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p34: Note that in the primal representation the number of terms in the summation is equal to the dimensionality of the feature space, while in the dual there are l terms (the sample size). According to the size of the feature space being considered, one or other of the representations can be more convenient.

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But SVC’s popularity is degraded by its pricy computation and poor labeling performance. Different from existing modifications that only resolve one of two bottlenecks, this paper presents an improved SVC, iSVC, to address two bottlenecks simultaneously. iSVC’s contributions are as follows: (1) It includes a reduction strategy that can help to develop clustering model on a qualified subset. The reduction strategy is based on the Schrödinger equation to find the crucial data towards model formulation. (2) The original objective is modified; it cooperates with the reduction strategy to produce the model with subtle loss of quality. (3) iSVC employs a new label approach to label data according to the geometric properties of feature space. The new approach labels data in a simple but effective way without suffering from the randomness originated in the old algorithm. (4) The geometric property is proofed to guarantee the new labeling approach’s validation. Theoretical analysis and empirical evidence suggest that iSVC overcomes two bottlenecks well. And when compared with some common clustering methods, it does a good job in performance and efficiency, which opens a broad way of applications for SVC.", "publicationTitle": "Engineering Applications of Artificial Intelligence", "publisher": "", "place": "", "date": "June 2010", "volume": "23", "issue": "4", "section": "", "partNumber": "", "partTitle": "", "pages": "552-559", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Engineering Applications of Artificial Intelligence", "DOI": "10.1016/j.engappai.2010.01.029", "citationKey": "", "url": "http://www.sciencedirect.com/science/article/pii/S0952197610000709", "accessDate": "2012-11-08T12:50:25Z", "PMID": "", "PMCID": "", "ISSN": "0952-1976", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "ScienceDirect", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "Geometric properties of feature space", "type": 1 }, { "tag": "New labeling approach", "type": 1 }, { "tag": "Reduction strategy", "type": 1 }, { "tag": "Schrödinger equation", "type": 1 }, { "tag": "Support vector clustering", "type": 1 } ], "collections": [ "K5GZW23S" ], "relations": {}, "dateAdded": "2012-11-08T12:50:25Z", "dateModified": "2012-11-08T12:50:25Z" } }, { "key": "664W3TIF", "version": 2, "library": { "type": "group", "id": 113003, "name": "Clustering methods", "links": { "alternate": { "href": "https://www.zotero.org/groups/clustering_methods", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/113003/items/664W3TIF", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/clustering_methods/items/664W3TIF", "type": "text/html" } }, "meta": { "createdByUser": { "id": 48412, "username": "olegus", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/olegus", "type": "text/html" } } }, "creatorSummary": "Ben-Hur et al.", "parsedDate": "2000", "numChildren": 2 }, "data": { "key": "664W3TIF", "version": 2, "itemType": "conferencePaper", "title": "A support vector clustering method", "creators": [ { "creatorType": "author", "firstName": "A.", "lastName": "Ben-Hur" }, { "creatorType": "author", "firstName": "D.", "lastName": "Horn" }, { "creatorType": "author", "firstName": "H.T.", "lastName": "Siegelmann" }, { "creatorType": "author", "firstName": "V.", "lastName": "Vapnik" } ], "abstractNote": "We present a novel kernel method for data clustering using a description of the data by support vectors. The kernel reflects a projection of the data points from data space to a high dimensional feature space. Cluster boundaries are defined as spheres in feature space, which represent complex geometric shapes in data space. We utilize this geometric representation of the data to construct a simple clustering algorithm", "proceedingsTitle": "15th International Conference on Pattern Recognition, 2000. Proceedings", "conferenceName": "15th International Conference on Pattern Recognition, 2000. Proceedings", "publisher": "", "place": "", "date": "2000", "eventPlace": "", "volume": "2", "issue": "", "numberOfVolumes": "", "pages": "724 -727 vol.2", "series": "", "seriesNumber": "", "DOI": "10.1109/ICPR.2000.906177", "ISBN": "", "citationKey": "", "url": "", "accessDate": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "IEEE Xplore", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "cluster boundaries", "type": 1 }, { "tag": "complex geometric shapes", "type": 1 }, { "tag": "data clustering", "type": 1 }, { "tag": "data point projection", "type": 1 }, { "tag": "data