# A Novel Clustering-Based Feature Representation for the Classification of Hyperspectral Imagery

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Clustering

**X**= {

**x**

**,**

_{1}**x**

**, …**

_{2}**x**

_{n}} be the n pixels in a hyperspectral image, and the pixels are grouped into k clusters

**C**= {

**c**

_{1},

**c**

_{2}, …

**c**

_{k}}. The clusters should satisfy the following conditions: (1) ${\cup}_{i=1}^{m}{\mathit{c}}_{\mathit{i}}=\mathit{X}$; (2)

**c**

_{i}∩

**c**

_{j};= ∅︀, i ≠ j, i, j = 1,2, …, k; and (3)

**c**

_{i}= ∅︀, i = 1,2, …, k. In spite of the fact that the clustering task can be fulfilled by various algorithms, their fundamental concepts are similar, i.e., points belonging to the same cluster are more similar to each other than points belonging to the other clusters. In this paper, the following four clustering methods are employed to generate the codes of a hyperspectral image.

- (1)
- K-Means: This is a centroid-based clustering method that uses the cluster centers to construct the model for the data grouping. For the sake of minimizing the sum of the distance between points to the centroid vectors, an iterative algorithm is used to modify the model until the desired result is achieved [20]. In the reassignment step, the points are assigned to their nearest cluster centroid:$$\begin{array}{c}{\mathit{c}}_{i}^{(t)}=\left\{{\mathit{x}}_{p}:\Vert {\mathit{x}}_{p}-{\mathit{\mu}}_{i}^{(t)}\Vert <\Vert {\mathit{x}}_{p}-{\mathit{\mu}}_{j}^{(t)}\Vert \right\}\\ \forall 1\le p\le n,1\le i,j\le k,i\ne j\end{array}$$where t represents the t-th iteration, and
**μ**_{i}is the mean of the points in cluster**c**_{i}. - (2)
- Iterative Self-Organizing Data Analysis Technique Algorithm (ISODATA): The basic idea of ISODATA is similar to k-means in that it minimizes the intra-cluster variability by a reassignment and update process. However, the algorithm improves on k-means by introducing a merging and splitting method during the iteration. Clusters are merged if the distance of their centers is less than a given threshold, or the number of points in a cluster is less than the predefined value. Conversely, a single cluster is divided into two clusters if the standard deviation is higher than a user-specified value, or the number of points exceeds a certain threshold. In this way, the final clustering result is obtained when all the predefined conditions are reached [21].
- (3)
- Fuzzy C-Means (FCM): Differing from the deterministic clustering approaches, the FCM algorithm uses a membership level to describe the relationship between points and clusters [22]. Meanwhile, the centroids of the clusters are related to the coefficients which represent the grades of membership of the clusters, and can be expressed by the weighted mean of all the points:$${\mathit{\mu}}_{i}^{(t+1)}=\frac{{\sum}_{{\mathit{x}}_{p}\in {\mathit{c}}_{i}^{(t)}}{\mathit{w}}_{pi}^{(t)}{\mathit{x}}_{p}}{{\sum}_{{\mathit{x}}_{p}\in {\mathit{c}}_{i}^{(t)}}{\mathit{w}}_{pi}^{(t)}}$$where
**w**_{pi}is the degree of**x**_{p}belonging to cluster**c**_{i}, which is defined as:$${\mathit{w}}_{pi}={\left(\sum _{j=1}^{k}{\left(\frac{\left|\right|{\mathit{x}}_{p}-{\mathit{\mu}}_{i}\left|\right|}{\left|\right|{\mathit{x}}_{p}-{\mathit{\mu}}_{j}\left|\right|}\right)}^{\frac{2}{m-1}}\right)}^{-1}$$where m donates the level of the cluster fuzziness.In order to obtain the cluster label of each point, the final clusters are obtained by assigning points to the cluster with the maximum membership degree. - (4)
- Exception Maximization (EM) Algorithm: EM is frequently used for data clustering in machine learning, and works in two alternating steps: (1) the expectation (E) step, which refers to computing the expected value with the previous estimates of the model parameters; and (2) the maximization (M) step, which refers to altering the parameters by maximizing the expectation function [23]. The fundamental principle of the algorithm is to find a maximum likelihood estimate of the parameters through the iterative model. Each feature vector will then be assigned to one cluster on the basis of the maximum posteriori probability.

