Active Deep Learning for Classification of Hyperspectral Images

Peng Liu; Hui Zhang; Kie B. Eom

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Active Deep Learning for Classification of Hyperspectral Images

Peng Liu, Hui Zhang, Kie B. Eom

arXiv:1611.10031v1Nov 30, 2016cs.LGcs.CVstat.ML

TL;DR

Hyperspectral-image classification with deep networks is constrained by the cost and scarcity of good-quality labeled samples. The paper proposes weighted incremental dictionary learning to select samples using representativeness and uncertainty, and reports effective classification with fewer training samples than competing active-learning methods.

Problem
Deep-network hyperspectral classification requires many good-quality labeled samples, but obtaining such samples is expensive and their availability is limited.
Method
The proposed WI-DL algorithm uses DBN information from unsupervised and supervised stages to combine representativeness and uncertainty when selecting training samples.
Results
WI-DL performed well in remotely sensed hyperspectral-image classification and achieved higher accuracy with fewer training samples than RS, MUS, and QBC.
Takeaways & Limitations
Active selection using representativeness and uncertainty can train a deep network efficiently for hyperspectral-image classification.

Abstract

from arXiv · show

Active deep learning classification of hyperspectral images is considered in this paper. Deep learning has achieved success in many applications, but good-quality labeled samples are needed to construct a deep learning network. It is expensive getting good labeled samples in hyperspectral images for remote sensing applications. An active learning algorithm based on a weighted incremental dictionary learning is proposed for such applications. The proposed algorithm selects training samples that maximize two selection criteria, namely representative and uncertainty. This algorithm trains a deep network efficiently by actively selecting training samples at each iteration. The proposed algorithm is applied for the classification of hyperspectral images, and compared with other classification algorithms employing active learning. It is shown that the proposed algorithm is efficient and effective in classifying hyperspectral images.

I. INTRODUCTION

Deep networks are promising for hyperspectral classification but require many labeled samples, which are costly and limited. The paper therefore proposes active learning that uses information from both unsupervised and supervised stages to select training samples.

Deep-network hyperspectral classification is impractical when labeled samples are limited and feature spaces are large.Training deep networks is expensive and requires many training samples.
Active learning iteratively selects informative unlabeled examples, adds them to the training set, and retrains the classifier.The selected samples are intended to make training more efficient than random sampling.
Existing remote-sensing active-learning methods are often tied to particular classifiers or application structures.Examples include random sampling, maximum uncertainty sampling, query-by-committee, and classifier-specific methods.
The proposed scheme uses information from both unsupervised and supervised stages of deep-network training.Its efficacy is demonstrated experimentally for remotely sensed hyperspectral-image classification.
The paper proposes representativeness and uncertainty as active-learning criteria and combines them in an objective function.The paper then presents an optimization algorithm for the combined objective and evaluates it experimentally.

II. DBN

The paper describes DBNs as stacked RBMs trained through unsupervised feature learning followed by supervised fine tuning. It motivates selecting training data using representations from the unsupervised stage and uncertainty from the supervised stage.

DBN architecture: The DBN maps each hyperspectral pixel feature vector to a class-label vector through an input layer, hidden layers, and an output layer.The input layer has M units and the output layer has C units corresponding to the feature and label vectors.
RBM training: RBM parameters are learned from a log-likelihood gradient containing data-distribution and model-distribution expectations.Contrastive divergence approximates the difficult model expectation using Gibbs sampling and gradient updates.
DBN training: A DBN is formed by stacking RBMs and learns a deep hierarchical representation through two training stages.The stages are unsupervised layer-wise feature learning with contrastive divergence and supervised discriminative fine tuning.
Motivation: Deep-network training is difficult with few samples or high-dimensional features, so the proposed method estimates representativeness and uncertainty from different DBN stages.The unsupervised stage supports representativeness estimation, while supervised fine tuning supports uncertainty estimation.
Proposed active learning: The weighted incremental dictionary-learning algorithm integrates representativeness and uncertainty in an objective function to select training samples.The method is introduced as the proposed active-learning algorithm for improving DBN training efficiency.

III. CRITERIA FOR ACTIVE LEARNING

Active learning selects informative unlabeled samples using importance criteria. This section motivates combining representativeness with uncertainty and introduces WI-DL to maximize both when choosing training data.

