feature-space neighborhoods, even when the representation retains useful global class structure. To diagnose and repair this failure, we propose Local Reference Geometry (LRG), a lightweight post-hoc feature augmentation module applied between a fixed feature extractor and the classifier head. Using training features only, LRG measures local exposure and class-mixture risk, then augments each fixed feature with a standardized signed displacement from nearby training geometry and an LDA-projected residual summary. On controlled UCR/Bake Off Redux imbalance benchmarks, paired raw-versus-LRG comparisons show gains for learned, pretrained, and fixed representations, including when LRG is combined with training-level interventions and post-encoder classifier corrections. Ablations show that the gain comes from the signed local residual appended to the original feature, rather than from generic prototype distances, affinity features, scalar statistics, or VLAD-style codes. Further analyses support the proposed local-geometry failure hypothesis: minority neighborhoods become increasingly rest-exposed under imbalance, training-local risk identifies error-prone regions, and LRG gains concentrate in those high-risk regions.

I. INTRODUCTION

The paper identifies a training-local geometry failure in imbalanced time series representations and proposes LRG, a post-hoc residual augmentation that operates without changing the feature extractor. It evaluates LRG as complementary to data-level, training-level, and classifier-level interventions.

  • Imbalance can leave minority samples in sparse, mixed, or rest-dominated neighborhoods even when coarse feature-space class structure remains useful.
  • LRG measures minority-neighborhood exposure and class-mixture risk using training features and labels, then appends signed local residual information to fixed features.
  • LRG is a post-hoc representation-level intervention that leaves the encoder or transform unchanged and can operate on learned, pretrained, or fixed representations.
  • Across controlled tasks, paired comparisons report gains for learned, pretrained, and fixed representations, including combinations with imbalance-aware methods and post-encoder corrections.
  • LRG complements sampling, loss, logit, calibration, and threshold interventions because it exposes local information rather than merely changing how existing coordinates are weighted.

C. Feature-Space Geometry and Diagnostic Representations

The paper positions LRG among feature-space encodings and neighborhood diagnostics while defining an evaluation setup that preserves multiclass labels and evaluates minority-versus-rest behavior.

  • Unlike prototype, affinity, projection, and VLAD-style representations designed as general encodings or classifiers, LRG adds a local repair coordinate after feature extraction.
  • LRG shares a training-neighborhood perspective with overlap and hardness diagnostics but uses relative rest exposure and signed residuals for feature-space repair.
  • A representation extractor maps each time series to a feature vector, after which the classifier head trains on training features and evaluates on test features.
  • The benchmark keeps multiclass labels separate during head training and treats only the training-defined minority class as the minority target.
  • Minority-oriented evaluation binarizes predictions into the minority class versus rest and reports sensitivity, specificity, and Min-F1.

B. Training-Local Geometry Diagnostics

The diagnostics quantify whether minority neighborhoods are more exposed to rest-class samples than expected from the training prior, using a shared training-only reference frame for diagnosis and repair.

  • Relative rest exposure (RRE) normalizes minority samples’ local non-minority-neighbor fraction by the split-specific random-neighbor expectation.
  • RRE equals one when local rest exposure matches the training prior, while larger values indicate greater-than-expected rest exposure.
  • All neighborhood diagnostics use training features and labels, and task-level RRE is averaged only after within-task computation.
  • LRG uses one training-local reference frame whose scalar outputs diagnose unreliable regions and vector outputs supply signed residual coordinates for repair.
  • The reference frame is built from standardized, normalized training features partitioned into k-means regions with centers, radii, and assigned members.
  • K-means anchors the local frame without requiring minority prototypes, while labels are reserved for the LDA residual and diagnostic risk analysis.

B. Local Affinity and Residual

LRG assigns features soft affinities to local reference regions and augments them with standardized signed residual coordinates. These residuals enable smooth, region-conditioned affine corrections while preserving the raw feature decision functions.

  • Soft affinities assign each feature to multiple nearby local reference regions, smoothing hard cluster boundaries.Interface samples can inherit a reference center from several nearby anchors.
  • The residual measures signed, direction-aware displacement from the local training frame after radial scaling.Scaling makes residual magnitudes comparable across dense and diffuse regions.
  • Residual augmentation retains every decision function available on the raw feature while adding local displacement information.The added terms are tied to the local reference frame rather than arbitrary nonlinear capacity.
  • A linear downstream head can express smooth region-conditioned affine corrections using the shared residual representation.Soft affinities produce a smooth correction instead of independent classifiers for separate regions.
  • Signed residuals encode deviation direction, unlike scalar affinity, purity, or reliability features that only mark local proximity or risk.LRG uses one lightweight downstream head rather than neural or region-specific classifiers.

