A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Unsupervised and semi-supervised clustering with learnable cluster dependent kernels.

Despite the large number of existing clustering methods, clustering remains a challenging task especially when the structure of the data does not correspond to easily separable categories, and when clusters vary in size, density and shape. Existing kernel based approaches allow to adapt a specific similarity measure in order to make the problem easier. Although good results were obtained using the Gaussian kernel function, its performance depends on the selection of the scaling parameter. Moreover, since one global parameter is used for the entire data set, it may not be possible to find one optimal scaling parameter when there are large variations between the distributions of the different clusters in the feature space. One way to learn optimal scaling parameters is through an exhaustive search of one optimal scaling parameter for each cluster. However, this approach is not practical since it is computationally expensive especially when the data includes a large number of clusters and when the dynamic range of possible values of the scaling parameters is large. Moreover, it is not trivial to evaluate the resulting partition in order to select the optimal parameters. To overcome this limitation, we introduce two new fuzzy relational clustering techniques that learn cluster dependent Gaussian kernels. The first algorithm called clustering and Local Scale Learning algorithm (LSL) minimizes one objective function for both the optimal partition and for cluster dependent scaling parameters that reflect the intra-cluster characteristics of the data. The second algorithm, called Fuzzy clustering with Learnable Cluster dependent Kernels (FLeCK) learns the scaling parameters by optimizing both the intra-cluster and the inter-cluster dissimilarities. Consequently, the learned scale parameters reflect the relative density, size, and position of each cluster with respect to the other clusters. We also introduce semi-supervised versions of LSL and FLeCK. These algorithms generate a fuzzy partition of the data and learn the optimal kernel resolution of each cluster simultaneously. We show that the incorporation of a small set of constraints can guide the clustering process to better learn the scaling parameters and the fuzzy memberships in order to obtain a better partition of the data. In particular, we show that the partial supervision is even more useful on real high dimensional data sets where the algorithms are more susceptible to local minima. All of the proposed algorithms are optimized iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes these algorithms simple and fast. Moreover, our algorithms are formulated to work on relational data. This makes them applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. Our extensive experiments show that FLeCK and SS-FLeCK outperform existing algorithms. In particular, we show that when data include clusters with various inter-cluster and intra-cluster distances, learning cluster dependent kernel is crucial in obtaining a good partition

PLPD: reliable protein localization prediction from imbalanced and overlapped datasets

Subcellular localization is one of the key functional characteristics of proteins. An automatic and efficient prediction method for the protein subcellular localization is highly required owing to the need for large-scale genome analysis. From a machine learning point of view, a dataset of protein localization has several characteristics: the dataset has too many classes (there are more than 10 localizations in a cell), it is a multi-label dataset (a protein may occur in several different subcellular locations), and it is too imbalanced (the number of proteins in each localization is remarkably different). Even though many previous works have been done for the prediction of protein subcellular localization, none of them tackles effectively these characteristics at the same time. Thus, a new computational method for protein localization is eventually needed for more reliable outcomes. To address the issue, we present a protein localization predictor based on D-SVDD (PLPD) for the prediction of protein localization, which can find the likelihood of a specific localization of a protein more easily and more correctly. Moreover, we introduce three measurements for the more precise evaluation of a protein localization predictor. As the results of various datasets which are made from the experiments of Huh et al. (2003), the proposed PLPD method represents a different approach that might play a complimentary role to the existing methods, such as Nearest Neighbor method and discriminate covariant method. Finally, after finding a good boundary for each localization using the 5184 classified proteins as training data, we predicted 138 proteins whose subcellular localizations could not be clearly observed by the experiments of Huh et al. (2003)

Grassmann Learning for Recognition and Classification

Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition

An inter-domain supervision framework for collaborative clustering of data with mixed types.

We propose an Inter-Domain Supervision (IDS) clustering framework to discover clusters within diverse data formats, mixed-type attributes and different sources of data. This approach can be used for combined clustering of diverse representations of the data, in particular where data comes from different sources, some of which may be unreliable or uncertain, or for exploiting optional external concept set labels to guide the clustering of the main data set in its original domain. We additionally take into account possible incompatibilities in the data via an automated inter-domain compatibility analysis. Our results in clustering real data sets with mixed numerical, categorical, visual and text attributes show that the proposed IDS clustering framework gives improved clustering results compared to conventional methods, over a wide range of parameters. Thus the automatically extracted knowledge, in the form of seeds or constraints, obtained from clustering one domain, can provide additional knowledge to guide the clustering in another domain. Additional empirical evaluations further show that our approach, especially when using selective mutual guidance between domains, outperforms common baselines such as clustering either domain on its own or clustering all domains converted to a single target domain. Our approach also outperforms other specialized multiple clustering methods, such as the fully independent ensemble clustering and the tightly coupled multiview clustering, after they were adapted to the task of clustering mixed data. Finally, we present a real life application of our IDS approach to the cluster-based automated image annotation problem and present evaluation results on a benchmark data set, consisting of images described with their visual content along with noisy text descriptions, generated by users on the social media sharing website, Flickr

