EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning

Hao ZhuPiotr Koniusz

article2022CVPR63 citations

Proposes an unsupervised subspace projection and a constrained Wasserstein clustering method to efficiently separate novel classes at test time without backbone fine-tuning, achieving strong performance gains across multiple transductive few-shot benchmarks.

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Modern computer vision models typically require large volumes of labeled data to achieve high accuracy, making deployment costly and difficult in specialized domains where human annotation requires rare expertise. Few-shot learning addresses this bottleneck by enabling models to recognize new visual categories from only a few labeled examples. The article introduces an efficient inference approach designed to boost classification accuracy by learning a compact, discriminant feature space directly during test time without requiring expensive retraining or complex meta-learning pipelines.

The article develops and evaluates two modular techniques: Unsupervised Discriminant Subspace Learning (EASE) and Constrained Wasserstein Mean Shift Clustering (SIAMESE). EASE captures the underlying structure of image data by generating similarity and dissimilarity relationships across labeled and unlabeled samples, solving for an optimal linear projection via closed-form singular value decomposition. SIAMESE then refines the estimated class centers and final label assignments using optimal transport principles that account for class balance constraints and known support labels. The framework was evaluated across five standard benchmark image datasets (mini-ImageNet, tiered-ImageNet, CIFAR-FS, CUB, and OpenMIC) under both transductive and semi-supervised conditions using standard deep neural network backbones.

The empirical findings demonstrate significant improvements over existing approaches. When paired together, the proposed methods outperformed previous state-of-the-art methods across all tested benchmarks, achieving up to an 84.54% accuracy in 1-shot tasks on tiered-ImageNet with a ResNet-12 backbone. In semi-supervised settings, the method provided consistent accuracy gains ranging between 3% and 6% over leading baselines on mini-ImageNet. The approach proved robust across different network architectures, including standard pre-trained networks trained without episodic meta-learning, and operated roughly ten times faster than competing transductive algorithms, requiring only 6 to 9 milliseconds per classification task.

These results show that high-accuracy few-shot classification can be achieved using fast, plug-and-play mathematical operations at inference time rather than costly architectural modifications or specialized training regimes. This significantly lowers computational costs and latency for deploying vision models to edge or enterprise systems that must adapt to new classes on the fly. Organizations seeking to deploy image recognition under severe data constraints should consider integrating test-time subspace projection and optimal transport clustering into their existing computer vision backbones.

Decision-makers should note that the primary performance gains rely on the transductive setting, which assumes access to a batch of unlabeled query samples rather than classifying a single isolated image at a time. Performance also scales with query set size and may degrade if unlabeled data contains entirely unrelated or out-of-distribution classes. Before enterprise deployment, teams should conduct pilot testing on domain-specific data to ensure query batch sizes and data distributions align with operating conditions.

Australian National University CSIRO’s Data61 few-shot learning fisher discriminant analysis subspace learning transductive few-shot learning unsupervised discriminant subspace learning Wasserstein mean shift clustering

allenhaozhu/EASE Zhu et al (2022).pdf

Paper: Meta-Learning for Semi-Supervised Few-Shot Classification, Mengye Ren et al. (2018). It introduces the semi-supervised episodic few-shot classification setup and prototype clustering on unlabeled data that EASE directly builds upon.
Paper: Prototypical Networks for Few-shot Learning, Jake Snell et al. (2017). It establishes metric-based prototypical classification, which provides the foundational class-prototype formulation extended by SIAMESE.
Paper: A Closer Look at Few-shot Classification, Wei-Yu Chen et al. (2019). It provides the standardized benchmarking protocols and pre-trained feature backbone baselines upon which transductive few-shot subspace methods operate.
Paper: Few-Shot Learning with Graph Neural Networks, Victor Garcia et al. (2017). It formalizes transductive few-shot learning by modeling support and query samples jointly via similarity structures.
Paper: Meta-Learning With Differentiable Convex Optimization, Kwonjoon Lee et al. (2019). It demonstrates learning convex, discriminative classifiers directly on top of deep embeddings for few-shot adaptation.
Paper: TADAM: Task dependent adaptive metric for improved few-shot learning, Boris N. Oreshkin et al. (2018). It examines task-dependent metric adaptation and distance scaling for few-shot image classification.
Paper: Unsupervised Visual Domain Adaptation Using Subspace Alignment, Basura Fernando et al. (2013). It introduces foundational linear subspace alignment methods via SVD for unsupervised domain adaptation.
Paper: A survey on semi-supervised learning, Jesper E. van Engelen et al. (2019). It surveys the core assumptions and graph-based label propagation principles underlying transductive and semi-supervised learning.