**v**

_{p,i}is the new intensity value in band i, and N is the number of neighboring bands considered.

#### 2.2. Cluster Histogram

_{i}denotes the frequency of cluster i located in the local window W for a pixel p, and k is the number of clusters.

#### 2.3. Classification

**x**

_{i},y

_{i})|y

_{i}∊{− +1}} and a mapping function Φ(·), the model can be described as f(

**x**) = 〈

**w**

**,**Φ(

**x**)〉 + w

_{0}, where

**w**and w

_{0}denote the weight vector and the bias term. In order to find the hyperplane to ensure that the distance from it to the nearest point on each side is maximized, and the number of points with slack variables ξ > 0 is reduced, the cost function should be minimized as follows:

_{i}.

## 3. Experimental Section

#### 3.1. Datasets

#### 3.2. Parameter Analysis

#### 3.3. Results and Comparisons

#### 3.3.1. 3D Wavelet Texture

^{x}L

^{y}L

^{z}, L

^{x}H

^{y}L

^{z}, L

^{x}L

^{y}H

^{z}, L

^{x}H

^{y}H

^{z}, H

^{x}L

^{y}L

^{z}, H

^{x}H

^{y}L

^{z}, H

^{x}L

^{y}H

^{z}, H

^{x}H

^{y}H

^{z}}, where L and H represent the low-pass and high-pass sub-bands, respectively. x and y are the spatial coordinates of the image, and z is the spectral band [28]. These sub-bands are stacked with the original spectral bands as the input feature for the spectral-spatial classification. In this study, the parameters of the 3D wavelet texture are set as: window size = {4, 8, 16, 32}.

#### 3.3.2. GLCM

#### 3.3.3. DMPs

#### 3.4. Discussion

- (1)
- Dimensionality of the hyperspectral bands. The Indian Pines image is taken as an example for investigating the effect of the spectral dimensionality for the MCH method. The dimensions of the spectral features used for the clustering are reduced to 10, 30, and 50, according to Equation (4). From Table 9, it can be seen that the spectral dimension of the clustering has little effect on the final classification accuracy. It is therefore sensible to appropriately reduce the spectral dimensionality in order to increase the efficiency of the MCH method, since the computational complexity of clustering is affected by the feature dimensionality.
- (2)
- Initialization of the clustering. To analyze the influence of initialization of the clustering on the classification, the accuracies with different initial clustering centers that are randomly generated are reported in Table 10 for the Indian Pines image. It can be seen that, although the clustering approach gives slightly different clustering results for the different runs, the classification accuracies are stable and the proposed MCH is robust to the clustering initialization.
- (3)
- Comparison with a state-of-the-art spectral-spatial classification technique. In order to further validate the effectiveness of the proposed MCH method, the state-of-the-art spectral-spatial classification approach of Tarabalka et al. [10] is carried out for comparison. In this approach, the pixelwise SVM classification result is refined by majority voting based on a clustering-based segmentation. A post-processing is then performed in order to reduce the classification noise. The comparison results are shown in Table 11, where it can be clearly seen that the MCH method significantly outperforms the state-of-the-art spectral-spatial classification approach of Tarabalka et al. [10].

## 4. Conclusions

- (1)
- The clustering strategy is able to generate a series of primitive codes which effectively represent the spectral signals in an image.
- (2)
- The cluster histogram in a series of multiscale neighborhoods centered by each pixel is effective in exploiting both the spectral and spatial features. Furthermore, the multi-window strategy assigns large weights to the pixels near the center, which is reasonable due to the complex and multiscale characteristics of the remote sensing data.
- (3)
- The MCH feature extraction and classification method can achieve satisfactory results rapidly and conveniently without defining complicated textural or structural features. It can also be easily carried out in real applications.