space", "type": 1 }, { "tag": "geometric representation", "type": 1 }, { "tag": "high-dimensional feature space", "type": 1 }, { "tag": "learning automata", "type": 1 }, { "tag": "pattern clustering", "type": 1 }, { "tag": "support vector clustering method", "type": 1 }, { "tag": "support vector machines", "type": 1 } ], "collections": [ "2PEHHD56" ], "relations": {}, "dateAdded": "2012-11-07T16:46:57Z", "dateModified": "2012-11-08T12:46:04Z" } }, { "key": "E8F8ID2G", "version": 1, "library": { "type": "group", "id": 113003, "name": "Clustering methods", "links": { "alternate": { "href": "https://www.zotero.org/groups/clustering_methods", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/113003/items/E8F8ID2G", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/clustering_methods/items/E8F8ID2G", "type": "text/html" } }, "meta": { "createdByUser": { "id": 48412, "username": "olegus", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/olegus", "type": "text/html" } } }, "creatorSummary": "Sul and Tovchigrechko", "parsedDate": "2011-05", "numChildren": 2 }, "data": { "key": "E8F8ID2G", "version": 1, "itemType": "conferencePaper", "title": "Parallelizing BLAST and SOM Algorithms with MapReduce-MPI Library", "creators": [ { "creatorType": "author", "firstName": "Seung-Jin", "lastName": "Sul" }, { "creatorType": "author", "firstName": "A.", "lastName": "Tovchigrechko" } ], "abstractNote": "Most bioinformatics algorithms are developed in a serial form due to a fast pace of changes in the subject domain and the fact that many bioinformatics tasks can be parallelized as collections of serial jobs communicating at the file system level (High-Throughput Computing, HTC). Recently, a MapReduce-MPI library was made available by Sandia Lab to ease porting of a large class of serial applications to the High Performance Computing (HPC) architectures dominating large federated resources such as NSF Tera Grid. Using this library, we have created two open-source bioinformatics applications. The first one addresses a problem of adapting existing complex and highly optimized serial bioinformatics algorithm to HPC architecture in a minimally invasive way. We built a parallel BLAST implementation that calls the high-level methods of unmodified NCBI C++ Toolkit. We demonstrated scaling for up to 1000 cores on TACC Ranger cluster when processing the sufficiently large input datasets. Using unmodified NCBI Toolkit ensures that the results are compatible across the multitude of settings in the original serial algorithm, and that future versions of the upstream code can be easily integrated. The second application is a Self-Organizing Map (SOM) machine-learning algorithm, popular in bioinformatics applications such as metagenomic binning. The nature of the SOM requires a global synchronization step with a frequency that necessitates the use of an HPC environment. Our implementation of the \"batch SOM\" uses a mix of MapReduce-MPI and direct MPI calls and scales to 1000 cores as well. This allows easy processing of datasets with a size that is out of range of the serial SOM implementations. Both implementations are available in the open source at http://andreyto.github.com/mgtaxa/.", "proceedingsTitle": "2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)", "conferenceName": "2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)", "publisher": "", "place": "", "date": "May 2011", "eventPlace": "", "volume": "", "issue": "", "numberOfVolumes": "", "pages": "481 -489", "series": "", "seriesNumber": "", "DOI": "10.1109/IPDPS.2011.180", "ISBN": "", "citationKey": "", "url": "", "accessDate": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "IEEE Xplore", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "BLAST", "type": 1 }, { "tag": "C++ language", "type": 1 }, { "tag": "HPC", "type": 1 }, { "tag": "HTC", "type": 1 }, { "tag": "MapReduce-MPI Library", "type": 1 }, { "tag": "NCBI C++ Toolkit", "type": 1 }, { "tag": "NSF Tera Grid", "type": 1 }, { "tag": "SOM algorithm", "type": 1 }, { "tag": "bioinformatics", "type": 1 }, { "tag": "bioinformatics algorithm", "type": 1 }, { "tag": "file system level", "type": 1 }, { "tag": "global synchronization", "type": 1 }, { "tag": "high performance computing", "type": 1 }, { "tag": "high-throughput computing", "type": 1 }, { "tag": "learning (artificial intelligence)", "type": 1 }, { "tag": "machine-learning algorithm", "type": 1 }, { "tag": "message passing", "type": 1 }, { "tag": "open-source bioinformatics application", "type": 1 }, { "tag": "parallel processing", "type": 1 }, { "tag": "public domain software", "type": 1 }, { "tag": "self-organising feature maps", "type": 1 }, { "tag": "self-organizing map", "type": 1 } ], "collections": [ "HKWWHIR7" ], "relations": {}, "dateAdded": "2012-11-07T16:46:57Z", "dateModified": "2012-11-08T12:46:04Z" } }, { "key": "66TDPBJA", "version": 2, "library": { "type": "group", "id": 