Paper: Revisiting Prototypical Network for Cross Domain Few-Shot Learning, Fei Zhou et al. (2023). It extends prototypical few-shot classification to challenging cross-domain distributions where test-time feature spaces diverge significantly.
Paper: Rethinking the Correlation in Few-Shot Segmentation: A Buoys View, Yuan Wang et al. (2023). It applies optimal transport and structural correlation alignment mechanisms between support and query representations to few-shot dense prediction tasks.
Paper: Few-Shot Object Detection with Foundation Models, Guangxing Han et al. (2024). It builds on modern foundation model representations and metric matching principles to scale few-shot learning to object detection.

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Abstract

Few-shot learning (FSL) has received a lot of attention due to its remarkable ability to adapt to novel classes. Although many techniques have been proposed for FSL, they mostly focus on improving FSL backbones. Some works also focus on learning on top of the features generated by these backbones to adapt them to novel classes. We present an unsuPervised discriminAnt Subspace lEarning (EASE) that improves transductive few-shot learning performance by learning a linear projection onto a subspace built from features of the support set and the unlabeled query set in the test time. Specifically, based on the support set and the unlabeled query set, we generate the similarity matrix and the dissimilarity matrix based on the structure prior for the proposed EASE method, which is efficiently solved with SVD. We also introduce conStraIned wAsserstein MEan Shift clustEring (SIAMESE) which extends Sinkhorn K-means by incorporating labeled support samples. SIAMESE works on the features obtained from EASE to estimate class centers and query predictions. On the mini-ImageNet, tiered-ImageNet, CIFAR-FS, CUB and OpenMIC benchmarks, both steps significantly boost the performance in transductive FSL and semi-supervised FSL.

Topics

few-shot learning fisher discriminant analysis subspace learning supervised machine learning unsupervised learning method locality preserving projections online learning

Keywords

transductive few-shot learning unsupervised discriminant subspace learning Wasserstein mean shift clustering transductive inference label propagation low-rank representation semi-supervised few-shot learning

1. Introduction
2. Related Work
3. Methodology
3.1. Model Description
3.2. Unsupervised Discriminant Subspace Learning
3.3. Constrained Wasserstein Mean Shift Clustering (SIAMESE)
4. Experiments
4.1. FSL benchmarks used in our experiments
4.2. Ablations
5. Conclusions
References

Knowls

Knowl 1 — Unsupervised Discriminant Subspace Learning (EASE) Objective and Solution
model/method
Unsupervised Discriminant Subspace Learning (EASE) optimizes an orthonormal linear projection matrix $W \in \mathbb{R}^{O' \times O}$ (with $O' \ll O$ ) at test time to project feature representations $f_\theta(X) \in \mathbb{R}^{(L+U) \times O}$ of a support set $S$ ( $L = K \times N$ samples) and query set $Q$ ( $U = K \times B$ samples) into a lower-dimensional, discriminative subspace without using label supervision.

