Expediting Exploration by Attribute-to-Feature Mapping for Cold-Start Recommendations
Proceedings of the Eleventh ACM Conference on Recommender Systems, 2017
The item cold-start problem is inherent to collaborative filtering (CF) recommenders where items ... more The item cold-start problem is inherent to collaborative filtering (CF) recommenders where items and users are represented by vectors in a latent space. It emerges since CF recommenders rely solely on historical user interactions to characterize their item inventory. As a result, an effective serving of new and trendy items to users may be delayed until enough user feedback is received, thus, reducing both users' and content suppliers' satisfaction. To mitigate this problem, many commercial recommenders apply random exploration and devote a small portion of their traffic to explore new items and gather interactions from random users. Alternatively, content or context information is combined into the CF recommender, resulting in a hybrid system. Another hybrid approach is to learn a mapping between the item attribute space and the CF latent feature space, and use it to characterize the new items providing initial estimates for their latent vectors. In this paper, we adopt the attribute-to-feature mapping approach to expedite random exploration of new items and present LearnAROMA - an advanced algorithm for learning the mapping, previously proposed in the context of classification. In particular, LearnAROMA learns a Gaussian distribution over the mapping matrix. Numerical evaluation demonstrates that this learning technique achieves more accurate initial estimates than logistic regression methods. We then consider a random exploration setting, in which new items are further explored as user interactions arrive. To leverage the initial latent vector estimates with the incoming interactions, we propose DynamicBPR - an algorithm for updating the new item latent vectors without retraining the CF model. Numerical evaluation reveals that DynamicBPR achieves similar accuracy as a CF model trained on all the ratings, using 71% less exploring users than conventional random exploration.
Motivation: One of the major features of genomic DNA sequences, distinguishing them from texts in... more Motivation: One of the major features of genomic DNA sequences, distinguishing them from texts in most spoken or artificial languages, is their high repetitiveness. Variation in the repetitiveness of genomic texts reflects the presence and density of different biologically important messages. Thus, deviation from an expected number of repeats in both directions indicates a possible presence of a biological signal. Linguistic complexity corresponds to repetitiveness of a genomic text, and potential regulatory sites may be discovered through construction of typical patterns of complexity distribution. Results: We developed software for fast calculation of linguistic sequence complexity of DNA sequences. Our program utilizes suffix trees to compute the number of subwords present in genomic sequences, thereby allowing calculation of linguistic complexity in time linear in genome size. The measure of linguistic complexity was applied to the complete genome of Haemophilus influenzae. Maps...
Dynamic Creative Optimization in Verizon Media Native Advertising
2020 IEEE International Conference on Big Data (Big Data)
Verizon media (VZM) native advertising serves billions of impressions daily, reaching a yearly ru... more Verizon media (VZM) native advertising serves billions of impressions daily, reaching a yearly run-rate of many hundred of million USD. Driving VZM native models for predicting advertise (ad) event probabilities, such as clicks and conversions, is OFFSET - a feature enhanced collaborative-filtering ( CF) based e vent prediction algorithm. The predicted probabilities are then used in VZM native auctions to determine which ads to present for each serving event. Dynamic creative optimization (DCO) is a new VZM native product that was launched recently and is gaining increasingly more attention from advertisers. The DCO product allows advertisers to provide several assets per each native ad attribute, creating a plurality of combinations for each DCO ad. Since different combinations may appeal to different crowds, it may be beneficial to present certain combinations more frequently than others to maximize revenue. Inspired by the success of our Carousel asset optimization product, we present a post-auction successive elimination based approach for ranking DCO combinations according to their measured click through rates (CTR). This reinforcement learning multi-arm bandit like solution was evaluated during an online beta test phase done with selected advertisers, showing 21.8% CTR and 21.5% revenue lifts over a control bucket serving all combinations uniformly at random. The good performance of our DCO product attracts advertisers and it already shows a yearly run-rate of several million USD in revenue.
