Question: What are the two standard hashing algorithms experimented with by authors?
Evidence: To assess the performance of binary paragraph vectors, we carried out experiments on three datasets: 20 Newsgroups, a cleansed version (also called v2) of Reuters Corpus Volume 1 (RCV1) and English Wikipedia. As paragraph vectors can be trained with relatively large vocabularies, we did not perform any stemming of the source text. However, we removed stop words as well as words shorter than two characters and longer than 15 characters. Results reported by BIBREF15 indicate that performance of PV-DBOW can be improved by including n-grams in the model. We therefore evaluated two variants of Binary PV-DBOW: one predicting words in documents and one predicting words and bigrams. Since 20 Newsgroups is a relatively small dataset, we used all words and bigrams from its documents. This amounts to a vocabulary with slightly over one million elements. For the RCV1 dataset we used words and bigrams with at least 10 occurrences in the text, which gives a vocabulary with approximately 800 thousands elements. In case of English Wikipedia we used words and bigrams with at least 100 occurrences, which gives a vocabulary with approximately 1.5 million elements.
The 20 Newsgroups dataset comes with reference train/test sets. In case of RCV1 we used half of the documents for training and the other half for evaluation. In case of English Wikipedia we held out for testing randomly selected 10% of the documents. We perform document retrieval by selecting queries from the test set and ordering other test documents according to the similarity of the inferred codes. We use Hamming distance for binary codes and cosine similarity for real-valued representations. Results are averaged over queries. We assess the performance of our models with precision-recall curves and two popular information retrieval metrics, namely mean average precision (MAP) and the normalized discounted cumulative gain at the 10th result (NDCG@10) BIBREF16 . The results depend, of course, on the chosen document relevancy measure. Relevancy measure for the 20 Newsgroups dataset is straightforward: a retrieved document is relevant to the query if they both belong to the same newsgroup. In RCV1 each document belongs to a hierarchy of topics, making the definition of relevancy less obvious. In this case we adopted the relevancy measure used by BIBREF3 . That is, the relevancy is calculated as the fraction of overlapping labels in a retrieved document and the query document. Overall, our selection of test datasets and relevancy measures for 20 Newsgroups and RCV1 follows BIBREF3 , enabling comparison with semantic hashing codes. To assess the relevancy of articles in English Wikipedia we can employ categories assigned to them. However, unlike in RCV1, Wikipedia categories can have multiple parent categories and cyclic dependencies. Therefore, for this dataset we adopted a simplified relevancy measure: two articles are relevant if they share at least one category. We also removed from the test set categories with less than 20 documents as well as documents that were left with no categories. Overall, the relevancy is measured over more than INLINEFORM0 categories, making English Wikipedia harder than the other two benchmarks.
We use AdaGrad BIBREF17 for training and inference in all experiments reported in this work. During training we employ dropout BIBREF18 in the embedding layer. To facilitate models with large vocabularies, we approximate the gradients with respect to the softmax logits using the method described by BIBREF9 . Binary PV-DM networks use the same number of dimensions for document codes and word embeddings.
Performance of 128- and 32-bit binary paragraph vector codes is reported in Table TABREF8 and in Figure FIGREF7 . For comparison we also report performance of real-valued paragraph vectors. Note that the binary codes perform very well, despite their far lower capacity: on 20 Newsgroups and RCV1 the 128-bit Binary PV-DBOW trained with bigrams approaches the performance of the real-valued paragraph vectors, while on English Wikipedia its performance is slightly lower. Furthermore, Binary PV-DBOW with bigrams outperforms semantic hashing codes: comparison of precision-recall curves from Figures FIGREF7 a and FIGREF7 b with BIBREF3 shows that 128-bit codes learned with this model outperform 128-bit semantic hashing codes on 20 Newsgroups and RCV1. Moreover, the 32-bit codes from this model outperform 128-bit semantic hashing codes on the RCV1 dataset, and on the 20 Newsgroups dataset give similar precision up to approximately 3% recall and better precision for higher recall levels. Note that the difference in this case lies not only in retrieval precision: the short 32-bit Binary PV-DBOW codes are more efficient for indexing than long 128-bit semantic hashing codes.
We also compared binary paragraph vectors against codes constructed by first inferring short, real-valued paragraph vectors and then using a separate hashing algorithm for binarization. When the dimensionality of the paragraph vectors is equal to the size of binary codes, the number of network parameters in this approach is similar to that of Binary PV models. We experimented with two standard hashing algorithms, namely random hyperplane projection BIBREF19 and iterative quantization BIBREF20 . Paragraph vectors in these experiments were inferred using PV-DBOW with bigrams. Results reported in Table TABREF9 show no benefit from using a separate algorithm for binarization. On the 20 Newsgroups and RCV1 datasets Binary PV-DBOW yielded higher MAP than the two baseline approaches. On English Wikipedia iterative quantization achieved MAP equal to Binary PV-DBOW, while random hyperplane projection yielded lower MAP. Some gain in precision of top hits can be observed for iterative quantization, as indicated by NDCG@10. However, precision of top hits can also be improved by querying with Real-Binary PV-DBOW model (Section SECREF15 ). It is also worth noting that end-to-end inference in Binary PV models is more convenient than inferring real-valued vectors and then using another algorithm for hashing.
 BIBREF15 argue that PV-DBOW outperforms PV-DM on a sentiment classification task, and demonstrate that the performance of PV-DBOW can be improved by including bigrams in the vocabulary. We observed similar results with Binary PV models. That is, including bigrams in the vocabulary usually improved retrieval precision. Also, codes learned with Binary PV-DBOW provided higher retrieval precision than Binary PV-DM codes. Furthermore, to choose the context size for the Binary PV-DM models, we evaluated several networks on validation sets taken out of the training data. The best results were obtained with a minimal one-word, one-sided context window. This is the distributed memory architecture most similar to the Binary PV-DBOW model.
We experimented with two standard hashing algorithms, namely random hyperplane projection (Charikar, 2002) and iterative quantization (Gong and Lazebnik, 2011).
Answer: They are namely random hyperplane projection and iterative quantization.