Active learning ranks unlabeled candidates by model-derived scores, adds selected samples to the training set, and retrains the classifier iteratively.The approach is described as more efficient than random selection because selected samples are more suitable for training.
Information density combines uncertainty with representativeness of the underlying data distribution to identify informative samples.The framework uses both structural information and explicit class-label information.
The selected sample x∗ is obtained by maximizing information density, which depends on a similarity function and an uncertainty function.Similarity measures representativeness, while the uncertainty function measures uncertainty for the candidate sample.
WI-DL proposes deep-learning-specific similarity and uncertainty functions and combines them to rank and select informative training samples.The algorithm selects samples that maximize both criteria.

A. Sparsity for Representativeness Estimation

The paper estimates sample representativeness through sparse dictionary learning. Deep-network hidden-layer features are represented using dictionary atoms, so selected samples can characterize the dataset’s structure.

A. Sparsity for Representativeness Estimation: A dictionary is an overcomplete set of data-derived basis vectors that can represent complex characteristics without a predefined analytic basis.The dictionary-learning assumption is that structure is extracted directly from data.
A. Sparsity for Representativeness Estimation: A representative active-learning subset can serve as a dictionary when it characterizes the entire dataset efficiently.The dictionary atoms are intended to capture the dataset’s structure.
A. Sparsity for Representativeness Estimation: Dictionary atoms are selected from the last hidden-layer outputs because deep learning projects inputs into learned, reduced-dimensional feature representations.The method uses the feature information produced by the DBN’s unsupervised coding stage.
A. Sparsity for Representativeness Estimation: Each feature vector is modeled as h_n = Dα using a dictionary D and sparse coefficient vector α.The dictionary contains p normalized atoms, and α contains their representation coefficients.
A. Sparsity for Representativeness Estimation: The redundant dictionary condition p > C and small k = ∥α∥0 imply that each feature vector uses only a few dictionary atoms.This sparse representation models a feature vector as a linear combination of a few columns of D.
A. Sparsity for Representativeness Estimation: Traditional dictionary-learning methods such as K-SVD are not directly applicable because active learning must account for uncertainty as well as representativeness.The paper therefore requires a method that incorporates both selection criteria.

B. Information Entropy for Uncertainty Estimation

The paper measures uncertainty with prediction entropy. For hidden-layer representations, entropy is computed from class probabilities and then combined with sparse-representation-based representativeness.

B. Information Entropy for Uncertainty Estimation: Uncertainty sampling queries instances about which the active learner is least certain, commonly using entropy as the uncertainty measure.Entropy is based on the classifier’s current prediction.
B. Information Entropy for Uncertainty Estimation: For a deep network, an input x is projected to a hidden layer h, whose entropy is defined from the predicted class probabilities p(y_j|h).The probability p(y_j|h) denotes that x maps to h and belongs to class j.
B. Information Entropy for Uncertainty Estimation: The entropy-based uncertainty function is classifier-structure-independent and straightforward to implement.It is subsequently combined with sparse representation to construct the active-learning algorithm.
B. Information Entropy for Uncertainty Estimation: The method combines sparse-representation representativeness with entropy-based uncertainty to search for the most informative samples.Both criteria are used in the discrimination function for sample selection.

IV. ACTIVE LEARNING WITH SPARSE REPRESENTATION AND UNCERTAINTY

The WI-DL method searches for informative samples in deep-network feature space by combining sparse-representation representativeness with uncertainty. Its incremental dictionary-learning procedure uses uncertainty to initialize and weight atom selection, then updates the dictionary on current residuals.

WI-DL selects samples by jointly optimizing representativeness and uncertainty rather than using either criterion alone.The method constructs a discriminant function that combines sparse-representation measurements with entropy-based uncertainty.
Active-learning searches occur in projected feature data H, while the corresponding samples in X are labeled and added to training.The one-to-one relationship between X and H lets the method search compact deep-network features before labeling original samples.
Dictionary updating alternates sparse coding and atom updates, using SVD to obtain updated atoms and recomputing residuals for the next iteration.The algorithm replaces selected atoms with candidates from the unlabeled set and removes them from further consideration.
At each iteration, WI-DL sorts candidate features by uncertainty and initializes the new dictionary with the top m uncertain samples.These initial atoms are subsequently updated using the incremental dictionary-learning procedure.
Weighted OMP incorporates atom uncertainty by selecting candidate atoms according to maximum weighted projection values during sparse coding.This modifies conventional OMP, which selects atoms by similarity alone.
Unlike traditional dictionary learning, WI-DL applies uncertainty-weighted selection to current residual data because active learning is incremental.Its distinctive design considers both representativeness and uncertainty when selecting dictionary atoms.