## Acknowledgments

## Conflicts of Interest

**Author Contributions**All authors made great contributions to the work. Qikai Lu and Xin Huang designed the research and analyzed the results. Qikai Lu wrote the manuscript and performed the experiments. Xin Huang supervised the study and gave insightful suggestions to the manuscript. Liangpei Zhang provided the background knowledge and contributed in the revision of the paper.

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**Figure 2.**Demonstration of the MCH (W is the local window, and H is the corresponding cluster histogram).

**Figure 7.**Classification accuracies of the proposed algorithm with different cluster numbers (40, 80, 120, 160, 200) for: (

**a**) the Indian Pines image; and (

**b**) the Pavia University image.

**Figure 8.**Classification accuracies of the proposed algorithm with different window sizes (3, 11, 19, 27, and multiscale) for: (

**a**) the Indian Pines image; and (

**b**) the Pavia University image.

Class | # Training Samples | # Test Samples |
---|---|---|

Corn-notill | 50 | 1434 |

Corn-mintill | 50 | 834 |

Corn | 50 | 234 |

Grass/pasture | 50 | 497 |

Grass/trees | 50 | 747 |

Hay-windrowed | 50 | 489 |

Soybeans-notill | 50 | 968 |

Soybeans-mintill | 50 | 2468 |

Soybeans-cleantill | 50 | 614 |

Wheat | 50 | 212 |

Woods | 50 | 1294 |

Bldg-Grass-Tree-Drives | 50 | 380 |

Total | 600 | 10,171 |

Class | # Training Samples | # Test Samples |
---|---|---|

Roads | 50 | 3299 |

Grass | 50 | 3075 |

Water | 50 | 2882 |

Trails | 50 | 1017 |

Trees | 50 | 2027 |

Shadows | 50 | 1093 |

Roofs | 50 | 5811 |

Total | 350 | 19,024 |

Class | # Training Samples | # Test Samples |
---|---|---|

Trees | 50 | 3064 |

Asphalt | 50 | 6631 |

Bitumen | 50 | 1330 |

Gravel | 50 | 2099 |

Metal sheets | 50 | 1345 |

Shadows | 50 | 947 |

Bricks | 50 | 3682 |

Meadows | 50 | 18,649 |

Bare soil | 50 | 5029 |

Total | 450 | 42,776 |

Class | #Training Samples | # Test Samples |
---|---|---|

Buildings | 50 | 84,421 |

Roads | 50 | 18,149 |

Water | 50 | 38,875 |

Trees/grass | 50 | 40,630 |

Shadows | 50 | 12,532 |

Total | 250 | 194,607 |

Spectral-Spatial Classification | MCH | |||||||
---|---|---|---|---|---|---|---|---|

Raw | 3D Wavelet | GLCM | DMPs | k-Means | ISO | FCM | EM | |

Corn-notill | 49.51 | 56.33 | 61.33 | 76.93 | 90.15 | 88.12 | 89.09 | 90.39 |

Corn-mintill | 44.51 | 63.36 | 66.17 | 88.83 | 93.87 | 93.59 | 93.33 | 95.06 |

Corn | 40.98 | 49.31 | 67.90 | 87.09 | 97.03 | 97.75 | 95.85 | 97.31 |

Grass/pasture | 70.99 | 86.31 | 76.45 | 90.01 | 96.75 | 97.06 | 97.15 | 96.79 |

Grass/trees | 82.27 | 90.90 | 91.08 | 94.71 | 99.44 | 99.68 | 99.67 | 99.57 |

Hay-windrowed | 97.86 | 98.76 | 98.28 | 98.86 | 99.74 | 99.80 | 99.70 | 99.62 |

Soybeans-notill | 55.51 | 60.28 | 62.15 | 76.17 | 89.89 | 87.98 | 88.86 | 90.14 |

Soybeans-mintill | 57.17 | 65.02 | 67.28 | 88.32 | 95.08 | 95.05 | 94.98 | 95.15 |

Soybeans-cleantill | 42.90 | 50.10 | 63.11 | 81.19 | 95.28 | 95.23 | 95.03 | 96.41 |