2021 IEEE International Conference on Big Data (Big Data)
Real-world content recommendation marketplaces exhibit certain behaviors and are imposed by const... more Real-world content recommendation marketplaces exhibit certain behaviors and are imposed by constraints that are not always apparent in common static offline data sets. One example that is common in ad marketplaces is swift ad turnover. New ads are introduced and old ads disappear at high rates every day. Another example is ad discontinuity, where existing ads may appear and disappear from the market for non negligible amounts of time due to a variety of reasons (e.g., depletion of budget, pausing by the advertiser, flagging by the system, and more). These behaviors sometimes cause the model's loss surface to change dramatically over short periods of time. To address these behaviors, fresh models are highly important, and to achieve this (and for several other reasons) incremental training on small chunks of past events is often employed. These behaviors and algorithmic optimizations occasionally cause model parameters to grow uncontrollably large, or diverge. In this work present a systematic method to prevent model parameters from diverging by imposing a carefully chosen set of constraints on the model's latent vectors. We then devise a method inspired by primal-dual optimization algorithms to fulfill these constraints in a manner which both aligns well with incremental model training, and does not require any major modifications to the underlying model training algorithm. We analyze, demonstrate, and motivate our method on OFFSET , a collaborative filtering algorithm which drives Verizon Media (VZM) native advertising, which is one of VZM's largest and faster growing businesses, reaching a run-rate of many hundreds of millions USD per year. Finally, we conduct an online experiment which shows a substantial reduction in the number of diverging instances, and a significant improvement to both user experience and revenue.
Dynamic Length Factorization Machines for CTR Prediction
2021 IEEE International Conference on Big Data (Big Data), 2021
Ad click-though rate prediction (pCTR) is one of the core tasks of online advertising. Driving th... more Ad click-though rate prediction (pCTR) is one of the core tasks of online advertising. Driving the pCTR models of Yahoo Gemini native advertising is OFFSET - a feature enhanced collaborative-filtering based event prediction algorithm. Due to data sparsity issues OFFSET models both users and items by mapping their features into a latent space, where the resulting user vector is a non-linear function of the user feature vectors (e.g., age, gender, hour, etc.) which allows pairwise dependencies. This pairwise dependencies concept is also used by other algorithms such as the Field-aware Factorization Machines (FFM). However, both in OFFSET and in FFM, the different pairwise interactions are modeled by latent vectors of constant and equal lengths. When prediction models are used online for serving real traffic, where the total serving model size is often limited, a non uniform representation of the pairwise interactions should be considered in order to maximize the accuracy of the model while consuming the same or even less space. In this work we present a Dynamic Length Factorization Machines (DLFM) algorithm that dynamically optimizes the length of the vectors for each feature interaction during training, while not exceeding a maximal overall latent vector size. After showing good online performance of 1.46% revenue lift and a 2.15% CTR lift, serving Gemini native traffic, the DLFM was pushed into production. Since integrated into production, the DLFM has not only improved the accuracy of the model by optimizing the length of each latent space, but has also reduced the total size of the model by 25%. Although the algorithm was applied to OFFSET, we show that DLFM can be applied to any FFM-like algorithm to optimize its pairwise feature vector lengths. We also present an Educated Model Initialization - a novel mechanism for initializing a new model based on an existing model that has some mutual user features. Using this mechanism, we managed to reduce the training time of our models by more than 90% when compared to an equivalent model that is trained from "scratch".
Ad Close Mitigation for Improved User Experience in Native Advertisements
Proceedings of the 13th International Conference on Web Search and Data Mining, 2020
Verizon Media native advertising (also known as Yahoo Gemini native) serves billions of ad impres... more Verizon Media native advertising (also known as Yahoo Gemini native) serves billions of ad impressions daily, reaching several hundreds of millions USD in revenue yearly. Although we strive to provide the best experience for our users, there will always be some users that dislike our ads in certain cases. To address these situations Gemini native platform provides an ad close mechanism that enables users to close ads that they dislike and also to provide a reasoning for their action. Surprisingly, users do care about their ad experience and their engagement with the ad close mechanism is quite significant. While the ad close rate (ACR) is lower than the click through rate (CTR), they are of the same order of magnitude, especially on Yahoo mail properties. Since ad close events indicate bad user experience caused mostly by poor ad quality, we would like to exploit the ad close signals to improve user experience and reduce the number of ad close events while maintaining a predefined total revenue loss. In this work we present our ad close mitigation (ACM) solution that penalizes ads with high closing likelihood, in our auctions. In particular, we use the ad close signal and other available features to predict the probability of an ad close event, and calculate the expected loss due to such event for using the true expected revenue in the auction. We show that this approach fundamentally changes the generalized second price (GSP) auction and provides incentive for advertisers to improve their ads' quality. Our solution was tested in both offline and large scale online settings, serving real Gemini native traffic. Results of the online experiment show that we are able to reduce the number of ad close events by more than 20%, while decreasing the revenue in less than 0.4%. In addition, we present a large scale analysis of the ad close signal that supports various design decisions and sheds light on ways the ad close mechanism affects different crowds.
