Source-linked AI summary
Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization
Kamran Ghasedi Dizaji, Amirhossein Herandi, Cheng Deng, Weidong Cai, Heng Huang
TL;DR
High-dimensional and large-scale image clustering remains difficult because existing methods face scalability, representation, optimization, and tuning limitations. DEPICT addresses these issues with a jointly trained convolutional autoencoder and discriminative clustering objective regularized by reconstruction loss and cluster-frequency priors. It achieves superior or competitive results with faster running times and no labeled data for hyper-parameter tuning.
Problem
Existing clustering methods struggle with efficiency and scalability on high-dimensional and large-scale image data, while image-specific methods also have representation, optimization, and tuning limitations.
Method
DEPICT stacks multinomial logistic regression on a convolutional autoencoder, minimizes regularized KL divergence, adds reconstruction regularization, and jointly trains all layers.
Results
DEPICT achieves superior or competitive clustering results with faster running times, and joint learning provides the best results among the compared learning strategies.
Takeaways & Limitations
DEPICT is presented as a candidate for real-world clustering tasks because it handles high-dimensional and large-scale data without labeled-data hyper-parameter tuning.
Abstract
from arXiv · showhide
Image clustering is one of the most important computer vision applications, which has been extensively studied in literature. However, current clustering methods mostly suffer from lack of efficiency and scalability when dealing with large-scale and high-dimensional data. In this paper, we propose a new clustering model, called DEeP Embedded RegularIzed ClusTering (DEPICT), which efficiently maps data into a discriminative embedding subspace and precisely predicts cluster assignments. DEPICT generally consists of a multinomial logistic regression function stacked on top of a multi-layer convolutional autoencoder. We define a clustering objective function using relative entropy (KL divergence) minimization, regularized by a prior for the frequency of cluster assignments. An alternating strategy is then derived to optimize the objective by updating parameters and estimating cluster assignments. Furthermore, we employ the reconstruction loss functions in our autoencoder, as a data-dependent regularization term, to prevent the deep embedding function from overfitting. In order to benefit from end-to-end optimization and eliminate the necessity for layer-wise pretraining, we introduce a joint learning framework to minimize the unified clustering and reconstruction loss functions together and train all network layers simultaneously. Experimental results indicate the superiority and faster running time of DEPICT in real-world clustering tasks, where no labeled data is available for hyper-parameter tuning.
1. Introduction
Existing clustering methods struggle with high-dimensional and large-scale image data, motivating DEPICT’s joint deep embedding and clustering framework. DEPICT combines discriminative clustering, convolutional autoencoding, reconstruction regularization, and end-to-end learning without labeled-data hyper-parameter tuning.
- Motivation: High-dimensional data harms standard clustering performance, while large-scale datasets sharply increase time complexity.Prior approaches commonly reduce dimensionality or subsample data to address these challenges.
- Motivation: Real-world image clustering is limited by hand-crafted features, shallow embeddings, non-joint optimization, and labeled-data hyper-parameter tuning.These limitations can prevent embeddings from capturing nonlinear structure or becoming optimal for clustering.
- DEPICT: DEPICT stacks a multinomial logistic regression layer on a multi-layer convolutional autoencoder for discriminative clustering.Its clustering objective minimizes KL divergence and uses a cluster-frequency prior to penalize unbalanced assignments and outlier allocation.
- DEPICT: Reconstruction loss regularizes the deep clustering model with data-dependent information to reduce overfitting to spurious correlations.The reconstruction objective is used as an auxiliary regularizer during parameter training.
- Joint learning: Joint learning unifies clustering and reconstruction losses, updates parameters and assignments alternately, and avoids layer-wise pretraining.The standard non-joint fine-tuning process may overwrite pretrained encoder parameters.
- Results: Joint DEPICT produces a more discriminative MNIST embedding than non-joint DEPICT, while DEPICT achieves superior or competitive benchmark results with faster running times.The reported advantages also include avoiding labeled-data hyper-parameter tuning.
2. Related Works
Related work spans many clustering paradigms and increasingly combines clustering with learned representations. Prior methods use joint optimization, sparse coding, stacked autoencoders, recurrent convolutional representations, or matrix factorization, but DEPICT differs by avoiding supervisory signals for hyper-parameter tuning.
- Clustering paradigms: Clustering methods include hierarchical, centroid-based, graph-based, sequential, regression-based, and subspace models.They are also broadly categorized as generative or discriminative according to how clusters are represented and identified.
- Joint embedding and clustering: Earlier joint methods combine clustering with feature embedding or selection, including kernelized K-means, simultaneous embedding, and codebook optimization.These approaches address representation learning and cluster assignment together in different model families.
- Deep representations: Other approaches learn nonlinear or deep embeddings with stacked autoencoders or deep semi-NMF, then cluster the embedded data using K-means.These methods separate embedding learning from the subsequent K-means assignment stage.
- Deep representations: JULE jointly updates convolutional representations and agglomerative clusters through a recurrent framework and unified loss.The related methods discussed use varied alternating or joint optimization strategies for representation and clustering.
- DEPICT distinction: In contrast, DEPICT does not require supervisory signals for hyper-parameter tuning.This distinguishes its clustering workflow from approaches relying on labeled guidance for tuning.
3. Deep Embedded Regularized Clustering
DEPICT jointly learns a convolutional autoencoder embedding and soft-max clustering model by minimizing KL-based clustering and reconstruction objectives. Its alternating optimization uses balanced target assignments and clean/noisy pathways to regularize representations and promote noise-invariant predictions.