Action recognition in visual sensor networks: a data fusion perspective

Visual Sensor Networks have emerged as a new technology to bring computer vision algorithms to the real world. However, they impose restrictions in the computational resources and bandwidth available to solve target problems. This thesis is concerned with the definition of new efficient algorithms to perform Human Action Recognition with Visual Sensor Networks. Human Action Recognition systems apply sequence modelling methods to integrate the temporal sensor measurements available. Among sequence modelling methods, the Hidden Conditional Random Field has shown a great performance in sequence classification tasks, outperforming many other methods. However, a parameter estimation procedure has not been proposed with feature and model selection properties. This thesis fills this lack proposing a new objective function to optimize during training. The L2 regularizer employed in the standard objective function is replaced by an overlapping group-L1 regularizer that produces feature and model selection effects in the optima. A gradient-based search strategy is proposed to find the optimal parameters of the objective function. Experimental evidence shows that Hidden Conditional Random Fields with their parameters estimated employing the proposed method have a higher predictive accuracy than those estimated with the standard method, with an smaller inference cost. This thesis also deals with the problem of human action recognition from multiple cameras, with the focus on reducing the amount of network bandwidth required. A multiple view dimensionality reduction framework is developed to obtain similar low dimensional representation for the motion descriptors extracted from multiple cameras. An alternative is proposed predicting the action class locally at each camera with the motion descriptors extracted from each view and integrating the different action decisions to make a global decision on the action performed. The reported experiments show that the proposed framework has a predictive performance similar to 3D state of the art methods, but with a lower computational complexity and lower bandwidth requirements. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Las Redes de Sensores Visuales son una nueva tecnología que permite el despliegue de algoritmos de visión por computador en el mundo real. Sin embargo, estas imponen restricciones en los recursos de computo y de ancho de banda disponibles para la resolución del problema en cuestión. Esta tesis tiene por objeto la definición de nuevos algoritmos con los que realizar reconocimiento de actividades humanas en redes de sensores visuales, teniendo en cuenta las restricciones planteadas. Los sistemas de reconocimiento de acciones aplican métodos de modelado de secuencias para la integración de las medidas temporales proporcionadas por los sensores. Entre los modelos para el modelado de secuencias, el Hidden Conditional Random Field a mostrado un gran rendimiento en la clasificación de secuencias, superando a otros métodos existentes. Sin embargo, no se ha definido un procedimiento para la integración de sus parámetros que incluya selección de atributos y selección de modelo. Esta tesis tiene por objeto cubrir esta carencia proponiendo una nueva función objetivo para optimizar durante la estimación de los parámetros obtimos. El regularizador L2 empleado en la función objetivo estandar se va a remplazar for un regularizador grupo-L1 solapado que va a producir los efectos de selección de modelo y atributos deseados en el óptimo. Se va a proponer una estrategia de búsqueda con la que obtener el valor óptimo de estos parámetros. Los experimentos realizados muestran que los modelos estimados utilizando la función objetivo prouesta tienen un mayor poder de predicción, reduciendo al mismo tiempo el coste computacional de la inferencia. Esta tesis también trata el problema del reconocimiento de acciones humanas emepleando multiples cámaras, centrándonos en reducir la cantidad de ancho de banda requerido par el proceso. Para ello se propone un nueva estructura en la que definir algoritmos de reducción de dimensionalidad para datos definidos en multiples vistas. Mediante su aplicación se obtienen representaciones de baja dimensionalidad similares para los descriptores de movimiento calculados en cada una de las cámaras.También se propone un método alternativo basado en la predicción de la acción realizada con los descriptores obtenidos en cada una de las cámaras, para luego combinar las diferentes predicciones en una global. La experimentación realizada muestra que estos métodos tienen una eficacia similar a la alcanzada por los métodos existentes basados en reconstrucción 3D, pero con una menor complejidad computacional y un menor uso de la red