Clustering Time Series from Mixture Polynomial Models with Discretised Data

Clustering time series is an active research area with applications in many fields. One common feature of time series is the likely presence of outliers. These uncharacteristic data can significantly effect the quality of clusters formed. This paper evaluates a method of over-coming the detrimental effects of outliers. We describe some of the alternative approaches to clustering time series, then specify a particular class of model for experimentation with k-means clustering and a correlation based distance metric. For data derived from this class of model we demonstrate that discretising the data into a binary series of above and below the median improves the clustering when the data has outliers. More specifically, we show that firstly discretisation does not significantly effect the accuracy of the clusters when there are no outliers and secondly it significantly increases the accuracy in the presence of outliers, even when the probability of outlier is very low

Temporal Clustering

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological surveys and contagious disease surveillance. In this more general setting existing algorithms for classical (i.e. static) clustering problems are not applicable anymore. We propose a set of optimization problems which we collectively refer to as temporal clustering. The quality of a solution to a temporal clustering instance can be quantified using three parameters: the number of clusters k, the spatial clustering cost r, and the maximum cluster displacement delta between consecutive time steps. We consider spatial clustering costs which generalize the well-studied k-center, discrete k-median, and discrete k-means objectives of classical clustering problems. We develop new algorithms that achieve trade-offs between the three objectives k, r, and delta. Our upper bounds are complemented by inapproximability results

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

A Scalable Algorithm for Metric High-Quality Clustering in Information Retrieval Tasks

We consider the problem of finding efficiently a high quality k-clustering of n points in a (possibly discrete) metric space. Many methods are known when the point are vectors in a real vector space, and the distance function is a standard geometric distance such as L1, L2 (Euclidean) or L2 2 (squared Euclidean distance). In such cases efficiency is often sought via sophisticated multidimensional search structures for speeding up nearest neighbor queries (e.g. variants of kd-trees). Such techniques usually work well in spaces of moderately high dimension say up to 6 or 8). Our target is a scenario in which either the metric space cannot be mapped into a vector space, or, if this mapping is possible, the dimension of such a space is so high as to rule out the use of the above mentioned techniques. This setting is rather typical in Information Retrieval applications. We augment the well known furthest-point-first algorithm for kcenter clustering in metric spaces with a filtering step based on the triangular inequality and we compare this algorithm with some recent fast variants of the classical k-means iterative algorithm augmented with an analogous filtering schemes. We extensively tested the two solutions on synthetic geometric data and real data from Information Retrieval applications. The main conclusion we draw is that our modified furthest-point-first method attains solutions of better or comparable quality within a fraction of the time used by the fast k-means algorithm. Thus our algorithm is valuable when either real time constraints or the large amount of data highlight the poor scalability of traditional clustering methods

An Enhanced Initialization Method to Find an Initial Center for K-modes Clustering

Data mining is a technique which extracts the information from the large amount of data. To group the objects having similar characteristics, clustering method is used. K-means clustering algorithm is very efficient for large data sets deals with numerical quantities however it not works well for real world data sets which contain categorical values for most of the attributes. K-modes algorithm is used in the place of K-means algorithm. In the existing system, the initialization of K- modes clustering from the view of outlier detection is considered. It avoids that various initial cluster centers come from the same cluster. To overcome the above said limitation, it uses Initial_Distance and Initial_Entropy algorithms which use a new weightage formula to calculate the degree of outlierness of each object. K-modes algorithm can guarantee that the chosen initial cluster centers are not outliers. To improve the performance further, a new modified distance metric -weighted matching distance is used to calculate the distance between two objects during the process of initialization. As well as, one of the data pre-processing methods is used to improve the quality of data. Experiments are carried out on several data sets from UCI repository and the results demonstrated the effectiveness of the initialization method in the proposed algorithm

Accurate MapReduce Algorithms for k-Median and k-Means in General Metric Spaces

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular k-median and k-means variants which, given a set P of points from a metric space and a parameter k<|P|, require to identify a set S of k centers minimizing, respectively, the sum of the distances and of the squared distances of all points in P from their closest centers. Our specific focus is on general metric spaces, for which it is reasonable to require that the centers belong to the input set (i.e., S subseteq P). We present coreset-based 3-round distributed approximation algorithms for the above problems using the MapReduce computational model. The algorithms are rather simple and obliviously adapt to the intrinsic complexity of the dataset, captured by the doubling dimension D of the metric space. Remarkably, the algorithms attain approximation ratios that can be made arbitrarily close to those achievable by the best known polynomial-time sequential approximations, and they are very space efficient for small D, requiring local memory sizes substantially sublinear in the input size. To the best of our knowledge, no previous distributed approaches were able to attain similar quality-performance guarantees in general metric spaces

Distributed k-Means with Outliers in General Metrics

Center-based clustering is a pivotal primitive for unsupervised learning and data analysis. A popular variant is the k-means problem, which, given a set P of points from a metric space and a parameter k < |P|, requires finding a subset S ⊂ P of k points, dubbed centers, which minimizes the sum of all squared distances of points in P from their closest center. A more general formulation, introduced to deal with noisy datasets, features a further parameter z and allows up to z points of P (outliers) to be disregarded when computing the aforementioned sum. We present a distributed coreset-based 3-round approximation algorithm for k-means with z outliers for general metric spaces, using MapReduce as a computational model. Our distributed algorithm requires sublinear local memory per reducer, and yields a solution whose approximation ratio is an additive term O(γ) away from the one achievable by the best known polynomial-time sequential (possibly bicriteria) approximation algorithm, where γ can be made arbitrarily small. An important feature of our algorithm is that it obliviously adapts to the intrinsic complexity of the dataset, captured by its doubling dimension D. To the best of our knowledge, no previous distributed approaches were able to attain similar quality-performance tradeoffs for general metrics

K-Boost: a Scalable Algorithm for High-Quality Clustering of Microarray Gene Expression Data

Motivation: Microarray technology for profiling gene expression levels is a popular tool in modern biological research. Applications range from tissue classification to the detection of metabolic networks, from drug discovery to time-critical personalized medicine. Given the increase in size and complexity of the data sets produced, their analysis is becoming problematic in terms of time/quality tradeoffs. Clustering genes with similar expression profiles is a key initial step for subsequent manipulations and the increasing volumes of data to be analyzed requires methods that are at the same time efficient (completing an analysis in minutes rather than hours) and effective (identifying significant clusters with high biological correlations). Results: In this paper we propose K-Boost, a novel clustering algorithm based on a combination of the Furthest-Point-First (FPF) heuristic for solving the metric k-centers problem, a stability-based method for determining the number of clusters (i.e. the value of k), and a k-means-like cluster refinement. K-Boost is able to detect the optimal number of clusters to produce. It is scalable to large data-sets without sacrificing output quality as measured by several internal and external criteria

Fine-tuning an algorithm for semantic document clustering using a similarity graph

In this article, we examine an algorithm for document clustering using a similarity graph. The graph stores words and common phrases from the English language as nodes and it can be used to compute the degree of semantic similarity between any two phrases. One application of the similarity graph is semantic document clustering, that is, grouping documents based on the meaning of the words in them. Since our algorithm for semantic document clustering relies on multiple parameters, we examine how fine-tuning these values affects the quality of the result. Specifically, we use the Reuters-21578 benchmark, which contains 11,362 newswire stories that are grouped in 82 categories using human judgment. We apply the k-means clustering algorithm to group the documents using a similarity metric that is based on keywords matching and one that uses the similarity graph. We evaluate the results of the clustering algorithms using multiple metrics, such as precision, recall, f-score, entropy, and purity