Let $X = [x_1, \dots, x_{L+U}]^\top$ contain all support and query image samples, and let $\tilde{A}_{sim} = D_{sim}^{-1/2} A_{sim} D_{sim}^{-1/2}$ and $\tilde{A}_{dis} = D_{dis}^{-1/2} A_{dis} D_{dis}^{-1/2}$ denote the normalized affinity matrices for sample similarity and dissimilarity, with Laplacian matrices $L_{sim} = I - \tilde{A}_{sim}$ and $L_{dis} = I - \tilde{A}_{dis}$ . The optimization problem balances preserving similarity and maximizing dissimilarity using a balancing hyperparameter $\alpha > 0$ :

$W^* = \arg\min_{W W^\top = I} W f_\theta(X)^\top (\alpha \tilde{A}_{dis} - \tilde{A}_{sim}) f_\theta(X) W^\top$

The optimal projection matrix $W^*$ is obtained in closed form by solving a generalized eigenvalue problem: selecting the $O'$ leading eigenvectors corresponding to the top- $O'$ largest eigenvalues of the matrix:

$M_{EASE} = f_\theta(X)^\top (\tilde{A}_{sim} - \alpha \tilde{A}_{dis}) f_\theta(X)$
Knowl 2 — Low-Rank Representation (LRR) Similarity Matrix Construction
model/method
To construct the sample similarity matrix $A_{sim}$ under the prior that feature vectors in a $K$ -way task lie in a union of $K$ distinct subspaces (yielding a $K$ -block-diagonal affinity structure), EASE computes a self-representation coefficient matrix $Z \in \mathbb{R}^{(L+U) \times (L+U)}$ via low-rank representation (LRR):

$\arg\min_Z \|f_\theta(X) - f_\theta(X)Z\|_F^2 \quad \text{s.t.} \quad \text{rank}(Z) = K$

where $f_\theta(X) \in \mathbb{R}^{(L+U) \times O}$ is the concatenated feature matrix of $L$ support points and $U$ query points.

This rank-constrained problem is solved via the thin/skinny Singular Value Decomposition (SVD) of $f_\theta(X) = U \Sigma V^\top$ :
1. For each row of $V$ , only the components corresponding to the top- $K$ largest singular values in $\Sigma$ are retained.
2. The representation matrix is calculated as $Z = V^\top V$ .
3. The non-negative, zero-diagonal similarity affinity matrix is formed as:
$W_{sim} = |Z| - \text{diag}(|Z|)$
1. The normalized similarity matrix is $\tilde{A}_{sim} = D_{sim}^{-1/2} W_{sim} D_{sim}^{-1/2}$ , where $D_{sim} = \text{diag}(d_1, \dots, d_{L+U})$ with $d_i = \sum_j (W_{sim})_{ij}$ .
Knowl 3 — Dense Dissimilarity Matrix Construction and Equivalence to Variance Maximization
model/method
In a $K$ -way few-shot task with $N$ support and $B$ query examples per class (total $L+U = (N+B)K$ samples), off-diagonal pairs can be assumed to represent differing entities in the absence of class labels. The unnormalized dissimilarity matrix $A_{dis} \in \mathbb{R}^{(N+B)K \times (N+B)K}$ is constructed as the adjacency matrix of a densely connected graph without self-loops:

$A_{dis} = \frac{1}{(N+B)K} e e^\top - I$

where $e = [1, 1, \dots, 1]^\top \in \mathbb{R}^{(N+B)K}$ is the all-ones vector and $I$ is the identity matrix.

Because each row and column sum of $A_{dis}$ equals $(N+B)K$ , symmetric degree normalization yields $\tilde{A}_{dis} = \frac{1}{(N+B)K} A_{dis}$ .

Minimizing $W f_\theta(X)^\top \tilde{A}_{dis} f_\theta(X) W^\top$ is equivalent to maximizing the total sample variance in the projected subspace (analogous to Principal Component Analysis, PCA), since:

