3,416 research outputs found
Fast redshift clustering with the Baire (ultra) metric
The Baire metric induces an ultrametric on a dataset and is of linear
computational complexity, contrasted with the standard quadratic time
agglomerative hierarchical clustering algorithm. We apply the Baire distance to
spectrometric and photometric redshifts from the Sloan Digital Sky Survey
using, in this work, about half a million astronomical objects. We want to know
how well the (more cos\ tly to determine) spectrometric redshifts can predict
the (more easily obtained) photometric redshifts, i.e. we seek to regress the
spectrometric on the photometric redshifts, and we develop a clusterwise
nearest neighbor regression procedure for this.Comment: 14 pages, 6 figure
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Anytime Hierarchical Clustering
We propose a new anytime hierarchical clustering method that iteratively
transforms an arbitrary initial hierarchy on the configuration of measurements
along a sequence of trees we prove for a fixed data set must terminate in a
chain of nested partitions that satisfies a natural homogeneity requirement.
Each recursive step re-edits the tree so as to improve a local measure of
cluster homogeneity that is compatible with a number of commonly used (e.g.,
single, average, complete) linkage functions. As an alternative to the standard
batch algorithms, we present numerical evidence to suggest that appropriate
adaptations of this method can yield decentralized, scalable algorithms
suitable for distributed/parallel computation of clustering hierarchies and
online tracking of clustering trees applicable to large, dynamically changing
databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a
conferenc
Fast, Linear Time Hierarchical Clustering using the Baire Metric
The Baire metric induces an ultrametric on a dataset and is of linear
computational complexity, contrasted with the standard quadratic time
agglomerative hierarchical clustering algorithm. In this work we evaluate
empirically this new approach to hierarchical clustering. We compare
hierarchical clustering based on the Baire metric with (i) agglomerative
hierarchical clustering, in terms of algorithm properties; (ii) generalized
ultrametrics, in terms of definition; and (iii) fast clustering through k-means
partititioning, in terms of quality of results. For the latter, we carry out an
in depth astronomical study. We apply the Baire distance to spectrometric and
photometric redshifts from the Sloan Digital Sky Survey using, in this work,
about half a million astronomical objects. We want to know how well the (more
costly to determine) spectrometric redshifts can predict the (more easily
obtained) photometric redshifts, i.e. we seek to regress the spectrometric on
the photometric redshifts, and we use clusterwise regression for this.Comment: 27 pages, 6 tables, 10 figure
Analyzing and Visualizing State Sequences in R with TraMineR
This article describes the many capabilities offered by the TraMineR toolbox for categorical sequence data. It focuses more specifically on the analysis and rendering of state sequences. Addressed features include the description of sets of sequences by means of transversal aggregated views, the computation of longitudinal characteristics of individual sequences and the measure of pairwise dissimilarities. Special emphasis is put on the multiple ways of visualizing sequences. The core element of the package is the state se- quence object in which we store the set of sequences together with attributes such as the alphabet, state labels and the color palette. The functions can then easily retrieve this information to ensure presentation homogeneity across all printed and graphical displays. The article also demonstrates how TraMineRâÂÂs outcomes give access to advanced analyses such as clustering and statistical modeling of sequence data.
Deep Unsupervised Similarity Learning using Partially Ordered Sets
Unsupervised learning of visual similarities is of paramount importance to
computer vision, particularly due to lacking training data for fine-grained
similarities. Deep learning of similarities is often based on relationships
between pairs or triplets of samples. Many of these relations are unreliable
and mutually contradicting, implying inconsistencies when trained without
supervision information that relates different tuples or triplets to each
other. To overcome this problem, we use local estimates of reliable
(dis-)similarities to initially group samples into compact surrogate classes
and use local partial orders of samples to classes to link classes to each
other. Similarity learning is then formulated as a partial ordering task with
soft correspondences of all samples to classes. Adopting a strategy of
self-supervision, a CNN is trained to optimally represent samples in a mutually
consistent manner while updating the classes. The similarity learning and
grouping procedure are integrated in a single model and optimized jointly. The
proposed unsupervised approach shows competitive performance on detailed pose
estimation and object classification.Comment: Accepted for publication at IEEE Computer Vision and Pattern
Recognition 201
New approaches for clustering high dimensional data
Clustering is one of the most effective methods for analyzing datasets that contain a large number of objects with numerous attributes. Clustering seeks to identify groups, or clusters, of similar objects. In low dimensional space, the similarity between objects is often evaluated by summing the difference across all of their attributes. High dimensional data, however, may contain irrelevant attributes which mask the existence of clusters. The discovery of groups of objects that are highly similar within some subsets of relevant attributes becomes an important but challenging task. My thesis focuses on various models and algorithms for this task. We first present a flexible clustering model, namely OP-Cluster (Order Preserving Cluster). Under this model, two objects are similar on a subset of attributes if the values of these two objects induce the same relative ordering of these attributes. OPClustering algorithm has demonstrated to be useful to identify co-regulated genes in gene expression data. We also propose a semi-supervised approach to discover biologically meaningful OP-Clusters by incorporating existing gene function classifications into the clustering process. This semi-supervised algorithm yields only OP-clusters that are significantly enriched by genes from specific functional categories. Real datasets are often noisy. We propose a noise-tolerant clustering algorithm for mining frequently occuring itemsets. This algorithm is called approximate frequent itemsets (AFI). Both the theoretical and experimental results demonstrate that our AFI mining algorithm has higher recoverability of real clusters than any other existing itemset mining approaches. Pair-wise dissimilarities are often derived from original data to reduce the complexities of high dimensional data. Traditional clustering algorithms taking pair-wise dissimilarities as input often generate disjoint clusters from pair-wise dissimilarities. It is well known that the classification model represented by disjoint clusters is inconsistent with many real classifications, such gene function classifications. We develop a Poclustering algorithm, which generates overlapping clusters from pair-wise dissimilarities. We prove that by allowing overlapping clusters, Poclustering fully preserves the information of any dissimilarity matrices while traditional partitioning algorithms may cause significant information loss
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