Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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Laplacian Eigenmaps for dimensionality reduction and data representation

Presents a review of 200 references in content-based image retrieval. The paper starts with discussing the working conditions of content-based retrieval: patterns of use, types of pictures, the role of semantics, and the sensory gap. Subsequent sections discuss computational steps for image retrieval systems. Step one of the review is image processing for retrieval sorted by color, texture, and local geometry. Features for retrieval are discussed next, sorted by: accumulative and global features, salient points, object and shape features, signs, and structural combinations thereof. Similarity of pictures and objects in pictures is reviewed for each of the feature types, in close connection to the types and means of feedback the user of the systems is capable of giving by interaction. We briefly discuss aspects of system engineering: databases, system architecture, and evaluation. In the concluding section, we present our view on: the driving force of the field, the heritage from computer vision, the influence on computer vision, the role of similarity and of interaction, the need for databases, the problem of evaluation, and the role of the semantic gap.

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Content-based image retrieval at the end of the early years

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space

We have witnessed great interest and a wealth of promise in content-based image retrieval as an emerging technology. While the last decade laid foundation to such promise, it also paved the way for a large number of new techniques and systems, got many new people involved, and triggered stronger association of weakly related fields. In this article, we survey almost 300 key theoretical and empirical contributions in the current decade related to image retrieval and automatic image annotation, and in the process discuss the spawning of related subfields. We also discuss significant challenges involved in the adaptation of existing image retrieval techniques to build systems that can be useful in the real world. In retrospect of what has been achieved so far, we also conjecture what the future may hold for image retrieval research.

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Image retrieval: Ideas, influences, and trends of the new age

A polynomial characterization of hypergraphs using the Ihara zeta function

Clustering shock trees

In this paper a new method of speech segmentation is suggested. It is based on power fluctuations of the wavelet spectrum for a speech signal. In most approaches to speech recognition, the speech signals are segmented using constant-time segmentation. Constant segmentation needs to use windows to decrease the boundary distortions. A more natural approach is to segment the speech signals on the basis of time-frequency analysis. Boundaries are assigned in places where some energy of a frequency band rapidly changes. Most methods of non-constant segmentation need training for particular data or are realized as a part of modelling. In this paper we apply the discrete wavelet transform (DWT) to analyse speech signals, the resulting power spectrum and its derivatives. This information allows us to locate the boundaries of phonemes. It is the first stage of speech recognition process. Additionally we present an evaluation by comparing our method with hand segmentation. The segmentation method proves effective for finding most phoneme boundaries. Results are more useful for speech recognition than constant segmentation.

Wavelet method of speech segmentation

In this paper we explore how to use spectral methods for embedding and clustering unweighted graphs. We use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode adjacency matrices and intermode edge-distance. We embed these vectors in a pattern-space using two contrasting approaches. The first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of pattern vectors. We illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects.

Spectral clustering of graphs

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts that guarantees positive semidefinite optimal assignment kernels. These base kernels give rise to hierarchies from which the optimal assignment kernels are computed in linear time by histogram intersection. We apply these results by developing the Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high classification accuracy on widely-used benchmark data sets improving over the original Weisfeiler-Lehman kernel.

Richard C. Wilson

Papers

A polynomial characterization of hypergraphs using the Ihara zeta function

Clustering shock trees

Wavelet method of speech segmentation

Spectral clustering of graphs

On Valid Optimal Assignment Kernels and Applications to Graph Classification