Math Search for the Masses: Multimodal Search Interfaces and Appearance-Based Retrieval

We summarize math search engines and search interfaces produced by the Document and Pattern Recognition Lab in recent years, and in particular the min math search interface and the Tangent search engine. Source code for both systems are publicly available. "The Masses" refers to our emphasis on creating systems for mathematical non-experts, who may be looking to define unfamiliar notation, or browse documents based on the visual appearance of formulae rather than their mathematical semantics.Comment: Paper for Invited Talk at 2015 Conference on Intelligent Computer Mathematics (July, Washington DC

An Efficient Hidden Markov Model for Offline Handwritten Numeral Recognition

Traditionally, the performance of ocr algorithms and systems is based on the recognition of isolated characters. When a system classifies an individual character, its output is typically a character label or a reject marker that corresponds to an unrecognized character. By comparing output labels with the correct labels, the number of correct recognition, substitution errors misrecognized characters, and rejects unrecognized characters are determined. Nowadays, although recognition of printed isolated characters is performed with high accuracy, recognition of handwritten characters still remains an open problem in the research arena. The ability to identify machine printed characters in an automated or a semi automated manner has obvious applications in numerous fields. Since creating an algorithm with a one hundred percent correct recognition rate is quite probably impossible in our world of noise and different font styles, it is important to design character recognition algorithms with these failures in mind so that when mistakes are inevitably made, they will at least be understandable and predictable to the person working with theComment: 6pages, 5 figure

Deep Adaptive Learning for Writer Identification based on Single Handwritten Word Images

There are two types of information in each handwritten word image: explicit information which can be easily read or derived directly, such as lexical content or word length, and implicit attributes such as the author's identity. Whether features learned by a neural network for one task can be used for another task remains an open question. In this paper, we present a deep adaptive learning method for writer identification based on single-word images using multi-task learning. An auxiliary task is added to the training process to enforce the emergence of reusable features. Our proposed method transfers the benefits of the learned features of a convolutional neural network from an auxiliary task such as explicit content recognition to the main task of writer identification in a single procedure. Specifically, we propose a new adaptive convolutional layer to exploit the learned deep features. A multi-task neural network with one or several adaptive convolutional layers is trained end-to-end, to exploit robust generic features for a specific main task, i.e., writer identification. Three auxiliary tasks, corresponding to three explicit attributes of handwritten word images (lexical content, word length and character attributes), are evaluated. Experimental results on two benchmark datasets show that the proposed deep adaptive learning method can improve the performance of writer identification based on single-word images, compared to non-adaptive and simple linear-adaptive approaches.Comment: Under view of Pattern Recognitio

Tensorizing Neural Networks

Deep neural networks currently demonstrate state-of-the-art performance in several domains. At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required by commonly used fully-connected layers, making it hard to use the models on low-end devices and stopping the further increase of the model size. In this paper we convert the dense weight matrices of the fully-connected layers to the Tensor Train format such that the number of parameters is reduced by a huge factor and at the same time the expressive power of the layer is preserved. In particular, for the Very Deep VGG networks we report the compression factor of the dense weight matrix of a fully-connected layer up to 200000 times leading to the compression factor of the whole network up to 7 times

Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment

Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other