Dissimilarity-Based Query Strategy (DQS)

• DQS is an active learning query strategy that refines anomaly detection thresholds using a minimal number of labeled queries.
• It applies dynamic time warping on full anomaly-score sequences to evaluate dissimilarity and ensure diverse, non-redundant selections.
• Empirical results show DQS excels in low-budget scenarios, effectively outperforming random and uncertainty-based methods under key conditions.

Searching arXiv for the cited DQS paper and closely related work to ground the encyclopedia entry. Dissimilarity-Based Query Strategy (DQS) is an active-learning query strategy for time series anomaly detection that uses a small number of queried labels to refine decision-threshold selection rather than to replace the underlying anomaly detector. Its defining idea is to maximize the diversity of queried samples by evaluating similarity between anomaly-score sequences with dynamic time warping (DTW), so that the queried set is diverse, representative, and non-redundant. In the formulation introduced for multivariate time series, DQS is positioned as a low-budget alternative to random, top-score, and threshold-near uncertainty querying, and its main reported advantage is strongest performance in small-budget scenarios, with more mixed behavior under mislabelling (Correia et al., 6 Sep 2025).

1. Definition and problem setting

DQS was introduced for settings in which anomaly detection is nominally unsupervised, but threshold selection remains a bottleneck. The method does not alter the anomaly detector itself. Instead, it queries a small number of labels from an oracle and uses them to set a better threshold than a purely unsupervised procedure can provide. The motivation is that many unsupervised approaches for time series anomaly detection depend heavily on threshold selection, and thresholding can be distorted by anomalous samples in the validation or training split (Correia et al., 6 Sep 2025).

The strategy operates on anomaly scores rather than directly on raw time series. For each time series $\mathcal{S}_n$, a model $\mathcal{M}$ produces a univariate anomaly-score sequence

$$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$

Querying is then performed over the set of anomaly-score sequences rather than over the original observations. This design reflects the paper’s aim to improve threshold calibration for an existing detector rather than to learn a new representation from scratch (Correia et al., 6 Sep 2025).

The specific gap DQS addresses is that earlier query strategies in time series anomaly detection select samples randomly, select the most anomalous samples, or select samples near a threshold, but do not explicitly maximize diversity among queried samples. DQS therefore prefers samples whose anomaly-score patterns are dissimilar to the already queried ones. The intended effect is better threshold refinement when labels are scarce and each query must be informative (Correia et al., 6 Sep 2025).

2. Selection rule and DTW-based dissimilarity

The core dissimilarity measure in DQS is DTW applied to anomaly-score sequences. DTW is used because it can compare sequences of different lengths and does not require pointwise alignment. In the paper’s formulation, the local alignment cost for two univariate sequences $\mathbf{x}$ and $\mathbf{y}$ is

$\mathbf{C}_{u,v} = (x_u-y_v)^2.$

The cumulative cost matrix is then computed by dynamic programming, and the DTW distance is the square root of the cumulative cost of the optimal alignment path. In this terminology, a large DTW distance means high dissimilarity between two anomaly-score sequences (Correia et al., 6 Sep 2025).

DQS is iterative within each query round and uses a budget $B$. The first query in the first round is chosen randomly from the candidate set. For subsequent queries, the procedure first finds the candidate sequence that is most similar to any already queried sample, and then, among the remaining candidates, selects the one that is most dissimilar to that most-similar sequence. The operational effect is to expand the queried set away from already covered score patterns rather than repeatedly selecting near-duplicates (Correia et al., 6 Sep 2025).

This mechanism is notable because the dissimilarity computation is not applied to raw feature vectors, labels, or scalar anomaly scores. It is applied to full anomaly-score sequences. As a consequence, DQS treats temporal score morphology as the object of comparison. This is especially relevant for variable-length sequences, where fixed-length vector comparison would be less natural (Correia et al., 6 Sep 2025).

3. Role in threshold refinement

DQS functions as a threshold-calibration layer in an otherwise unsupervised anomaly-detection pipeline. In the experimental setup, the detector is TeVAE. The procedure is: train the detector in an unsupervised way, produce anomaly scores for validation sequences, treat those validation sequences as the candidate pool for active learning, query a small budget of sequences using DQS, obtain oracle labels, use those labels to refine the threshold by grid-searching candidate thresholds, apply the refined threshold to the most recent model, and repeat as more data becomes available (Correia et al., 6 Sep 2025).

The candidate pool is explicitly taken from the validation subset rather than the training set. The stated reason is that training data already influences the model and would be reconstructed with lower anomaly scores, which would bias the query process. DQS is therefore coupled to the validation distribution, where threshold selection is being calibrated, rather than to the data used directly for fitting the detector (Correia et al., 6 Sep 2025).

Two threshold baselines structure the evaluation. The unsupervised threshold $\tau_\text{us}$ is set as the maximum anomaly score observed in the validation subset. The hypothetical best threshold $\tau_\text{best}$ is obtained by grid-searching on the test set to maximize $F_1$; it serves as an upper bound rather than as a deployable method. Within this framework, DQS is evaluated as one way of using a limited number of labels to move threshold selection away from $\mathcal{M}$0 and toward the performance implied by $\mathcal{M}$1 (Correia et al., 6 Sep 2025).

4. Experimental behavior under budget and mislabelling constraints

The reported experiments use the PATH dataset, described as a discrete-sequence, multivariate time series dataset representing automotive powertrain dynamics. The unlabelled data is split into 34 progressively larger temporal chunks corresponding roughly to 1 day, 7 days, 14 days, 21 days, and 28 days. The evaluation uses three folds and seeds 1 to 3, and the validation subset is 20% of the unlabeled subset (Correia et al., 6 Sep 2025).