$f_\theta(X)^\top \left( I - \frac{1}{(N+B)K} e e^\top \right) f_\theta(X)$

represents the empirical sample covariance matrix of the task features.
Knowl 4 — Constrained Wasserstein Mean Shift Clustering (SIAMESE) Algorithm
algorithm
Constrained Wasserstein Mean Shift Clustering (SIAMESE) estimates class prototypes $\tilde{C} = [\tilde{c}_1, \dots, \tilde{c}_K]^\top \in \mathbb{R}^{K \times O'}$ and soft assignment probabilities $P \in \mathbb{R}^{(L+U) \times K}$ for projected features $H = f_\theta(X)W^\top \in \mathbb{R}^{(L+U) \times O'}$ . It extends Sinkhorn K-means by enforcing hard label clamping $P_{1:L} = Y_{1:L}$ on the $L$ labeled support samples, ensuring class distribution balance via optimal transport marginals $r = \mathbf{1}_{L+U}$ and $c = (N+B)\mathbf{1}_K$ .
Input: Projected sample matrix $H = [h_1, \dots, h_{L+U}]^\top \in \mathbb{R}^{(L+U) \times O'}$ , one-hot support labels $Y_{1:L} \in \{0, 1\}^{L \times K}$ , support size per class $N$ , queries per class $B$ , regularization $\lambda$ , learning rate $\alpha$ , step limit $n_{\text{step}}$ , convergence threshold $\epsilon$
Output: Predicted class labels $y_i \in \{1, \dots, K\}$ for query samples $i \in \{L+1, \dots, L+U\}$
Initialize prototypes $\tilde{c}_k = \frac{1}{|S_k|} \sum_{(h_i, y_i) \in S_k} h_i$ for $k = 1, \dots, K$
Initialize marginal constraints $r = \mathbf{1}_{L+U}$ , $c = (N + B) \mathbf{1}_K$
Initialize iteration counter $t = 0$
while $t < n_{\text{step}}$ do
    Compute cost matrix $M_{i,j} = \|h_i - \tilde{c}_j\|_2^2$ for all $i \in \{1, \dots, L+U\}, j \in \{1, \dots, K\}$
    Compute initial transport weights $P = \exp(-\lambda M)$
    Normalize $P = P / \sum_{i,j} P_{i,j}$
    Initialize vector $u = \mathbf{0}_{L+U}$

    while $\max_i |u_i - \sum_j P_{i,j}| > \epsilon$ do
         $u = \sum_j P_{\cdot, j}$
         $P = \text{diag}(r / u) P$
         $P = P \text{diag}(c / \sum_i P_{i, \cdot})$
        Clamp support labels $P_{1:L} = Y_{1:L}$
    end while

    Compute target prototype centers $\Omega = P^\top H / (N + B)$
    Update prototypes $\tilde{C} \leftarrow \tilde{C} + \alpha (\Omega - \tilde{C})$
     $t \leftarrow t + 1$
end while
return $y_i = \arg\max_j P_{i,j}$ for all $i \in \{L+1, \dots, L+U\}$

Knowl 5 — Transductive Few-Shot Classification Performance on mini-ImageNet and tiered-ImageNet

data/table

The combination of EASE subspace projection and SIAMESE clustering was evaluated on standard 5-way 1-shot and 5-shot transductive few-shot image classification tasks over 10,000 episodes on mini-ImageNet and tiered-ImageNet benchmarks using ResNet-12 and WRN-28-10 backbones.