Wheat | 87.82 | 96.75 | 98.52 | 99.35 | 99.72 | 99.81 | 99.72 | 99.67 |

Woods | 86.47 | 93.60 | 91.63 | 98.73 | 99.91 | 99.92 | 99.92 | 99.90 |

Bldg-Grass-Tree-Drives | 50.34 | 77.26 | 79.91 | 97.56 | 99.37 | 99.66 | 99.03 | 99.63 |

OA | 61.83 | 70.73 | 73.40 | 88.08 | 95.34 | 94.90 | 95.00 | 95.60 |

kappa | 0.57 | 0.67 | 0.70 | 0.86 | 0.95 | 0.94 | 0.94 | 0.95 |

Spectral-Spatial Classification | MCH | |||||||
---|---|---|---|---|---|---|---|---|

Raw | 3D Wavelet | GLCM | DMPs | k-Means | ISO | FCM | EM | |

Roads | 91.70 | 91.79 | 92.04 | 95.37 | 98.98 | 98.87 | 98.81 | 98.84 |

Grass | 98.85 | 99.32 | 99.22 | 99.72 | 99.86 | 99.84 | 99.86 | 99.76 |

Water | 86.28 | 88.33 | 96.86 | 96.05 | 98.71 | 100.00 | 99.30 | 99.94 |

Trails | 66.10 | 90.94 | 90.42 | 97.02 | 99.64 | 99.63 | 99.61 | 99.44 |

Trees | 98.17 | 98.69 | 98.33 | 99.02 | 99.92 | 99.92 | 99.90 | 99.70 |

Shadows | 39.93 | 67.70 | 90.53 | 90.17 | 96.86 | 99.63 | 97.77 | 99.50 |

Roofs | 84.28 | 93.45 | 93.44 | 96.90 | 99.51 | 99.42 | 99.46 | 99.38 |

OA | 86.61 | 92.28 | 94.80 | 96.75 | 99.24 | 99.55 | 99.34 | 99.48 |

kappa | 0.84 | 0.91 | 0.94 | 0.96 | 0.99 | 0.99 | 0.99 | 0.99 |

Spectral-Spatial Classification | MCH | |||||||
---|---|---|---|---|---|---|---|---|

Raw | 3D Wavelet | GLCM | DMPs | k-Means | ISO | FCM | EM | |

Trees | 62.85 | 63.22 | 70.95 | 87.03 | 97.70 | 97.77 | 97.29 | 97.50 |

Asphalt | 77.94 | 80.60 | 78.81 | 96.16 | 97.99 | 97.90 | 96.86 | 99.59 |

Bitumen | 49.65 | 56.06 | 59.14 | 99.86 | 99.29 | 99.81 | 96.69 | 100.00 |

Gravel | 34.48 | 46.42 | 40.04 | 96.00 | 95.94 | 95.51 | 94.67 | 99.73 |

Metal sheets | 91.00 | 93.99 | 92.72 | 99.71 | 99.93 | 99.88 | 99.83 | 99.93 |

Shadows | 99.36 | 99.41 | 99.42 | 99.89 | 99.92 | 99.93 | 99.93 | 99.95 |

Bricks | 59.90 | 66.66 | 69.53 | 92.80 | 97.56 | 98.56 | 96.68 | 99.37 |

Meadows | 61.98 | 63.90 | 68.12 | 97.07 | 98.25 | 98.75 | 97.78 | 99.60 |

Bare soil | 31.97 | 33.89 | 39.04 | 99.35 | 95.17 | 96.85 | 94.34 | 99.99 |

OA | 59.42 | 62.67 | 64.84 | 96.18 | 97.73 | 98.23 | 97.00 | 99.51 |

kappa | 0.50 | 0.54 | 0.57 | 0.95 | 0.97 | 0.98 | 0.96 | 0.99 |

Spectral-Spatial Classification | MCH | |||||||
---|---|---|---|---|---|---|---|---|

