Levenshtein distance | EPFL Graph Search

In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after the Soviet mathematician Vladimir Levenshtein, who considered this distance in 1965. Levenshtein distance may also be referred to as edit distance, although that term may also denote a larger family of distance metrics known collectively as edit distance. It is closely related to pairwise string alignments. Definition The Levenshtein distance between two strings a, b (of length |a| and |b| respectively) is given by \operatorname{lev}(a, b) where : \operatorname{lev}(a, b) = \begin{cases} |a| & \text{ if } |b| = 0, \ |b| & \text{ if } |a| = 0, \ \operato

Improved Phone Posterior Estimation Through k-NN and MLP-Based Similarity

Benjamin Picart

In this work, we investigate the possible use of k-nearest neighbour (kNN) classifiers to perform frame-based acoustic phonetic classification, hence replacing Gaussian Mixture Models (GMM) or MultiLayer Perceptrons (MLP) used in standard Hidden Markov Models (HMMs). The driving motivation behind this idea is the fact that kNN is known to be an "optimal" classifier if a very large amount of training data is available (replacing the training of functional parameters by plain memorization of the training examples) and the correct distance metric is found. Nowadays, amount of training data is no longer an issue. In the current work, we thus specifically focused on the "correct" distance metric, mainly using an MLP to compute the probability that two input feature vectors are part of the same phonetic class or not. This MLP output can thus be used as a distance metric for kNN. While providing a "universal" distance metric, this work also enabled us to consider the speech recognition problem under a different angle, simply formulated in terms of hypothesis tests: "Given two feature vectors, what is the probability that these belong to the same (phonetic) class or not?". Actually, one of the main goals of the present thesis finally boils down to one interesting question: “Is it easier to classify feature vectors into C phonetic classes or to tell whether or not two feature vectors belong to the same class?”. This work was done with standard acoustic features as inputs (PLP) and with posterior features (resulting of another pre-training MLP). Both feature sets indeed exhibit different properties and metric spaces. For example, while the use of posteriors as input is motivated by the fact that they are speaker and environment independent (so they capture much of the phonetic information contained in the signal), they are also no longer Gaussian distributed. When showing mathematically that using the MLP as a similarity measure makes sense, we discovered that this measure was equivalent to a very simple metric that can be analytically computed without needing the use of an MLP. This new type of measure is in fact the scalar product between two posterior feature vectors. Experiments have been conducted on hypothesis tests and on kNN classification. Results of the hypothesis tests show that posterior feature vectors achieve better performance than acoustic feature vectors. Moreover, the use of the scalar product leads to better performance than the use of all other metrics (including the MLP-based distance metric), whatever the input features.

Idiap2009

Efficient image duplicate detection based on image analysis

Yannick Maret

This thesis is about the detection of duplicated images. More precisely, the developed system is able to discriminate possibly modified copies of original images from other unrelated images. The proposed method is referred to as content-based since it relies only on content analysis techniques rather than using image tagging as done in watermarking. The proposed content-based duplicate detection system classifies a test image by associating it with a label that corresponds to one of the original known images. The classification is performed in four steps. In the first step, the test image is described by using global statistics about its content. In the second step, the most likely original images are efficiently selected using a spatial indexing technique called R-Tree. The third step consists in using binary detectors to estimate the probability that the test image is a duplicate of the original images selected in the second step. Indeed, each original image known to the system is associated with an adapted binary detector, based on a support vector classifier, that estimates the probability that a test image is one of its duplicate. Finally, the fourth and last step consists in choosing the most probable original by picking that with the highest estimated probability. Comparative experiments have shown that the proposed content-based image duplicate detector greatly outperforms detectors using the same image description but based on a simpler distance functions rather than using a classification algorithm. Additional experiments are carried out so as to compare the proposed system with existing state of the art methods. Accordingly, it also outperforms the perceptual distance function method, which uses similar statistics to describe the image. While the proposed method is slightly outperformed by the key points method, it is five to ten times less complex in terms of computational requirements. Finally, note that the nature of this thesis is essentially exploratory since it is one of the first attempts to apply machine learning techniques to the relatively recent field of content-based image duplicate detection.

EPFL2007

Multivariate Boosting with Look-Up Tables for Face Processing

Cosmin Atanasoaei

This thesis proposes a novel unified boosting framework. We apply this framework to the several face processing tasks, face detection, facial feature localisation, and pose classification, and use the same boosting algorithm and the same pool of features (local binary features). This is in contrast with the standard approaches that make use of a variety of features and models, for example AdaBoost, cascades of boosted classifiers and Active Appearance Models. The unified boosting framework covers multivariate classification and regression problems and it is achieved by interpreting boosting as optimization in the functional space of the weak learners. Thus a wide range of smooth loss functions can be optimized with the same algorithm. There are two general optimization strategies we propose that extend recent works on TaylorBoost and Variational AdaBoost. The first proposition is an empirical expectation formulation that minimizes the average loss and the second is a variational formulation that includes an additional penalty for large variations between predictions. These two boosting formulations are used to train real-time models using local binary features. This is achieved using look-up-tables as weak learners and multi-block Local Binary Patterns as features. The resulting boosting algorithms are simple, efficient and easily scalable with the available resources. Furthermore, we introduce a novel coarse-to-fine feature selection method to handle high resolution models and a bootstrapping algorithm to sample representative training data from very large pools of data. The proposed approach is evaluated for several face processing tasks. These tasks include frontal face detection (binary classification), facial feature localization (multivariate regression) and pose estimation (multivariate classification). Several studies are performed to assess different optimization algorithms, bootstrapping parametrizations and feature sharing methods (for the multivariate case). The results show good performance for all of these tasks. In addition to this, two other contributions are presented. First, we propose a context-based model for removing the false alarms generated by a given generic face detector. Second, we propose a new face detector that predicts the Jaccard distance between the current location and the ground truth. This allows us to formulate the face detection problem as a regression task.

EPFL2012