Feature Enhancement via User Similarities Networks for Improved Click Prediction in Yahoo Gemini Native
Proceedings of the 28th ACM International Conference on Information and Knowledge Management, 2019
Yahoo's native advertising marketplace (also known as Gemini native) serves billions of ad im... more Yahoo's native advertising marketplace (also known as Gemini native) serves billions of ad impressions daily, reaching many hundreds of millions USD in yearly revenue. Driving Gemini native models that are used to predict ad click probability (pCTR) is OFFSET - a feature enhanced collaborative-filtering (CF) based event prediction algorithm. While some of the user features used by OFFSET have high coverage, other features, especially those based on click patterns, suffer from extremely low coverage. In this work, we present a framework that simplifies complex interactions between users and other entities in a bipartite graph. The one mode projection of this bipartite graph onto users represents a user similarity network, allowing us to quantify similarities between users. This network is combined with existing user features to create an enhanced feature set. In particular, we describe the implementation and performance of our framework using user Internet browsing data (e.g., visited pages URLs) to enhance the user category feature. Using our framework we effectively increase the feature coverage by roughly 15%. Moreover, online results evaluated on 1% of Gemini native traffic show that using the enhanced feature increases revenue by almost 1% when compared to the baseline operating with the original feature, which is a substantial increase at scale.
Vector quantization is a classical problem that appears in many fields. Unfortunately, the quanti... more Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally nonconvex, and therefore affords many local minima. The main problem is finding an initial approximation which is close to a "good" local minimum. Once such an approximation is found, the Lloyd-Max method may be used to reach a local minimum near it. In recent years, much improvement has been made with respect to reducing the computational costs of quantization algorithms, whereas the task of finding better initial approximations received somewhat less attention. We present a novel multiscale iterative scheme for the quantization problem. The scheme is based on redistributing the representation levels among aggregates of decision regions at changing scales. The rule governing the redistribution relies on the so-called point density function and on the number of representation levels in each aggregate. Our method focuses on achieving better local minima than those achieved by other contemporary methods such as LBG. When quantizing signals with sparse and patchy histograms, as may occur in color images, for example, the improvement in distortion relative to LBG may be arbitrarily large.
A multigrid framework for the one-dimensional (scalar) fixed-rate quantization problem is present... more A multigrid framework for the one-dimensional (scalar) fixed-rate quantization problem is presented. The framework is based on the Lloyd-Max iterative process, which is a central building block in many quantization algorithms. This process iteratively improves a given initial solution and generally converges to a local minimum of the quantization distortion. Contrary to the classical Lloyd-Max process, the convergence of the multigrid algorithm is practically independent of the number of representation levels sought. Using this approach, a local minimum is reached at the cost of just a few Lloyd-Max iterations. The complexity of the proposed method is () operations for the continuous case and 3 + () for the discrete case, where is the number of representation levels sought and is the size of the discrete probability density function. In addition to its independent attributes, this work is a precursor to the more important vector quantization problem, for which a multiscale framework is also being developed.
Vector quantization is a classical problem that appears in many fields. Unfortunately, the quanti... more Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally non-convex, and therefore affords many local minima. The main problem is finding an initial approximation that is close to a "good" local minimum. Once such an approximation is found, the Lloyd-Max method may be used to reach a local minimum near it. In recent years, much improvement has been made with respect to reducing the computational costs of quantization algorithms, whereas the task of finding better initial approximations received somewhat less attention. We present a novel greedy algorithm for the vector quantization problem. The algorithm begins by allocating a large number of representation levels throughout the input domain and thereafter iteratively aggregates pairs of representation levels and replaces them by a single one. The pair of representation levels that is aggregated is the one yielding the minimal increase in distortion among all such pairs. Our method achieves better solutions than other contemporary methods such as LBG. In addition, its computational complexity is low, typically quantizing data in time that is equivalent to just a few Lloyd-Max iterations. When quantizing signals with sparse and patchy histograms, e.g. cartoons, the improvement in distortion relative to LBG may be arbitrarily large.