113003, "name": "Clustering methods", "links": { "alternate": { "href": "https://www.zotero.org/groups/clustering_methods", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/113003/items/66TDPBJA", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/clustering_methods/items/66TDPBJA", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/113003/items/VKRSRHAR", "type": "application/json" } }, "meta": { "createdByUser": { "id": 48412, "username": "olegus", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/olegus", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "66TDPBJA", "version": 2, "parentItem": "VKRSRHAR", "itemType": "attachment", "linkMode": "imported_url", "title": "IEEE Xplore Full Text PDF", "accessDate": "2012-11-08T12:45:20Z", "url": "http://ieeexplore.ieee.org/ielx5/7762/21329/00989572.pdf?tp=&arnumber=989572&isnumber=21329", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Domeniconi and Gunopulos - 2001 - Incremental support vector machine construction.pdf", "md5": "c4e2364d0e66c66b02c13273f4fc9f5a", "mtime": 1352378725000, "tags": [], "relations": {}, "dateAdded": "2012-11-08T12:45:20Z", "dateModified": "2012-11-08T12:45:25Z" } }, { "key": "TR3TDRZ5", "version": 2, "library": { "type": "group", "id": 113003, "name": "Clustering methods", "links": { "alternate": { "href": "https://www.zotero.org/groups/clustering_methods", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/113003/items/TR3TDRZ5", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/clustering_methods/items/TR3TDRZ5", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/113003/items/VKRSRHAR", "type": "application/json" } }, "meta": { "createdByUser": { "id": 48412, "username": "olegus", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/olegus", "type": "text/html" } } } }, "data": { "key": "TR3TDRZ5", "version": 2, "parentItem": "VKRSRHAR", "itemType": "attachment", "linkMode": "imported_url", "title": "IEEE Xplore Abstract Record", "accessDate": "2012-11-08T12:45:23Z", "url": "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=989572", "note": "", "contentType": "text/html", "charset": "utf-8", "filename": "abs_all.html", "md5": "d4108c10ab0c22d7416ab91d0b4d00f8", "mtime": 1352378724000, "tags": [], "relations": {}, "dateAdded": "2012-11-08T12:45:23Z", "dateModified": "2012-11-08T12:45:23Z" } }, { "key": "VKRSRHAR", "version": 1, "library": { "type": "group", "id": 113003, "name": "Clustering methods", "links": { "alternate": { "href": "https://www.zotero.org/groups/clustering_methods", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/113003/items/VKRSRHAR", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/clustering_methods/items/VKRSRHAR", "type": "text/html" } }, "meta": { "createdByUser": { "id": 48412, "username": "olegus", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/olegus", "type": "text/html" } } }, "creatorSummary": "Domeniconi and Gunopulos", "parsedDate": "2001", "numChildren": 2 }, "data": { "key": "VKRSRHAR", "version": 1, "itemType": "conferencePaper", "title": "Incremental support vector machine construction", "creators": [ { "creatorType": "author", "firstName": "C.", "lastName": "Domeniconi" }, { "creatorType": "author", "firstName": "D.", "lastName": "Gunopulos" } ], "abstractNote": "SVMs (support vector machines) suffer from the problem of large memory requirement and CPU time when trained in batch mode on large data sets. We overcome these limitations, and at the same time make SVMs suitable for learning with data streams, by constructing incremental learning algorithms. We first introduce and compare different incremental learning techniques, and show that they are capable of producing performance results similar to the batch algorithm, and in some cases superior condensation properties. We then consider the problem of training SVMs using stream data. Our objective is to maintain an updated representation of recent batches of data. We apply incremental schemes to the problem and show that their accuracy is comparable to the batch algorithm", "proceedingsTitle": "ICDM 2001, Proceedings IEEE International Conference on Data Mining, 2001", "conferenceName": "ICDM 2001, Proceedings IEEE International Conference on Data Mining, 2001", "publisher": "", "place": "", "date": "2001", "eventPlace": "", "volume": "", "issue": "", "numberOfVolumes": "", "pages": "589 -592", "series": "", "seriesNumber": "", "DOI": "10.1109/ICDM.2001.989572", "ISBN": "", "citationKey": "", "url": "", "accessDate": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "IEEE Xplore", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "CPU time", "type": 1 }, { "tag": "SVMs", "type": 1 }, { "tag": "batch algorithm", "type": 1 }, { "tag": "batch mode", "type": 1 }, { "tag": "batch processing (computers)", "type": 1 }, { "tag": "condensation properties", "type": 1 }, { "tag": "data 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