Raw | 3D Wavelet | GLCM | DMPs | k-Means | ISO | FCM | EM | |

Buildings | 88.47 | 88.79 | 90.82 | 90.07 | 93.27 | 93.58 | 93.54 | 92.75 |

Roads | 67.41 | 67.92 | 70.92 | 71.95 | 77.69 | 78.63 | 78.38 | 76.42 |

Water | 99.61 | 98.92 | 98.79 | 99.34 | 99.99 | 99.94 | 99.98 | 99.86 |

Trees/grass | 97.16 | 97.29 | 98.35 | 96.30 | 99.32 | 99.26 | 99.12 | 99.21 |

Shadows | 95.43 | 93.82 | 93.12 | 91.34 | 95.95 | 95.30 | 96.03 | 94.71 |

OA | 90.21 | 90.21 | 91.68 | 91.07 | 94.26 | 94.45 | 94.43 | 93.75 |

kappa | 0.87 | 0.87 | 0.89 | 0.88 | 0.92 | 0.92 | 0.92 | 0.91 |

**Table 9.**Classification accuracies for the Indian Pines image with different spectral dimensions for clustering.

Dim. | k-Means | ISO | FCM | EM | ||||
---|---|---|---|---|---|---|---|---|

Mean | Std. | Mean | Std. | Mean | Std. | Mean | Std. | |

10 | 95.34 | 0.98 | 94.90 | 0.89 | 95.00 | 0.98 | 95.60 | 0.94 |

30 | 95.28 | 1.09 | 95.23 | 0.73 | 95.06 | 1.00 | 95.65 | 1.17 |

50 | 95.28 | 1.08 | 95.10 | 0.87 | 95.15 | 1.09 | 95.56 | 0.90 |

All | 95.46 | 0.89 | 95.14 | 0.87 | 94.74 | 0.93 | 95.40 | 0.84 |

**Table 10.**Classification accuracies for the Indian Pines image with different clustering initializations.

Run | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|---|

k-means | Mean | 95.65 | 95.53 | 94.94 | 95.22 | 95.62 | 95.26 | 95.28 | 95.26 | 94.96 | 95.29 |

Std. | 0.67 | 0.93 | 1.10 | 0.88 | 0.77 | 1.02 | 0.98 | 0.82 | 0.95 | 0.80 | |

FCM | Mean | 95.44 | 95.17 | 95.31 | 95.29 | 95.09 | 95.27 | 95.07 | 95.29 | 95.18 | 95.55 |

Std. | 1.03 | 1.01 | 0.98 | 0.90 | 0.94 | 1.00 | 0.97 | 1.12 | 1.00 | 0.97 | |

EM | Mean | 95.62 | 95.65 | 95.18 | 95.77 | 95.98 | 95.43 | 95.62 | 95.87 | 95.51 | 95.81 |

Std. | 0.80 | 0.60 | 1.04 | 0.95 | 0.65 | 1.00 | 0.73 | 0.39 | 0.70 | 0.89 |

**Table 11.**Comparison between MCH and the state-of-the art spectral-spatial classification technique of Tarabalka et al. [10] (PP = post-processing for reducing the classification noise).

Datasets | MCH | Tarabalka et al. [10] | ||||
---|---|---|---|---|---|---|

k-Means | ISO | FCM | EM | Without PP | With PP | |

University | 97.73 | 98.23 | 97.00 | 99.51 | 90.57 | 91.20 |

AVIRIS | 95.34 | 94.90 | 95.00 | 95.60 | 88.53 | 90.64 |

© 2014 by the authors; licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, Q.; Huang, X.; Zhang, L.
A Novel Clustering-Based Feature Representation for the Classification of Hyperspectral Imagery. *Remote Sens.* **2014**, *6*, 5732-5753.
https://doi.org/10.3390/rs6065732

**AMA Style**

Lu Q, Huang X, Zhang L.
A Novel Clustering-Based Feature Representation for the Classification of Hyperspectral Imagery. *Remote Sensing*. 2014; 6(6):5732-5753.
https://doi.org/10.3390/rs6065732

**Chicago/Turabian Style**

Lu, Qikai, Xin Huang, and Liangpei Zhang.
2014. "A Novel Clustering-Based Feature Representation for the Classification of Hyperspectral Imagery" *Remote Sensing* 6, no. 6: 5732-5753.
https://doi.org/10.3390/rs6065732