A multigrid framework for the 1-D (scalar) quantization problem is presented. The framework is ba... more A multigrid framework for the 1-D (scalar) quantization problem is presented. The framework is based on the Lloyd-Max iterative process, which is a central building block in many quantization algorithms. This process iteratively improves a given initial solution and generally converges to a local minimum of the quantization distortion. Contrary to the classical Lloyd-Max process, the convergence of the multigrid algorithm is practically independent of the number of representation levels sought. Using this approach, a local minimum with machine accuracy is reached in a matter of several iterations and the need for traditional stopping criteria for the process is alleviated. In addition, the proposed method often achieves better local minima than other quantization methods such as classical Lloyd-Max and LBG. The complexity of the proposed method is O(n) operations for the continuous case and 3N + O(n) for the discrete case, where n is the number of representation levels sought and N is the size of the discrete probability density function.
In a dynamically scalable hosting infrastructure for e-business computing, servers need to be qui... more In a dynamically scalable hosting infrastructure for e-business computing, servers need to be quickly allocated in order to satisfy a sudden demand for increased computing power for a hosted site. Khnum is the applications and data management component of Océano-a dynamically scalable hosting infrastructure for e-business computing utilities. It is responsible for server reconfiguration and for application deployment. Application deployment involves all services, configuration directives, executables and data of the application. A hosted site may include several applications. Khnum enables Océano to rapidly deploy multiple applications to tens of servers simultaneously in just a few minutes. It uses AFS as the infrastructure for secure storage, automatically mapping files and directories onto the new servers' local filesystems and multicasting hot AFS cache content to the new servers. To avoid overloading the AFS servers during the deployment process, the hot cache content is multicasted to all the new servers, avoiding the boot storming (or "rushing") effect. This, in turn, improves the scalability of the deployment process; experimental results attest to Khnum's scalability in simultaneously deploying applications to tens of servers.
Expediting Exploration by Attribute-to-Feature Mapping for Cold-Start Recommendations
Proceedings of the Eleventh ACM Conference on Recommender Systems, 2017
The item cold-start problem is inherent to collaborative filtering (CF) recommenders where items ... more The item cold-start problem is inherent to collaborative filtering (CF) recommenders where items and users are represented by vectors in a latent space. It emerges since CF recommenders rely solely on historical user interactions to characterize their item inventory. As a result, an effective serving of new and trendy items to users may be delayed until enough user feedback is received, thus, reducing both users' and content suppliers' satisfaction. To mitigate this problem, many commercial recommenders apply random exploration and devote a small portion of their traffic to explore new items and gather interactions from random users. Alternatively, content or context information is combined into the CF recommender, resulting in a hybrid system. Another hybrid approach is to learn a mapping between the item attribute space and the CF latent feature space, and use it to characterize the new items providing initial estimates for their latent vectors. In this paper, we adopt the attribute-to-feature mapping approach to expedite random exploration of new items and present LearnAROMA - an advanced algorithm for learning the mapping, previously proposed in the context of classification. In particular, LearnAROMA learns a Gaussian distribution over the mapping matrix. Numerical evaluation demonstrates that this learning technique achieves more accurate initial estimates than logistic regression methods. We then consider a random exploration setting, in which new items are further explored as user interactions arrive. To leverage the initial latent vector estimates with the incoming interactions, we propose DynamicBPR - an algorithm for updating the new item latent vectors without retraining the CF model. Numerical evaluation reveals that DynamicBPR achieves similar accuracy as a CF model trained on all the ratings, using 71% less exploring users than conventional random exploration.
Motivation: One of the major features of genomic DNA sequences, distinguishing them from texts in... more Motivation: One of the major features of genomic DNA sequences, distinguishing them from texts in most spoken or artificial languages, is their high repetitiveness. Variation in the repetitiveness of genomic texts reflects the presence and density of different biologically important messages. Thus, deviation from an expected number of repeats in both directions indicates a possible presence of a biological signal. Linguistic complexity corresponds to repetitiveness of a genomic text, and potential regulatory sites may be discovered through construction of typical patterns of complexity distribution. Results: We developed software for fast calculation of linguistic sequence complexity of DNA sequences. Our program utilizes suffix trees to compute the number of subwords present in genomic sequences, thereby allowing calculation of linguistic complexity in time linear in genome size. The measure of linguistic complexity was applied to the complete genome of Haemophilus influenzae. Maps...
