Typical graph-theoretic approaches for semi-supervised classification infer labels of unlabeled instances with the help of graph Laplacians. Founded on the spectral decomposition of the graph Laplacian, this paper learns a kernel matrix via minimizing the leave-one-out classification error on the labeled instances.  To this end, an efficient algorithm is presented based on linear programming, resulting in a transductive spectral kernel. The idea of our algorithm stems from regularization methodology and also has a nice interpretation in terms of spectral clustering. A simple classifier can be readily built upon the learned kernel, which suffices to give prediction for any data point aside from those in the available dataset. Besides this usage, the spectral kernel can be effectively used in tandem with conventional kernel machines such as SVMs. We demonstrate the efficacy of the proposed algorithm through experiments carried out on challenging classification tasks.

City-wide urban infrastructures are increasingly reliant on network technology to improve and ex-pand their services. As a side effect of this digitali-zation, large amounts of data can be sensed and analyzed to uncover patterns of human behavior. In this paper, we focus on the digital footprints from one type of emerging urban infrastructure: shared bicycling systems. We provide a spatiotemporal analysis of 13 weeks of bicycle station usage from Barcelona's shared bicycling system, called Bicing. We apply clustering techniques to identify shared behaviors across stations and show how these behaviors relate to location, neighborhood, and time of day. We then compare experimental results from four predictive models of near-term station usage. Finally, we analyze the impact of factors such as time of day and station activity in the prediction capabilities of the algorithms.

We present a streaming model for large-scale classification (in the context of ℓ2 -SVM) by leveraging connections between learning and computational geometry. The streaming model imposes the constraint that only a single pass over the data is allowed. The ℓ2 -SVM is known to have an equivalent formulation in terms of the minimum enclosing ball (MEB) problem, and an efficient algorithm based on the idea of core sets exists (CVM) [Tsang et al., 2005]. CVM learns a (1 + ε)-approximate MEB for a set of points and yields an approximate solution to corresponding SVM instance. However CVM works in batch mode requiring multiple passes over the data. This paper presents a single-pass SVM which is based on the minimum enclosing ball of streaming data. We show that the MEB updates for the streaming case can be easily adapted to learn the SVM weight vector in a way similar to using online stochastic gradient updates. Our algorithm performs polylogarithmic computation at each example, and requires very small and constant storage. Experimental results show that, even in such restrictive settings, we can learn efficiently in just one pass and get accuracies comparable to other state-of-the-art SVM solvers (batch and online). We also give an analysis of the algorithm, and discuss some open issues and possible extensions.

Automatic recognition of human activities is among the key capabilities of many intelligent systems with vision/perception. Most existing approaches to this problem require sophisticated feature extraction before classification can be performed. This paper presents a novel approach for human action recognition using only simple low-level visual features: motion captured from direct frame differencing. A codebook of key poses is first created from the training data through unsupervised clustering. Videos of actions are then coded as sequences of super-frames, defined as the key poses augmented with discriminative attributes. A weighted-sequence distance is proposed for comparing two super-frame sequences, which is further wrapped as a kernel embedded in a SVM classifier for the final classification. Compared with conventional methods, our approach provides a flexible non-parametric sequential structure with a corresponding distance measure for human action representation and classification without requiring complex feature extraction. The effectiveness of our approach is demonstrated with the widely-used KTH human activity dataset, for which the proposed method outperforms the existing state-of-the-art.

Many real-life datasets, such as those produced by gene expression studies, exhibit complex substructures at various levels of granularity and thus do not have unique well-defined numbers of clusters. In such cases, it is important to be able to trace the evolution of the individual clusters as the number of dimensions of the clustering is varied. While the dendrograms produced by bottom-up clustering methods such as hierarchical clustering are very useful for this purpose, the approach is known to produce unreliable clusters due to its instability w.r.t. resampling. Moreover, hierarchical clustering does not apply to overlapping (bi)clusters, such as those obtained in gene expression studies. On the other hand, the instability w.r.t. the initialization of top-down methods, such as k-means, prevents the comparison between clusters obtained at different dimensionalities. In this paper, we present a method for constructing generalized dendrograms for overlapping biclusters, which depict the evolution of the biclusters as their number is varied. An essential ingredient is a stable biclustering method based on positive tensor factorization of a number of nonnegative matrix factorization runs. We apply our approach to a large colon cancer dataset, which shows several distinct subclasses whose dimensional evolution must be carefully analyzed to enable a more meaningful biological interpretation and sub-classification.

The problem of market clearing in an economy is that of finding prices such that supply meets demand. In this work, we propose a kernel method to compute nonlinear clearing prices for instances where linear prices do not suffice. We first present a procedure that, given a sample of values and costs for a set of bundles, implicitly computes nonlinear clearing prices by solving an appropriately formulated quadratic program. We then use this as a subroutine in an elicitation procedure that queries demand and supply incrementally over rounds, only as much as needed to reach clearing prices. An empirical evaluation demonstrates that, with a proper choice of kernel function, the method is able to find sparse nonlinear clearing prices with much less than full revelation of values and costs. When the kernel function is not suitable to clear the market, the method can be tuned to achieve approximate clearing.

However, most dimension reduction approaches are driven by objective functions that may not or only We will provide more detail on our solution to this problem partially suit the end users requirements. In this later but it is important to note the problem of focus in this work, we show how to incorporate general-purpose paper is different to spectral clustering (dimension reduction) domain expertise encoded as a graph into dimension in two keys ways. Firstly, we are projecting the entire space reduction in way that lends itself to an elegant D occupies not just the points in G or D. Secondly, we do generalized eigenvalue problem. We call not formulate the problem as some form of min-cut and then our approach Graph-Driven Constrained Dimension solve a relaxed version of the problem. Reduction via Linear Projection (GCDR-LP) Our work aims to find a reduced dimension space based on and show that it has several desirable properties.

Nonnegative Matrix Factorization (NMF) has been widely used in machine learning and data mining. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a local learning regularized nonnegative matrix factorization (LLNMF) for clustering. It imposes an additional constraint on NMF that the cluster label of each point can be predicted by the points in its neighborhood. This constraint encodes both the discriminative information and the geometric structure, and is good at clustering data on manifold. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. Experiments on many benchmark data sets demonstrate that the proposed method outperforms NMF as well as many state of the art clustering methods.

This paper addresses the problem of activity and event discovery in multi dimensional time series data by proposing a novel method for locating multi dimensional motifs in time series. While recent work has been done in finding single dimensional and multi dimensional motifs in time series, we address motifs in general case, where the elements of multi dimensional motifs have temporal, length, and frequency variations. The proposed method is validated by synthetic data, and empirical evaluation has been done on several wearable systems that are used by real subjects.

Domain adaptation solves a learning problem in a target domain by utilizing the training data in a different but related source domain. Intuitively, discovering a good feature representation across domains is crucial. In this paper, we propose to find such a representation through a new learning method, transfer component analysis ( TCA ), for domain adaptation. TCA tries to learn some transfer components across domains in a Reproducing Kernel Hilbert Space (RKHS) using Maximum Mean Discrepancy (MMD). In the subspace spanned by these transfer components , data distributions in different domains are close to each other. As a result, with the new representations in this subspace, we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain. The main contribution of our work is that we propose a novel feature representation in which to perform domain adaptation via a new parametric kernel using feature extraction methods, which can dramatically minimize the distance between domain distributions by projecting data onto the learned transfer components . Furthermore, our approach can handle large datsets and naturally lead to out-of-sample generalization. The effectiveness and efficiency of our approach in are verified by experiments on two real-world applications: cross-domain indoor WiFi localization and cross-domain text classification.