D. LDA-Projected Residual

LRG projects high-dimensional local residuals onto supervised, shrinkage-regularized LDA directions fitted from training residuals and labels. The resulting compact residual features are appended to fixed representations and processed by lightweight heads using training-only fitting.

  • Shrinkage-regularized LDA summarizes residuals along class-relevant directions rather than relearning global directions from raw features.Residual-space projection targets class-aligned local deviations that a raw-feature linear head may already capture globally.
  • For C classes, the LDA residual contains at most C −1 directions, and the default experiments retain q = 1.The implementation uses K = 8 local regions and temperature τ = 1.0.
  • The final LRG feature appends the raw feature, full residual, and LDA-projected residual before downstream classification.The supplied passages identify this appended representation and its fixed reference-frame components.
  • LRG fits standardization, LDA projection, reference geometry, and classifier heads using training features and labels, then keeps the reference frame fixed at evaluation.Evaluation features are standardized, assigned soft affinities, converted to residual coordinates, and passed to the fitted head.
  • After feature extraction, reference construction and test-time costs depend on feature dimension, local-region count, LDA dimension, and class count rather than original series length.The stated reference cost is O(InK_effd), while per-sample local-frame and LDA cost is O(K_effd + dq).

V. EXPERIMENTS

The experiments use paired imbalance benchmarks built from UCR and Bake Off Redux and evaluate LRG across learned, pretrained, and randomized feature representations. Classifier heads and training configurations are matched to each representation setting.

  • The benchmark downsamples one training class while preserving each dataset’s original binary or multiclass label space.Target ratios are defined relative to the largest original training class.
  • The full benchmark scope covers 3:1, 5:1, 10:1, and 20:1 ratios, yielding 138 dataset-ratio tasks per backbone.Higher imbalance ratios include fewer datasets because not every original split can realize them.
  • LRG is evaluated with learned encoders, frozen pretrained MOMENT features, and randomized MultiRocket-Hydra feature-transform representations.Learned backbones include InceptionTime-style networks, ResNet1D, TCN, TimesNet, PatchTST-style, and MLP encoders.
  • Classifier protocols are matched to representation settings, using mainly class-weighted logistic regression and threshold-tuned logistic regression for MultiRocket-Hydra.Post-encoder correction experiments use calibrated, threshold-tuned, or retrained heads with and without LRG.
  • Table I summarizes retained dataset-ratio tasks by target training ratio, with non-count entries reported as median (min-max).

C. Paired Protocol and Baseline Groups

The paired protocol isolates the contribution of adding LRG residual features to an otherwise fixed representation, split, and classifier setting. Across representation and intervention studies, LRG consistently improves imbalance-sensitive performance, with leading variants ranking favorably.

  • Paired Protocol: Each paired comparison holds the representation, split, and classifier protocol fixed, changing only the addition of LRG residual features.This directly tests whether local residuals improve an available representation rather than comparing unrelated classifiers.
  • Representation Evaluation: Balanced accuracy improves by 1.3-5.0 percentage points and Macro-F1 by 2.3-7.7 percentage points across every representation setting.The gains include learned, frozen pretrained, and randomized representations, with all learned and frozen rows winning more tasks than losing.
  • Intervention Compatibility: LRG improves all baseline settings and backbones after imbalance-aware losses, samplers, or over-sampling methods.In the average block, balanced accuracy gains 2.9-3.7 points, Macro-F1 gains 3.7-4.5 points, and Min-F1 gains 3.6-4.7 points.
  • Intervention Compatibility: TCN gains 4.3-5.1 points in balanced accuracy, 5.4-6.3 points in Macro-F1, and 5.5-6.9 points in Min-F1 across imbalance-aware methods.The largest gains occur where the raw TCN representation is less stable.
  • Representation Evaluation: Table II reports per-task W/T/L counts for +LRG against raw features, with parenthetical Wilcoxon evidence levels.
  • Rank Comparison: The leading group in Figure 1 consists of +LRG variants, while small BS+LRG versus LDAM+LRG rank reversals are metric-specific rather than stable ordering.Ranks are computed over the same 138 backbone-dataset-ratio problems, with lower rank better.