Dynamic Creative Optimization in Verizon Media Native Advertising
2020 IEEE International Conference on Big Data (Big Data)
Verizon media (VZM) native advertising serves billions of impressions daily, reaching a yearly ru... more Verizon media (VZM) native advertising serves billions of impressions daily, reaching a yearly run-rate of many hundred of million USD. Driving VZM native models for predicting advertise (ad) event probabilities, such as clicks and conversions, is OFFSET - a feature enhanced collaborative-filtering ( CF) based e vent prediction algorithm. The predicted probabilities are then used in VZM native auctions to determine which ads to present for each serving event. Dynamic creative optimization (DCO) is a new VZM native product that was launched recently and is gaining increasingly more attention from advertisers. The DCO product allows advertisers to provide several assets per each native ad attribute, creating a plurality of combinations for each DCO ad. Since different combinations may appeal to different crowds, it may be beneficial to present certain combinations more frequently than others to maximize revenue. Inspired by the success of our Carousel asset optimization product, we present a post-auction successive elimination based approach for ranking DCO combinations according to their measured click through rates (CTR). This reinforcement learning multi-arm bandit like solution was evaluated during an online beta test phase done with selected advertisers, showing 21.8% CTR and 21.5% revenue lifts over a control bucket serving all combinations uniformly at random. The good performance of our DCO product attracts advertisers and it already shows a yearly run-rate of several million USD in revenue.
2021 IEEE International Conference on Big Data (Big Data)
Real-world content recommendation marketplaces exhibit certain behaviors and are imposed by const... more Real-world content recommendation marketplaces exhibit certain behaviors and are imposed by constraints that are not always apparent in common static offline data sets. One example that is common in ad marketplaces is swift ad turnover. New ads are introduced and old ads disappear at high rates every day. Another example is ad discontinuity, where existing ads may appear and disappear from the market for non negligible amounts of time due to a variety of reasons (e.g., depletion of budget, pausing by the advertiser, flagging by the system, and more). These behaviors sometimes cause the model's loss surface to change dramatically over short periods of time. To address these behaviors, fresh models are highly important, and to achieve this (and for several other reasons) incremental training on small chunks of past events is often employed. These behaviors and algorithmic optimizations occasionally cause model parameters to grow uncontrollably large, or diverge. In this work present a systematic method to prevent model parameters from diverging by imposing a carefully chosen set of constraints on the model's latent vectors. We then devise a method inspired by primal-dual optimization algorithms to fulfill these constraints in a manner which both aligns well with incremental model training, and does not require any major modifications to the underlying model training algorithm. We analyze, demonstrate, and motivate our method on OFFSET , a collaborative filtering algorithm which drives Verizon Media (VZM) native advertising, which is one of VZM's largest and faster growing businesses, reaching a run-rate of many hundreds of millions USD per year. Finally, we conduct an online experiment which shows a substantial reduction in the number of diverging instances, and a significant improvement to both user experience and revenue.
Dynamic Length Factorization Machines for CTR Prediction
2021 IEEE International Conference on Big Data (Big Data), 2021
Ad click-though rate prediction (pCTR) is one of the core tasks of online advertising. Driving th... more Ad click-though rate prediction (pCTR) is one of the core tasks of online advertising. Driving the pCTR models of Yahoo Gemini native advertising is OFFSET - a feature enhanced collaborative-filtering based event prediction algorithm. Due to data sparsity issues OFFSET models both users and items by mapping their features into a latent space, where the resulting user vector is a non-linear function of the user feature vectors (e.g., age, gender, hour, etc.) which allows pairwise dependencies. This pairwise dependencies concept is also used by other algorithms such as the Field-aware Factorization Machines (FFM). However, both in OFFSET and in FFM, the different pairwise interactions are modeled by latent vectors of constant and equal lengths. When prediction models are used online for serving real traffic, where the total serving model size is often limited, a non uniform representation of the pairwise interactions should be considered in order to maximize the accuracy of the model while consuming the same or even less space. In this work we present a Dynamic Length Factorization Machines (DLFM) algorithm that dynamically optimizes the length of the vectors for each feature interaction during training, while not exceeding a maximal overall latent vector size. After showing good online performance of 1.46% revenue lift and a 2.15% CTR lift, serving Gemini native traffic, the DLFM was pushed into production. Since integrated into production, the DLFM has not only improved the accuracy of the model by optimizing the length of each latent space, but has also reduced the total size of the model by 25%. Although the algorithm was applied to OFFSET, we show that DLFM can be applied to any FFM-like algorithm to optimize its pairwise feature vector lengths. We also present an Educated Model Initialization - a novel mechanism for initializing a new model based on an existing model that has some mutual user features. Using this mechanism, we managed to reduce the training time of our models by more than 90% when compared to an equivalent model that is trained from "scratch".