	mini-ImageNet		tiered-ImageNet
Method (Backbone)	1-shot (%)	5-shot (%)	1-shot (%)	5-shot (%)
ResNet-12 Backbone:
TPN	$55.51 \pm 0.86$	$69.86 \pm 0.65$	$59.91 \pm 0.94$	$73.30 \pm 0.75$
Transductive Tuning	$62.35 \pm 0.66$	$74.53 \pm 0.54$	–	–
MetaOptNet	$62.64 \pm 0.61$	$78.63 \pm 0.46$	$65.99 \pm 0.72$	$81.56 \pm 0.53$
DSN-MR	$64.60 \pm 0.72$	$79.51 \pm 0.50$	$67.39 \pm 0.82$	$82.85 \pm 0.56$
CAN-T	$67.19 \pm 0.55$	$80.64 \pm 0.35$	$73.21 \pm 0.58$	$84.93 \pm 0.38$
EASE + Soft K-means (ours)	$57.00 \pm 0.26$	$75.07 \pm 0.21$	$69.74 \pm 0.31$	$85.17 \pm 0.21$
QR + SIAMESE (ours)	$68.66 \pm 0.37$	$79.36 \pm 0.22$	$75.87 \pm 0.29$	$87.80 \pm 0.21$
EASE + SIAMESE (ours)	$\mathbf{70.47 \pm 0.30}$	$\mathbf{80.73 \pm 0.16}$	$\mathbf{84.54 \pm 0.27}$	$\mathbf{89.63 \pm 0.15}$
WRN-28-10 Backbone:
BD-CSPN	$70.31 \pm 0.93$	$81.89 \pm 0.60$	$78.74 \pm 0.95$	$86.92 \pm 0.63$
TIM	$77.8$	$87.4$	$82.1$	$89.8$
EPNet	$70.74 \pm 0.85$	$84.34 \pm 0.53$	$78.50 \pm 0.91$	$88.36 \pm 0.57$
LaplacianShot	$74.86 \pm 0.19$	$84.13 \pm 0.14$	$80.18 \pm 0.21$	$87.56 \pm 0.15$
iLCT	$83.05 \pm 0.79$	$88.82 \pm 0.42$	$88.50 \pm 0.75$	$92.46 \pm 0.42$
Oblique Manifold	$80.64 \pm 0.34$	$89.39 \pm 0.39$	$85.22 \pm 0.34$	$91.35 \pm 0.40$
EASE + Soft K-means (ours)	$67.42 \pm 0.27$	$84.45 \pm 0.18$	$75.87 \pm 0.29$	$85.17 \pm 0.21$
QR + SIAMESE (ours)	$79.90 \pm 0.34$	$86.88 \pm 0.19$	$84.31 \pm 0.30$	$90.55 \pm 0.19$
EASE + SIAMESE (ours)	$\mathbf{83.00 \pm 0.21}$	$\mathbf{88.92 \pm 0.13}$	$\mathbf{88.96 \pm 0.23}$	$\mathbf{92.63 \pm 0.13}$

The results demonstrate that EASE+SIAMESE consistently outperforms previous transductive state-of-the-art methods across both backbones and datasets, achieving up to 84.54% 1-shot accuracy on tiered-ImageNet with ResNet-12 and 88.96% with WRN-28-10.

Knowl 6 — Transductive Classification Performance on CUB, CIFAR-FS, and OpenMIC
empirical result
On fine-grained and cross-domain few-shot benchmarks under the 5-way 1-shot and 5-shot transductive settings:
1. CUB Benchmark:
  - ResNet-12: EASE+SIAMESE achieves $90.11 \pm 0.21\%$ (1-shot) and $93.13 \pm 0.11\%$ (5-shot), outperforming iLPC ( $89.00\%$ and $92.74\%$ ) and LR+ICI ( $86.53\%$ and $92.11\%$ ).
  - WRN-28-10: EASE+SIAMESE achieves $91.68 \pm 0.19\%$ (1-shot) and $94.12 \pm 0.09\%$ (5-shot), outperforming PT+MAP ( $91.37\%$ and $93.93\%$ ) and iLPC ( $91.03\%$ and $94.11\%$ ).
2. CIFAR-FS Benchmark:
  - ResNet-12: EASE+SIAMESE reaches $78.41 \pm 0.29\%$ (1-shot) and $85.67 \pm 0.11\%$ (5-shot), surpassing iLPC ( $77.14\%$ ) and DSN-MR ( $75.60\%$ ).
  - WRN-28-10: EASE+SIAMESE attains $87.60 \pm 0.23\%$ (1-shot) and $90.60 \pm 0.16\%$ (5-shot), outperforming PT+MAP ( $86.91\%$ and $90.50\%$ ) and SIB ( $80.00\%$ and $85.30\%$ ).
3. OpenMIC Benchmark (5-way 1-shot cross-domain transfers):
  - Across four domain transfer splits ( $p1 \to p2$ : $81.60\%$ , $p2 \to p3$ : $68.68\%$ , $p3 \to p4$ : $86.38\%$ , $p4 \to p1$ : $66.53\%$ ), EASE+SIAMESE achieves an average accuracy of $75.80\%$ , substantially exceeding inductive baselines including SoSN ( $67.85\%$ ) and DSN ( $69.59\%$ ).

