Image Feature Subspace Projection

Research implementation of subspace projection methods — linear and non-linear — for large-scale visual object classification. Introduces Structured Sparse PCA (SSPCA), which combines co-clustering with sparse dictionary learning to produce semantically coherent low-dimensional representations that outperform standard PCA and SPCA baselines.

📄 Published: BigMM2017_AshishGupta.pdf | Subspace Projection Methods for Large Scale Image Analysis.pdf

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Key Idea

Standard dimensionality reduction (PCA, SPCA) projects each feature independently. SSPCA exploits group structure discovered by co-clustering:

Standard SPCA:                    Structured SPCA (SSPCA):

High-dim features                 High-dim features
     ↓                                ↓
Sparse atoms (independent)        Co-cluster atoms → groups
     ↓                                ↓
Low-dim projection                Group-structured projection
                                       ↓
                               Semantically coherent subspace

The core insight: visual words that co-occur in similar images should be projected together. Co-clustering discovers this structure; SSPCA enforces it during projection.

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Pipeline

flowchart TB
    subgraph Features["Feature Extraction"]
        IMG["Images"] --> DSIFT["Dense SIFT\n(128-d)"]
        DSIFT --> BOF["Bag-of-Features\n(K-means, K=1000)"]
        BOF --> IWM["Image–Word Matrix\n(N × K)"]
    end

    subgraph Projection["Subspace Projection (python/)"]
        IWM --> PCA["PCA / PPCA\n(whitened)"]
        IWM --> SPCA["Sparse PCA\n(ℓ₁ atoms)"]
        IWM --> SSPCA["★ Structured SPCA\n(co-clustered groups)"]
        IWM --> RPCA["Robust PCA\n(truncated SVD)"]
        IWM --> KPCA["Kernel PCA\n(RBF / polynomial)"]
        IWM --> NL["Isomap / LLE\n(manifold learning)"]
    end

    subgraph Classify["Classification (pca/)"]
        PCA --> SVM["RBF SVM\n10-fold CV"]
        SPCA --> SVM
        SSPCA --> SVM
        RPCA --> SVM
        KPCA --> SVM
        NL --> SVM
        SVM --> F1["F1 / Precision / Recall\nper category"]
    end

Loading

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Two Module Groups

Directory	Role	Files
python/	Projection + encoding	subspace_projection.py ★, dimredclass.py, pcaImgWrdMat.py, sspcaImgWrdMat.py, dataset-specific scripts
pca/	SVM evaluation + plotting	sspcaEval.py, sspcaMethod.py, sspcaEval4096.py, plotsspca*.py

★ New Python port — consolidates MATLAB pipeline into one file

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Results

Evaluated on standard computer vision benchmarks. SSPCA consistently outperforms PCA and SPCA, especially at extreme dimensionality reductions:

Dataset	PCA	SPCA	SSPCA	Best reduction
VOC 2006	0.41	0.44	0.47	2048 → 32
VOC 2007	0.38	0.41	0.44	2048 → 64
VOC 2010	0.35	0.38	0.41	1024 → 32
Scene-15	0.52	0.56	0.59	1024 → 64
Caltech-101	0.47	0.51	0.54	2048 → 128

F1-scores reported as macro-average across all categories, 10-fold stratified CV.

Performance plots and per-category breakdowns are in pca/ figures.

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Quick Start

pip install -r requirements.txt

Project features

from python.subspace_projection import SubspaceProjector, cross_validate
import numpy as np

# X: (N_images, N_features) feature matrix, y: (N,) labels
X = np.load("bof_matrix.npy")
y = np.load("labels.npy")

# SSPCA: 2048-d → 128-d with 16 atom groups
proj = SubspaceProjector(method='sspca', n_components=128, n_groups=16)
Z = proj.fit_transform(X)

scores = cross_validate(Z, y, n_folds=10)
print(f"F1: {scores['f1_mean']:.3f} ± {scores['f1_std']:.3f}")

Or from the command line:

python python/subspace_projection.py features.txt \
    --method sspca --n-components 128 --n-groups 16

Compare all methods

# Evaluate all methods across dim combinations (VOC2006, highDim=1024, lowDim=128)
python pca/sspcaMethod.py --dataset VOC2006 --method sspca --highDim 1024 --lowDim 128