Ad Close Mitigation for Improved User Experience in Native Advertisements
Proceedings of the 13th International Conference on Web Search and Data Mining, 2020
Verizon Media native advertising (also known as Yahoo Gemini native) serves billions of ad impres... more Verizon Media native advertising (also known as Yahoo Gemini native) serves billions of ad impressions daily, reaching several hundreds of millions USD in revenue yearly. Although we strive to provide the best experience for our users, there will always be some users that dislike our ads in certain cases. To address these situations Gemini native platform provides an ad close mechanism that enables users to close ads that they dislike and also to provide a reasoning for their action. Surprisingly, users do care about their ad experience and their engagement with the ad close mechanism is quite significant. While the ad close rate (ACR) is lower than the click through rate (CTR), they are of the same order of magnitude, especially on Yahoo mail properties. Since ad close events indicate bad user experience caused mostly by poor ad quality, we would like to exploit the ad close signals to improve user experience and reduce the number of ad close events while maintaining a predefined total revenue loss. In this work we present our ad close mitigation (ACM) solution that penalizes ads with high closing likelihood, in our auctions. In particular, we use the ad close signal and other available features to predict the probability of an ad close event, and calculate the expected loss due to such event for using the true expected revenue in the auction. We show that this approach fundamentally changes the generalized second price (GSP) auction and provides incentive for advertisers to improve their ads' quality. Our solution was tested in both offline and large scale online settings, serving real Gemini native traffic. Results of the online experiment show that we are able to reduce the number of ad close events by more than 20%, while decreasing the revenue in less than 0.4%. In addition, we present a large scale analysis of the ad close signal that supports various design decisions and sheds light on ways the ad close mechanism affects different crowds.
Feature Enhancement via User Similarities Networks for Improved Click Prediction in Yahoo Gemini Native
Proceedings of the 28th ACM International Conference on Information and Knowledge Management, 2019
Yahoo's native advertising marketplace (also known as Gemini native) serves billions of ad im... more Yahoo's native advertising marketplace (also known as Gemini native) serves billions of ad impressions daily, reaching many hundreds of millions USD in yearly revenue. Driving Gemini native models that are used to predict ad click probability (pCTR) is OFFSET - a feature enhanced collaborative-filtering (CF) based event prediction algorithm. While some of the user features used by OFFSET have high coverage, other features, especially those based on click patterns, suffer from extremely low coverage. In this work, we present a framework that simplifies complex interactions between users and other entities in a bipartite graph. The one mode projection of this bipartite graph onto users represents a user similarity network, allowing us to quantify similarities between users. This network is combined with existing user features to create an enhanced feature set. In particular, we describe the implementation and performance of our framework using user Internet browsing data (e.g., visited pages URLs) to enhance the user category feature. Using our framework we effectively increase the feature coverage by roughly 15%. Moreover, online results evaluated on 1% of Gemini native traffic show that using the enhanced feature increases revenue by almost 1% when compared to the baseline operating with the original feature, which is a substantial increase at scale.