C. Post-Encoder Classifier Corrections

LRG remains beneficial when applied before post-encoder classifier corrections, indicating that local residual coordinates complement decision-rule adjustments. Controls and ablations attribute the gains specifically to signed residual augmentation appended to the original features.

  • LRG improves balanced accuracy, Macro-F1, and Min-F1 for every evaluated post-encoder correction.
  • VectorScale gains 2.16 points in balanced accuracy, 2.77 points in Macro-F1, and 2.15 points in Min-F1 with LRG.
  • cRT gains 1.82 points in balanced accuracy, 2.59 points in Macro-F1, and 1.85 points in Min-F1 with LRG.
  • Alternative local descriptors provide smaller or trade-off-limited improvements, whereas LRG improves all main metrics and sensitivity while preserving the original feature.
  • Appending rfull and rlda together produces the strongest balanced accuracy, Macro-F1, and Min-F1 among the residual ablations.
  • All tested parameter settings retain positive aggregate gains, with modest variation across K and τ and small multiclass gains from larger dLDA.
  • The residual blocks account for most of the reported minority-versus-strongest-rest margin, although correlated coordinates prevent unique causal attribution.

VII. ANALYSIS

The analysis tests whether imbalance alters minority local geometry and whether training-local diagnostics identify regions where errors and LRG gains concentrate.

  • The analysis examines whether stronger imbalance makes minority neighborhoods more rest-exposed across feature families.
  • It also tests whether training-only class-composition risk identifies error-prone regions before test labels are observed.
  • Finally, it evaluates whether LRG gains are larger in high-risk regions and examines sensitivity-specificity trade-offs under severe imbalance.

A. RQ1: Does Imbalance Alter Local Geometry?

Stronger imbalance increases minority rest exposure across feature families, while training-local risk stratifies error-prone regions and identifies where LRG repairs are concentrated.

  • A. RQ1: Does Imbalance Alter Local Geometry?: RRE increases as imbalance becomes more severe across fixed, learned, and pretrained feature families.
  • B. RQ2: Do Local Risks Track Errors and LRG Gains?: Training-only hybrid and false-positive risk scores are propagated through the shared local reference frame to stratify test regions.
  • B. RQ2: Do Local Risks Track Errors and LRG Gains?: High-risk regions enrich false positives and have higher total error rates across every feature family.
  • B. RQ2: Do Local Risks Track Errors and LRG Gains?: The high-risk bin has both higher raw error and a larger paired LRG error reduction, showing that gains concentrate in locally entangled regions.
  • B. RQ2: Do Local Risks Track Errors and LRG Gains?: At 10:1 imbalance, false negatives decrease from 132 to 40, while false positives increase from 0 to 3 in the Strawberry visualization.

C. RQ3: High-Imbalance Behavior and Head-Level Safety

At higher imbalance, minority neighborhoods become more rest-exposed and LRG gains increase, supporting a training-local geometry failure that signed residuals can help repair. LRG complements head-level interventions by adding directional local information without globally replacing the representation.

  • RRE rises from 0.299 at 3:1 to 0.454 at 20:1, showing increasingly rest-exposed minority neighborhoods after global-prior normalization.
  • At 20:1, LRG improves balanced accuracy by +2.87pp, Min-F1 by +6.65pp, sensitivity by +2.64pp, and specificity by +2.91pp across five post-encoder settings.Both sensitivity and specificity improve, so the high-imbalance gain is not merely specificity-driven false-positive repair.
  • The signed local residual provides a directional coordinate relative to nearby training geometry, whereas reliability, affinity, and risk statistics only diagnose local conditions.Diagnostics locate sparse, mixed, or error-prone regions; the residual supplies information a downstream head can use for repair.
  • LRG is complementary to sampling, loss, and threshold interventions because it exposes residual information while the downstream head controls the sensitivity–specificity operating point.
  • The compact k-means-and-scalar-scale design avoids unstable covariance estimates but cannot model anisotropic local geometry.Extremely sparse or diffuse minority support can produce unstable residual directions, and the LDA projection can become high-variance.
  • The benchmark is univariate, leaving multivariate archives and channel effects on local reference geometry for future work.
  • Across learned, pretrained, and fixed representations, the largest gains occur in local regions identified as risky by the same training-only framework.
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