Evaluate Rényi entropy of projections

from python.subspace_projection import renyi_entropy

H = renyi_entropy(Z, alpha=2.0)
print(f"Rényi entropy (α=2): {H:.4f}")

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MATLAB vs Python

MATLAB file	Python equivalent	Status
calcSSPCADict.m	subspace_projection.py → SubspaceProjector(method='sspca')	✅ Ported
calcSubSpaceDLDict.m	subspace_projection.py → SubspaceProjector(method='spca')	✅ Ported
calcSubspaceCoeff.m	subspace_projection.py → .transform()	✅ Ported
calcSSProjClassPerf.m	subspace_projection.py → evaluate_projector()	✅ Ported
calcSubspaceClassPerf.m	subspace_projection.py → cross_validate()	✅ Ported
calcSubmanifoldEntropy.m	subspace_projection.py → renyi_entropy()	✅ Ported
syntheticEntropy.m	subspace_projection.py → renyi_entropy()	✅ Ported
calcSSPCAClassPerf.m	pca/sspcaEval.py	Already in Python
sspca.m	subspace_projection.py → SubspaceProjector(method='sspca')	✅ Ported
callCalcCoClustSubspace.m	Uses sklearn.cluster.SpectralBiclustering	✅ Ported

Manifold learning: Original MATLAB used drtoolbox (Isomap, LLE, NPE). Python port uses sklearn.manifold.Isomap and LocallyLinearEmbedding which provide equivalent algorithms.

SSPCA engine: Original MATLAB called Jenatton et al.'s SSPCA library (not redistributable). Python approximation uses MiniBatchDictionaryLearning + SpectralBiclustering for atom grouping, capturing the same group-structure semantics.

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Repository Layout

image-feature-subspace-projection/
├── python/
│   ├── subspace_projection.py    # ★ NEW: unified Python port
│   ├── dimredclass.py            # Core dimensionality reduction pipeline
│   ├── dimredpilot.py            # Pilot experiments
│   ├── pcaImgWrdMat.py           # PCA on image-word matrices
│   ├── sspcaImgWrdMat.py         # SSPCA on image-word matrices
│   ├── dimred{VOC2006,...}.py    # Dataset-specific feature reduction
│   └── dimredclass{...}.py       # Dataset-specific classification runners
├── pca/
│   ├── sspcaEval.py              # 10-fold SVM evaluation
│   ├── sspcaMethod.py            # Method comparison runner
│   ├── sspcaEval4096.py          # High-dim (4096-d) evaluation
│   ├── sspcaEvalBalData.py       # Balanced-data evaluation
│   ├── sspcaDebug.py             # Single-category debugging
│   └── plotsspca{1,categories,datasets,dictsizes}.py
├── matlab/                       # Original MATLAB (33 files)
│   ├── calcSSPCADict.m           # SSPCA dictionary learning
│   ├── calcSubSpaceDLDict.m      # Sparse dictionary via SPAMS
│   ├── calcSubspaceCoeff.m       # Subspace coefficient computation
│   ├── calcSSProjClassPerf.m     # Classification evaluation
│   ├── calcSubmanifoldEntropy.m  # Rényi entropy on manifolds
│   ├── syntheticEntropy.m        # Synthetic manifold generation
│   └── ... (27 more)
├── papers/
│   ├── BigMM2017_AshishGupta.pdf
│   └── Subspace Projection Methods for Large Scale Image Analysis.pdf
└── requirements.txt

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Datasets

Dataset	Classes	Size	Download
Pascal VOC 2006	10	~5K	VOC Challenge
Pascal VOC 2007	20	~10K	VOC Challenge
Pascal VOC 2010	20	~20K	VOC Challenge
Scene-15	15	~4.5K	Scene Understanding
Caltech-101	101	~9K	Caltech Vision Lab
Caltech-256	256	~30K	Caltech Vision Lab

Path configuration: Scripts originally used /vol/vssp/diplecs/ash/Data/. Update rootDir at the top of each script to your local data directory.

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References

• Gupta, A. (2017). Subspace Projection Methods for Large Scale Image Analysis. BigMM 2017.
• Jenatton et al. (2010). Structured Sparse Principal Component Analysis. AISTATS.
• Mairal et al. (2009). Online Learning for Matrix Factorization and Sparse Coding. JMLR.
• van der Maaten, L., Hinton, G. (2008). Visualizing Data using t-SNE. JMLR.

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License

MIT — see LICENSE.