Vector quantization is a classical problem that appears in many fields. Unfortunately, the quanti... more Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally nonconvex, and therefore affords many local minima. The main problem is finding an initial approximation which is close to a "good" local minimum. Once such an approximation is found, the Lloyd-Max method may be used to reach a local minimum near it. In recent years, much improvement has been made with respect to reducing the computational costs of quantization algorithms, whereas the task of finding better initial approximations received somewhat less attention. We present a novel multiscale iterative scheme for the quantization problem. The scheme is based on redistributing the representation levels among aggregates of decision regions at changing scales. The rule governing the redistribution relies on the so-called point density function and on the number of representation levels in each aggregate. Our method focuses on achieving better local minima than those achieved by other contemporary methods such as LBG. When quantizing signals with sparse and patchy histograms, as may occur in color images, for example, the improvement in distortion relative to LBG may be arbitrarily large.
A multigrid framework for the one-dimensional (scalar) fixed-rate quantization problem is present... more A multigrid framework for the one-dimensional (scalar) fixed-rate quantization problem is presented. The framework is based on the Lloyd-Max iterative process, which is a central building block in many quantization algorithms. This process iteratively improves a given initial solution and generally converges to a local minimum of the quantization distortion. Contrary to the classical Lloyd-Max process, the convergence of the multigrid algorithm is practically independent of the number of representation levels sought. Using this approach, a local minimum is reached at the cost of just a few Lloyd-Max iterations. The complexity of the proposed method is () operations for the continuous case and 3 + () for the discrete case, where is the number of representation levels sought and is the size of the discrete probability density function. In addition to its independent attributes, this work is a precursor to the more important vector quantization problem, for which a multiscale framework is also being developed.
Vector quantization is a classical problem that appears in many fields. Unfortunately, the quanti... more Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally non-convex, and therefore affords many local minima. The main problem is finding an initial approximation that is close to a "good" local minimum. Once such an approximation is found, the Lloyd-Max method may be used to reach a local minimum near it. In recent years, much improvement has been made with respect to reducing the computational costs of quantization algorithms, whereas the task of finding better initial approximations received somewhat less attention. We present a novel greedy algorithm for the vector quantization problem. The algorithm begins by allocating a large number of representation levels throughout the input domain and thereafter iteratively aggregates pairs of representation levels and replaces them by a single one. The pair of representation levels that is aggregated is the one yielding the minimal increase in distortion among all such pairs. Our method achieves better solutions than other contemporary methods such as LBG. In addition, its computational complexity is low, typically quantizing data in time that is equivalent to just a few Lloyd-Max iterations. When quantizing signals with sparse and patchy histograms, e.g. cartoons, the improvement in distortion relative to LBG may be arbitrarily large.
A multigrid framework for the 1-D (scalar) quantization problem is presented. The framework is ba... more A multigrid framework for the 1-D (scalar) quantization problem is presented. The framework is based on the Lloyd-Max iterative process, which is a central building block in many quantization algorithms. This process iteratively improves a given initial solution and generally converges to a local minimum of the quantization distortion. Contrary to the classical Lloyd-Max process, the convergence of the multigrid algorithm is practically independent of the number of representation levels sought. Using this approach, a local minimum with machine accuracy is reached in a matter of several iterations and the need for traditional stopping criteria for the process is alleviated. In addition, the proposed method often achieves better local minima than other quantization methods such as classical Lloyd-Max and LBG. The complexity of the proposed method is O(n) operations for the continuous case and 3N + O(n) for the discrete case, where n is the number of representation levels sought and N is the size of the discrete probability density function.
In a dynamically scalable hosting infrastructure for e-business computing, servers need to be qui... more In a dynamically scalable hosting infrastructure for e-business computing, servers need to be quickly allocated in order to satisfy a sudden demand for increased computing power for a hosted site. Khnum is the applications and data management component of Océano-a dynamically scalable hosting infrastructure for e-business computing utilities. It is responsible for server reconfiguration and for application deployment. Application deployment involves all services, configuration directives, executables and data of the application. A hosted site may include several applications. Khnum enables Océano to rapidly deploy multiple applications to tens of servers simultaneously in just a few minutes. It uses AFS as the infrastructure for secure storage, automatically mapping files and directories onto the new servers' local filesystems and multicasting hot AFS cache content to the new servers. To avoid overloading the AFS servers during the deployment process, the hot cache content is multicasted to all the new servers, avoiding the boot storming (or "rushing") effect. This, in turn, improves the scalability of the deployment process; experimental results attest to Khnum's scalability in simultaneously deploying applications to tens of servers.
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Papers by Yair Koren