The baseline unsupervised threshold performs poorly and degrades over time. The reported values are $\mathcal{M}$2 at 1 day, $\mathcal{M}$3 at 7 days, $\mathcal{M}$4 at 14 days, $\mathcal{M}$5 at 21 days, and $\mathcal{M}$6 at 28 days. By contrast, the hypothetical best threshold is much higher and improves strongly over time: $\mathcal{M}$7, $\mathcal{M}$8, $\mathcal{M}$9, $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$0, and $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$1 over the same splits. These values are used in the paper to motivate active threshold refinement (Correia et al., 6 Sep 2025).

For query budgets $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$2, DQS is strongest in low-budget settings. At $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$3, the reported values include DQS $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$4 versus TQS $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$5, UQS $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$6, and RQS $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$7 at 7 days, then DQS $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$8 at 14 days, $$\mathbf{s}_{n} = \mathcal{M}(\mathcal{S}_{n}), \qquad \mathbf{s}_{n} \in \mathbb{R}^{T_n}.$$9 at 21 days, and $\mathbf{x}$0 at 28 days. For $\mathbf{x}$1, DQS is again best or near-best, with reported values including $\mathbf{x}$2 at 1 day, $\mathbf{x}$3 at 14 days, $\mathbf{x}$4 at 21 days, and $\mathbf{x}$5 at 28 days. For $\mathbf{x}$6, DQS remains strong at intermediate splits, with reported values including $\mathbf{x}$7 at 7 days, $\mathbf{x}$8 at 14 days, and $\mathbf{x}$9 at 21 days, but at the final 28-day split RQS slightly exceeds it, with RQS $\mathbf{y}$0 versus DQS $\mathbf{y}$1 (Correia et al., 6 Sep 2025).

The paper also studies mislabelling probabilities $\mathbf{y}$2 by flipping labels according to a Bernoulli process. Under noisy oracle conditions, DQS remains competitive, especially at moderate noise, but the picture becomes less clear. TQS appears more robust in some noisy-label settings, results scatter more as noise increases, and RQS performs worst at higher mislabelling rates. The reported conclusion is therefore conditional rather than absolute: DQS is best when the query budget is small, TQS may be more robust under mislabelling, and any query strategy is better than using the unsupervised threshold alone, even with mislabelling (Correia et al., 6 Sep 2025).

5. Relation to diversification and broader dissimilarity-based querying

DQS belongs to a broader family of dissimilarity-driven selection methods in which the query criterion is the marginal contribution of a candidate to set-level diversity. A closely related example in big-data query processing defines an element’s possible diversity gain as

$\mathbf{y}$3

and uses this score in a one-pass stream-model-based diversification framework. In that work, diversity is instantiated as variance for numerical data and as the sum of pairwise edit distances for string data, again making dissimilarity the basis of selection rather than relevance alone (Zhang et al., 2018).

A second line of work complicates the interpretation of any DQS-style method that relies on pairwise dissimilarity aggregation. In query answering, pairwise-distance-based diversity measures are shown to exhibit unintuitive behavior: with the sum of pairwise distances, adding a near-duplicate can artificially increase diversity a lot, while with the min operator, diversity can decrease when adding an element, violating monotonicity. The alternative proposed there is a volume-based diversity function

$\mathbf{y}$4

which is monotone and submodular and therefore admits the classic greedy $\mathbf{y}$5-approximation guarantee. This suggests that pairwise dissimilarity, while operationally useful, does not automatically endow a query strategy with well-behaved set-function structure (Arenas et al., 15 Sep 2025).

The broader research landscape also uses dissimilarity-based querying outside label selection for anomaly detection. In multi-robot sensing, the query object is the next sensing location, scored by a kriging-derived dissimilarity map so that robots move toward regions where the current model is least supported by past measurements (Kawase et al., 26 Mar 2026). In probabilistic interval prediction, the query object is a candidate future output paired with the current regressor, and dissimilarity to stored measurements is converted into an empirical conditional density (Carnerero et al., 2020). These cases indicate that “dissimilarity-based query strategy” can refer more generally to selecting labels, answers, locations, or predictions by measuring how poorly represented a candidate is by the current dataset.

6. Conceptual boundaries, misconceptions, and implications

A common misconception is to treat DQS as an anomaly detector. In the reported formulation, it is not. It is a query strategy used to obtain labels that refine threshold selection for an existing unsupervised detector. Its performance must therefore be interpreted jointly with the base detector, the candidate-pool construction, and the threshold-search procedure (Correia et al., 6 Sep 2025).

A second misconception is to assume that DQS operates on the raw multivariate time series. The method instead computes dissimilarity on anomaly-score sequences. This matters because the queried diversity is diversity in score-space behavior, not necessarily diversity in the original observation space. A plausible implication is that DQS is most aligned with threshold refinement when anomaly-score morphology is itself informative for separating anomalous from nominal cases (Correia et al., 6 Sep 2025).

A third misconception is that a dissimilarity-maximizing strategy must be uniformly superior. The reported evidence does not support that conclusion. DQS is strongest when the budget is very limited, but RQS slightly exceeds it at the 28-day split for $\mathbf{y}$6, and TQS appears more robust in some noisy-oracle regimes. More generally, the broader diversification literature shows that pairwise-discrepancy-based set functions may fail monotonicity or other desiderata, so empirical gains from dissimilarity-driven querying should not be conflated with universal structural optimality (Correia et al., 6 Sep 2025, Arenas et al., 15 Sep 2025).

Within these boundaries, DQS occupies a precise niche: it is a non-parametric, DTW-based active-learning strategy for low-budget threshold calibration in unsupervised multivariate time series anomaly detection. Its contribution is to make diversity among queried anomaly-score sequences an explicit design objective, and its principal empirical claim is that this objective is especially effective when the number of available labels is small (Correia et al., 6 Sep 2025).