- DEPICT Algorithm: DEPICT stacks a multinomial logistic regression soft-max layer on a multi-layer convolutional autoencoder for discriminative clustering.The soft-max layer and encoder form the clustering model, while the autoencoder supplies the embedding structure.
- DEPICT Algorithm: The objective minimizes KL divergence between model predictions P and auxiliary targets Q, while a KL term toward a uniform prior discourages imbalanced cluster frequencies.The prior can be replaced by an arbitrary distribution when additional cluster-frequency knowledge is available.
- DEPICT Algorithm: An alternating strategy estimates target assignments with fixed parameters and updates network parameters with the targets fixed, using backpropagation for the latter step.The parameter update is equivalent to a cross-entropy classification loss under the estimated target variables.
- DEPICT Architecture: Reconstruction losses regularize the deep embedding function against spurious correlations and undesirable local minima.The autoencoder reconstruction objective is used as a data-dependent regularization term alongside the clustering objective.
- DEPICT Architecture: Clean and corrupted encoder pathways provide target variables and predictions respectively, so KL(Q∥P̃) encourages features and assignments that are invariant to noise.The clean pathway computes more accurate targets, while the noisy pathway is trained for noise-invariant predictions.
- DEPICT Architecture: Joint learning simultaneously optimizes all autoencoder and soft-max parameters instead of layer-wise pretraining followed by fine-tuning.The unified clustering and reconstruction losses are optimized together across the network layers.
1 Initialize Q using a clustering algorithm
The algorithm initializes target assignments Q before iterative optimization and uses the autoencoder depth to organize its layerwise representation.
- 1 Initialize Q using a clustering algorithm: DEPICT begins its iterative procedure by initializing Q using a clustering algorithm.The supplied algorithm excerpt marks this initialization step before the loop continues while not converged.
- 1 Initialize Q using a clustering algorithm: The autoencoder depth is denoted by L, and the hidden-layer output size is defined for the layer inputs.These quantities determine the representation structure used by the autoencoder.
- 1 Initialize Q using a clustering algorithm: DEPICT differs from related joint-learning systems because it targets unsupervised clustering and avoids max-pooling switches and encoder–decoder lateral connections.The comparison is made against stacked what-where autoencoders and ladder networks.
4. Experiments
Experiments compare DEPICT with clustering baselines on image datasets, assess running time and learning strategies, and evaluate semi-supervised classification. DEPICT shows strong clustering performance, faster execution, benefits from joint learning, and competitive classification without supervisory hyper-parameter tuning.
- Evaluation of Clustering Algorithm: DEPICT outperforms other algorithms on four image datasets and achieves competitive results on the remaining two using ACC and NMI.The comparison includes multiple baseline and state-of-the-art clustering methods, with supervisory hyper-parameter tuning reported for the alternatives.
- Evaluation of Clustering Algorithm: DEPICT uses the same default hyper-parameters across datasets without tuning them using labeled data, unlike several alternative methods.DEC, SEC, LDMGI, and JULE variants report tuning hyper-parameters using supervisory signals.
- Running Time Comparison: 4.7 hours: DEPICT’s total runtime across all datasets, compared with 6.6 to 66.1 hours for the evaluated JULE variants.On large-scale and high-dimensional datasets, DEPICT’s runtime increases almost linearly, whereas the original JULE runtimes grow dramatically with input size and number.
- Evaluation of Learning Approach: MdA consistently outperforms the other learning approaches for DEPICT across all datasets.MdA trains the whole model simultaneously using joint reconstruction losses and the clustering objective; it also performs well for Deep-ConvAE+AC-PIC.
- Semi-Supervised Classification Performance: DEPICT achieves comparable semi-supervised classification results with state-of-the-art models while using only labeled training data and no hyper-parameter tuning.With examples such as 100 labeled data points, DEPICT outperforms several models and remains comparable to the Ladder network.
5. Conclusion
DEPICT combines regularized clustering with convolutional autoencoder embedding and joint learning, achieving strong, efficient clustering without labeled hyper-parameter tuning. Its joint learning efficiency was also confirmed in clustering and semi-supervised classification tasks.
- DEPICT stacks a soft-max layer on a multi-layer convolutional autoencoder and uses regularized relative entropy to encourage balanced cluster assignments.
- The autoencoder reconstruction loss enhances embedding learning, while joint training updates all network layers simultaneously and avoids layer-wise pretraining.
- DEPICT achieved superior or competitive results versus alternative methods, with faster running speed and no hyper-parameter tuning using labeled data.
- The efficiency of the joint learning approach was confirmed in clustering and semi-supervised classification tasks.
A. Architecture of Convolutional Autoencoder Networks
The convolutional autoencoder uses two convolutional layers and one fully connected layer in both encoder and decoder pathways, with dataset-specific architectural settings.
- Each encoder and decoder pathway contains two convolutional layers plus one fully connected layer.
- Kernel size, stride, and decoder padding or cropping vary across datasets to produce matching encoder-decoder output sizes for reconstruction loss calculation.
- The number of fully connected features is set equal to the number of clusters for each dataset.
- Table 5 provides the detailed convolutional autoencoder architecture for each dataset.
B. Visualization of learned embedding subspace
The learned embedding subspace is visualized across initial, reconstruction-trained intermediate, and fully trained final stages for six image datasets.
- Embedding representations are shown at initial, intermediate-before-clustering-loss, and final stages using the first two principal components.
- The final stage uses both clustering and reconstruction loss functions, following the intermediate stage trained only with reconstruction loss.
- Figure 4 presents the three embedding stages for MNIST-full, MNIST-test, and USPS datasets.
- Figure 5 presents the same three stages for FRGC, YTF, and CMU-PIE datasets.