Soil contamination by arsenic and heavy metals is an increasingly severe environmental problem. Efficiently investigation of soil contamination is the premise of soil protection and further the foundation of food security. Visible and near-infrared reflectance spectroscopy (VNIRS) has been widely used in soil science, due to its rapidity and convenience. With different spectrally active soil ch...

∀i, yi = [0, ..., 0 } {{ } j−1 , 1, 0, ..., 0 } {{ } c−j ] ⇒ xi W0 = x̄j W0, (1) where y i is the i-th row of the true cluster assignment matrix Y and x̄j is the mean of the data that belongs to class j. Denote X̄c = [x̄1, ..., x̄c]. Note that X̄c = XY Σ, where Σ ∈ Rc×c is a diagonal matrix with the i-th diagonal element as 1/ni, ni is the number of the data that belongs to class i. Then rank(X̄ c W0)...

Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters, with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost function for spectral clustering based on a measure of error between a given partition and a solut...

An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clustering algorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult t...

In this paper we present a comparison of multiple cluster algorithms and their suitability for clustering text data. The clustering is based on similarities only, employing the Kolmogorov complexity as a similiarity measure. This motivates the set of considered clustering algorithms which take into account the similarity between objects exclusively. Compared cluster algorithms are Median kMeans...

Spectral clustering is a flexible clustering technique that finds data clusters in the spectral embedding space of the data. It doesn’t assume convexity of the shape of clusters, and is able to find non-linear cluster boundaries. Constrained spectral clustering aims at incorporating user-defined pairwise constraints in to spectral clustering. Typically, there are two kinds of pairwise constrain...

The spectral clustering algorithm has been shown to be very effective in finding clusters of non-linear boundaries. Unfortunately, spectral clustering suffers from the scalability problem in both memory use and computational time. In this work, we parallelize the algorithm by dividing both memory use and computation on distributed machines. Empirical study on some small datasets shows the accur...

We present the results of exploratory data analysis for a data set that consists of crossposting information for 89,687 newsgroups over a period of 3.4 years. The data set we use is a part of Microsoft Netscan data. Our goal is to investigate the community structure of the newsgroup data set with a specific focus on spectral hierarchical clustering. We present a spectral hierarchical clustering...

Manifold learning based image clustering models are usually employed at local level to deal with images sampled from nonlinear manifold. Multimode patterns in image data matrices can vary from nominal to significant due to images with different expressions, pose, illumination, or occlusion variations. We show that manifold learning based image clustering models are unable to achieve well separa...

Spectral clustering has been successfully used in the field of pattern recognition and image processing. The efficiency of spectral clustering, however, depends heavily on the similarity measure adopted. A widely used similarity measure is the Gaussian kernel function where Euclidean distance is used. Unfortunately, the Gaussian kernel function is parameter sensitive and the Euclidean distance ...