Knowl 7 — Semi-Supervised Few-Shot Classification with Distractor Classes

data/table

In the semi-supervised few-shot learning setting, test episodes are augmented with an additional pool of unlabeled images that contain samples from both target classes and distractor categories. Experiments evaluate 5-way 1-shot and 5-shot tasks with a $30/50$ unlabeled pool setting across mini-ImageNet, tiered-ImageNet, CIFAR-FS, and CUB.

	mini-ImageNet		tiered-ImageNet		CIFAR-FS		CUB
Method (Backbone)	1-shot	5-shot	1-shot	5-shot	1-shot	5-shot	1-shot	5-shot
ResNet-12:
LR+ICI	$67.57$	$79.07$	$83.32$	$89.06$	$75.99$	$84.01$	$88.50$	–
iLPC	$70.99$	$81.06$	$85.04$	$89.63$	$78.57$	$85.84$	$90.11$	–
EASE+SIAMESE	$\mathbf{73.90}$	$\mathbf{81.68}$	$\mathbf{85.86}$	$\mathbf{89.64}$	$\mathbf{80.51}$	$\mathbf{85.96}$	$\mathbf{90.61}$	–
WRN-28-10:
LR+ICI	$81.31$	$88.53$	$88.48$	$92.03$	$86.03$	$89.57$	$90.82$	–
PT+MAP	$83.14$	$88.95$	$89.16$	$92.30$	$87.05$	$89.98$	$91.52$	–
iLPC	$83.58$	$89.68$	$89.35$	$92.61$	$87.03$	$90.34$	$91.69$	–
EASE+SIAMESE	$\mathbf{84.89}$	$\mathbf{89.47}$	$\mathbf{90.08}$	$\mathbf{92.67}$	$\mathbf{87.89}$	$\mathbf{90.18}$	$\mathbf{92.11}$	–

EASE+SIAMESE achieves performance gains of $3\%$ to $6\%$ over competing approaches on 1-shot mini-ImageNet (ResNet-12), demonstrating robustness against unrelated distractor samples in the unlabeled set.

Knowl 8 — Comparison of EASE with PCA and ICA Dimensionality Reduction on DenseNet Backbone

data/table

When evaluated on a standard DenseNet backbone trained directly with cross-entropy classification on base classes (without episodic meta-learning), replacing PCA or ICA in the task-adaptive feature subspace learning pipeline (TAFSSL) with EASE leads to superior accuracy across mini-ImageNet and tiered-ImageNet.

	mini-ImageNet		tiered-ImageNet
Method	1-shot (%)	5-shot (%)	1-shot (%)	5-shot (%)
SimpleShot (Inductive)	$65.77 \pm 0.19$	$82.23 \pm 0.13$	$71.20 \pm 0.22$	$86.33 \pm 0.15$
LaplacianShot	$75.57 \pm 0.19$	$84.72 \pm 0.13$	$80.30 \pm 0.20$	$87.93 \pm 0.15$
RAP-LaplacianShot	$75.58 \pm 0.20$	$85.63 \pm 0.13$	–	–
TAFSSL (PCA)	$70.53 \pm 0.25$	$80.71 \pm 0.16$	$80.07 \pm 0.25$	$86.42 \pm 0.17$
TAFSSL (ICA)	$72.10 \pm 0.25$	$81.85 \pm 0.16$	$80.82 \pm 0.25$	$86.97 \pm 0.17$
EASE + Soft K-means	$74.30 \pm 0.26$	$82.08 \pm 0.17$	$82.67 \pm 0.25$	$87.60 \pm 0.17$
QR + SIAMESE	$75.75 \pm 0.32$	$85.10 \pm 0.18$	$82.87 \pm 0.33$	$89.11 \pm 0.20$
EASE + SIAMESE (ours)	$\mathbf{79.42 \pm 0.27}$	$\mathbf{86.76 \pm 0.14}$	$\mathbf{86.17 \pm 0.25}$	$\mathbf{90.54 \pm 0.15}$

Compared to SimpleShot, EASE+SIAMESE improves performance by $13.65\%$ on 1-shot mini-ImageNet and $14.97\%$ on 1-shot tiered-ImageNet. It also surpasses TAFSSL(ICA) by $7.32\%$ and $5.35\%$ in 1-shot settings, indicating that EASE constructs a significantly more discriminative subspace than classical unsupervised projection techniques.

