Tensor-Based and Projection-Based Methods for Dimensionality Reduction of Hyperspectral Images

Dimensionality Reduction and Anomaly Detection Based on Kittler’s Taxonomy: Analyzing Water Bodies in Two Dimensional Spaces

“…In summary, although many studies [4][5][6][7][8][9][10][11][12][13][14][15] achieve the same or similar results from their data analysis activities in the low-and in the high-dimensional space, this study is responsible for introducing a new exception: when anomaly detection based on Kittler's Taxonomy is used in image analysis activities, the use of a low-dimensional space can lead to the occurrence of a type of anomaly different from the one that occurs for the high-dimensional space.…”

“…The main contribution of this study is to show researchers in the field of Remote Sensing that investigations regarding the occurrence of anomalies of the type Unexpected structure and structural components should take into account high-dimensional spaces instead of low-dimensional ones. While studies related to digital image analysis, such as [4][5][6][7][8][9][10][11][12][13][14][15], allow researchers to sustain the idea that data analysis in high dimension generates results similar to those analyzed in low dimension, this study contributes to show that there is at least one exception to this rule, when digital image analysis involves anomaly detection based on Kittler's Taxonomy.…”

“…Equation ( 6) mathematically describes the operations involved in this step [38][39][40][41]. In Equation (6), k indicates the indices of the spectral bands, g consists of a vector of injection gains, and w is a vector of weights. Thus, from the multi-spectral image interpolated to the scale of the panchromatic image (S(x, y)), the intensity of the I L component of the image was calculated.…”

“…The transformations and combinations of the data space performed by these techniques are of great importance in data processing, being used in a wide range of fields and study cases, such as water resources management [1], medicine [2], route selection [3], etc. The main advantages of using dimensionality reduction are widely described in the scientific literature, for example, in various studies involving digital image analysis [4][5][6][7][8][9][10][11][12][13][14][15]. These studies show that it is possible to obtain similar results both by analyzing data in high and low dimensions.…”

“…Two methods of dimensionality reduction were analyzed in the study published by [6]. This work applies the Tucker decomposition to decompose (or compress) the spectral information of a hyperspectral image.…”