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Diffusion bases methods for segmentation and clustering
Diffusion bases methods for segmentation and clustering
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机译:基于扩散的分割和聚类方法
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摘要
Methods for dimensionality reduction of large data volumes, in particular hyper-spectral data cubes, include providing a dataset Γ of data points given as vectors, building a weighted graph G on Γ with a weight function wε, wherein wε corresponds to a local coordinate-wise similarity between the coordinates in Γ; obtaining eigenvectors of a matrix derived from graph G and weight function wε, and projecting the data points in Γ onto the eigenvectors to obtain a set of projection values ΓB for each data point, whereby ΓB represents coordinates in a reduced space. In one embodiment, the matrix is constructed through the dividing each element of wε by a square sum of its row multiplied by a square sum of its column. In another embodiment the matrix is constructed through a random walk on graph G via a Markov transition matrix P, which is derived from wε. The reduced space coordinates are advantageously used to rapidly and efficiently perform segmentation and clustering.
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机译:大数据量(特别是高光谱数据立方体)的降维方法包括提供以矢量形式给出的数据点的数据集Γ,在Γ上建立具有权函数w ε Sub>的加权图G,其中w ε Sub>对应于Γ中坐标之间的局部坐标相似性;获得从图G和权重函数w ε Sub>导出的矩阵的特征向量,并将Γ中的数据点投影到特征向量上,以获得每个投影值的集合Γ B Sub>数据点,其中Γ B Sub>表示缩小空间中的坐标。在一个实施例中,通过将w ε Sub>的每个元素除以其行的平方和乘以其列的平方和来构造矩阵。在另一个实施例中,矩阵是通过马尔可夫转移矩阵P通过在图G上的随机游走而构造的,该马尔可夫转移矩阵P是从w ε Sub>导出的。减小的空间坐标有利地用于快速且有效地执行分割和聚类。
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