V. EXPERIMENTS AND RESULTS

The experiments evaluate WI-DL against RS, MUS, and QBC on three hyperspectral datasets. The study uses four-hidden-layer DBNs and compares the methods across classification settings.

WI-DL, RS, MUS, and QBC are compared on the PaviaC, PaviaU, and Botswana hyperspectral datasets.
The DBNs use four hidden layers, with each layer based on an RBM and trained through unsupervised pretraining followed by supervised fine-tuning.The initial weights are randomly selected between 0 and 1.

A. Experiment 1

The first experiment uses the Pavia Center dataset and evaluates four active-learning algorithms on three class-partitioned data sets. The data include nine selected land-cover classes and separate training, candidate, and testing samples.

The PaviaC dataset contains 115 original bands, with 102 retained after removing low-SNR bands, and test images of 1096 × 715 pixels.The data have 1.3 m spatial resolution and spectral coverage from 0.43 to 0.86 μm.
Nine classes are selected, and WI-DL, RS, MUS, and QBC are applied to three data sets with training, candidate, and testing partitions.The partitions contain different percentages of randomly selected class data derived from ground truth.

A DBN having four hidden layers, 102 input nodes corre-

The first experiment fine-tunes a DBN using actively selected atoms and compares WI-DL with RS, MUS, and QBC. WI-DL produces stronger classification results, while RS is fastest and WI-DL is generally faster than QBC.

Experiment 1: The DBN is fine-tuned by actively selecting atoms from the candidate set, starting from the training data as the initial dictionary.Fifty samples are used initially, and 1000 additional atoms are added during active learning.
Experiment 1: WI-DL correctly classifies more samples than the other algorithms, especially in the enlarged lower-left image area.The WI-DL result also matches the ground truth reasonably well.
Experiment 1: WI-DL outperforms the other methods and improves faster as the number of training samples increases.Among the other methods, performance is ranked MUS, RS, and QBC in the experiments.
Computation time: RS is fastest because random selection requires no computation, whereas WI-DL and QBC are relatively slow; WI-DL is usually faster than QBC.WI-DL complexity is mainly due to sparse coding, while QBC complexity is mainly due to training different committee members.

B. Experiment 2

Experiment 2 evaluates WI-DL against RS, MUS, and QBC on airborne ROSIS hyperspectral imagery from the University of Pavia. WI-DL produces better classification results and improves accuracy faster as training samples increase.

The comparison uses three randomly constructed data sets containing training, candidate, and testing samples with different percentages.Four active-learning algorithms are evaluated across the constructed data sets.
WI-DL classification matches the ground truth reasonably well and outperforms RS, MUS, and QBC in the enlarged comparison area.The experiment uses nine labeled classes from the University of Pavia dataset.
WI-DL accuracy improves faster than the other algorithms as more training samples are added.Classification-accuracy changes are examined as the number of training samples increases.

C. Experiment 3

Experiment 3 evaluates WI-DL, RS, MUS, and QBC on Hyperion imagery from Botswana. WI-DL matches the ground truth reasonably well, outperforms the alternatives, and improves accuracy faster as training samples increase.

The experiment applies WI-DL, RS, MUS, and QBC to three data sets constructed from ground-truth data with training, candidate, and testing subsets.The labeled data contain ten selected classes.
WI-DL classification matches the ground truth reasonably well and is better than RS, MUS, and QBC in the enlarged comparison area.The experiment uses Hyperion data acquired over the Okavango Delta, with 145 bands remaining after preprocessing.
WI-DL accuracy improves faster than the other algorithms as more training samples are added.Among the other methods, performance is ranked QBC, MUS, then RS.

VI. CONCLUSION

The conclusion presents WI-DL as an active-learning algorithm for training deep networks with remotely sensed hyperspectral images. It combines representativeness and uncertainty to select additional samples and achieves higher accuracy with fewer training samples.

WI-DL selects additional training samples using representativeness and uncertainty criteria integrated into a new objective function.The algorithm is based on active learning of deep networks and weighted incremental dictionary learning.
WI-DL is developed by minimizing the new two-criteria objective function to search for atoms.Its performance is compared with RS, MUS, and QBC.
WI-DL achieves higher classification accuracy with fewer training samples by actively selecting training samples.The conclusion reports that the algorithm performed well in classification experiments with remotely sensed hyperspectral images.