Knowl 9 — Ablation on Query Set Size, Subspace Dimension, and Inference Latency
empirical result
Ablation studies on mini-ImageNet reveal three key operational properties of EASE and SIAMESE:
1. Query Set Scaling: Varying query count per class from 2 to 50 shows that EASE maintains effective subspace learning starting from 5 queries. While pure SVD-based adaptation plateaus quickly as queries increase, EASE accuracy increases approximately linearly with query volume.
2. Subspace Dimension Robustness: Classification performance rises steeply when the projection dimension $O'$ increases from 5 to 20, after which performance gains stabilize slowly. Setting $O' = 40$ provides an optimal balance between accuracy and computational cost across all benchmarks. Unlike SVD, whose performance degrades beyond 20 dimensions, EASE maintains stable performance as dimension scales toward sample count.
3. Inference Latency: On mini-ImageNet (measured on an AMD 2700 CPU), EASE+SIAMESE requires $6.0\text{ ms}$ (1-shot) and $7.4\text{ ms}$ (5-shot) per episode with ResNet-12, and $8.0\text{ ms}$ (1-shot) and $8.7\text{ ms}$ (5-shot) with WRN-28-10. This is approximately $10\times$ faster than iterative transductive alternatives (iLPC at $45\text{--}70\text{ ms}$ , ICI at $34\text{--}52\text{ ms}$ ).

Coverage note — None was omitted; all primary methodological contributions (EASE subspace learning, LRR similarity, dense dissimilarity, SIAMESE clustering) and empirical evaluations (transductive FSL, semi-supervised FSL, ablations, latency) are covered.

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Citation

MLA

Zhu, H., and P. Koniusz. “EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning”. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 9068–78, https://doi.org/10.1109/CVPR52688.2022.00887.

APA

Zhu, H., & Koniusz, P. (2022). EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 9068–9078. https://doi.org/10.1109/CVPR52688.2022.00887

Chicago

Zhu, H., and P. Koniusz. 2022. “EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning”. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 9068–78. https://doi.org/10.1109/CVPR52688.2022.00887.

Harvard

Zhu, H. and Koniusz, P. (2022) “EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning”, 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp. 9068–9078. Available at: https://doi.org/10.1109/CVPR52688.2022.00887.

Vancouver

1. Zhu H, Koniusz P (2022) EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning. In: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp 9068–9078

BibTeX

@inproceedings{Zhu_2022, title={EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning}, url={http://dx.doi.org/10.1109/CVPR52688.2022.00887}, DOI={10.1109/cvpr52688.2022.00887}, booktitle={2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, publisher={IEEE}, author={Zhu, Hao and Koniusz, Piotr}, year={2022}, month=June, pages={9068–9078} }

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EASE: Unsupervised Discriminant Subspace Learning for Transductive Few-Shot Learning

Abstract

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Table of Contents

Knowls

Knowl 1 — Unsupervised Discriminant Subspace Learning (EASE) Objective and Solution

Knowl 2 — Low-Rank Representation (LRR) Similarity Matrix Construction

Knowl 3 — Dense Dissimilarity Matrix Construction and Equivalence to Variance Maximization

Knowl 4 — Constrained Wasserstein Mean Shift Clustering (SIAMESE) Algorithm

Knowl 5 — Transductive Few-Shot Classification Performance on mini-ImageNet and tiered-ImageNet

Knowl 6 — Transductive Classification Performance on CUB, CIFAR-FS, and OpenMIC

Knowl 7 — Semi-Supervised Few-Shot Classification with Distractor Classes

Knowl 8 — Comparison of EASE with PCA and ICA Dimensionality Reduction on DenseNet Backbone

Knowl 9 — Ablation on Query Set Size, Subspace Dimension, and Inference Latency

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