Dimitrios Gunopulos

Automatic subspace clustering of high dimensional data for data mining applications

Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate cluster in large high dimensional datasets.

Discovering similar multidimensional trajectories

We investigate techniques for analysis and retrieval of object trajectories in two or three dimensional space. Such data usually contain a large amount of noise, that has made previously used metrics fail. Therefore, we formalize non-metric similarity functions based on the longest common subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translation of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and time warping distance functions (for real and synthetic data) and show the superiority of our approach, especially in the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.

Mining Process Models from Workflow Logs

Modern enterprises increasingly use the workflow paradigm to prescribe how business processes should be performed. Processes are typically modeled as annotated activity graphs. We present an approach for a system that constructs process models from logs of past, unstructured executions of the given process. The graph so produced conforms to the dependencies and past executions present in the log. By providing models that capture the previous executions of the process, this technique allows easier introduction of a workflow system and evaluation and evolution of existing process models. We also present results from applying the algorithm to synthetic data sets as well as process logs obtained from an IBM Flowmark installation.

Constraint-based rule mining in large, dense databases

Constraint-based rule miners find all rules in a given data-set meeting user-specified constraints such as minimum support and confidence. We describe a new algorithm that directly exploits all user-specified constraints including minimum support, minimum confidence, and a new constraint that ensures every mined rule offers a predictive advantage over any of its simplifications. Our algorithm maintains efficiency even at low supports on data that is dense (e.g. relational tables). Previous approaches such as Apriori and its variants exploit only the minimum support constraint, and as a result are ineffective on dense data due to a combinatorial explosion of “frequent itemsets”.

On indexing mobile objects

We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the l-dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O’s needed to answer the d-dimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included.

A local search mechanism for peer-to-peer networks

One important problem in peer-to-peer (P2P) networks is searching and retrieving the correct information. However, existing searching mechanisms in pure peer-to-peer networks are inefficient due to the decentralized nature of such networks. We propose two mechanisms for information retrieval in pure peer-to-peer networks. The first, the modified Breadth-First Search (BFS) mechanism, is an extension of the current Gnuttela protocol, allows searching with keywords, and is designed to minimize the number of messages that are needed to search the network. The second, the Intelligent Search mechanism, uses the past behavior of the P2P network to further improve the scalability of the search procedure. In this algorithm, each peer autonomously decides which of its peers are most likely to answer a given query. The algorithm is entirely distributed, and therefore scales well with the size of the network. We implemented our mechanisms as middleware platforms. To show the advantages of our mechanisms we present experimental results using the middleware implementation.

Indexing multi-dimensional time-series with support for multiple distance measures

Although most time-series data mining research has concentrated on providing solutions for a single distance function, in this work we motivate the need for a single index structure that can support multiple distance measures. Our specific area of interest is the efficient retrieval and analysis of trajectory similarities. Trajectory datasets are very common in environmental applications, mobility experiments, video surveillance and are especially important for the discovery of certain biological patterns. Our primary similarity measure is based on the Longest Common Subsequence (LCSS) model, that offers enhanced robustness, particularly for noisy data, which are encountered very often in real world applications. However, our index is able to accommodate other distance measures as well, including the ubiquitous Euclidean distance, and the increasingly popular Dynamic Time Warping (DTW). While other researchers have advocated one or other of these similarity measures, a major contribution of our work is the ability to support all these measures without the need to restructure the index. Our framework guarantees no false dismissals and can also be tailored to provide much faster response time at the expense of slightly reduced precision/recall. The experimental results demonstrate that our index can help speed-up the computation of expensive similarity measures such as the LCSS and the DTW.

Locally adaptive metric nearest-neighbor classification

Nearest-neighbor classification assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions with finite samples due to the curse of dimensionality. Severe bias can be introduced under these conditions when using the nearest-neighbor rule. We propose a locally adaptive nearest-neighbor classification method to try to minimize bias. We use a chi-squared distance analysis to compute a flexible metric for producing neighborhoods that are highly adaptive to query locations. Neighborhoods are elongated along less relevant feature dimensions and constricted along most influential ones. As a result, the class conditional probabilities are smoother in the modified neighborhoods, whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other techniques using both simulated and real-world data.

Finding Similar Time Series

Similarity of objects is one of the crucial concepts in several applications, including data mining. For complex objects, similarity is nontrivial to define. In this paper we present an intuitive model for measuring the similarity between two time series. The model takes into account outliers, different scaling functions, and variable sampling rates. Using methods from computational geometry, we show that this notion of similarity can be computed in polynomial time. Using statistical approximation techniques, the algorithms can be speeded up considerably. We give preliminary experimental results that show the naturalness of the notion.

Automatic Subspace Clustering of High Dimensional Data

Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.