{"created":"2023-05-15T14:21:24.219914+00:00","id":3055,"links":{},"metadata":{"_buckets":{"deposit":"d681caae-ec11-443b-9f90-9c0a52fd521f"},"_deposit":{"created_by":3,"id":"3055","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3055"},"status":"published"},"_oai":{"id":"oai:bunkyo.repo.nii.ac.jp:00003055","sets":["1:26:233"]},"author_link":["3965"],"item_5_biblio_info_13":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2003-07-01"},"bibliographicPageEnd":"73","bibliographicPageStart":"41","bibliographicVolumeNumber":"29","bibliographic_titles":[{"bibliographic_title":"情報研究"},{"bibliographic_title":"Information and Communication Sｔudies"}]}]},"item_5_date_43":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2009-05-21"}]},"item_5_description_12":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"It is well known that the K-L orthonormal system gives the optimality of the expansion of each sampled pattern. From a point of view of a degree DAS of average similarity suggested by S.Suzuki,next six matters (?)?(vi) known so far of the K-L system in any separable Hilbert space can be proved or solved in this paper: (?)The K-L system maximizes a sum of DAS as a unitary invariant. (ii)The K-L system consists of an eigenvectors of a positive correlation operator H on a general separable Hilbert space. (iii)An integral equation can be derived which the K-L system must satisfy. (iv)The expansion coefficients obtained by expanding a pattern by using the K-L system are uncorrelated each other. (v)The eigenvalue problem of the K-L system can be solved. (vi)The K-L system minimizes an entropy which can measure an efficiency of the orthogonal expansions of patterns.\n\\n本論文では,各サンプルパターンを直交展開するときに最大の表現能率性を与えるK-L正規直交系につき,S.Suzukiの平均類似度に関連させ,これまで知られているすべての諸性質が証明されている.K-L正規直交系を様々な分野,特にパターン情報処理分野などに注意深く応用するのに便利となっている.具体的には,次の6つの事柄(?)?(§)が可分な一般抽象ヒルベルト空間で証明あるいは解決される:(?)K-L正規直交系は平均類似度(測度的ユニタリ不変量)の総和を最大にすること.(ii)可分なヒルベルト空間では,K-L正規直交系は正値自己共役作用素としての相関作用素Hの固有ベクトル系であること.(iii)K-L正規直交系が満たす積分方程式を関数空間で導くこと.(iv)各直交展開係数間は無相関であること.(v)固有値問題を解いて,K-L正規直交系を具体的に表現すること.(vi)測度的ユニタリ不変量を各成分に持ち,直交展開における表現能率性の目安を与えるエントロピーを簡単な条件の下で,最小にする正規直交系はK-L正規直交系であること.","subitem_description_type":"Abstract"}]},"item_5_description_38":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_5_source_id_19":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"03893367"}]},"item_5_text_39":{"attribute_name":"本文言語","attribute_value_mlt":[{"subitem_text_value":"日本語"}]},"item_5_text_42":{"attribute_name":"ID","attribute_value_mlt":[{"subitem_text_value":"BKS0000022"}]},"item_5_text_7":{"attribute_name":"Author","attribute_value_mlt":[{"subitem_text_value":"Suzuki, Shoichi"}]},"item_5_text_8":{"attribute_name":"所属機関","attribute_value_mlt":[{"subitem_text_value":"文教大学情報学部"}]},"item_5_text_9":{"attribute_name":"Institution","attribute_value_mlt":[{"subitem_text_value":"Bunkyo University Faculty of Information and Communications"}]},"item_5_version_type_35":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"鈴木, 昇一"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-03-24"}],"displaytype":"detail","filename":"BKS0000022.pdf","filesize":[{"value":"428.2 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"BKS0000022.pdf","url":"https://bunkyo.repo.nii.ac.jp/record/3055/files/BKS0000022.pdf"},"version_id":"03a73dd4-ca88-42f1-8dda-29a06d3a46bd"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"パターン認識"},{"subitem_subject":"モデル構成作用素"},{"subitem_subject":"ゲーデル論理"},{"subitem_subject":"論理的含意"},{"subitem_subject":"非単調推論"},{"subitem_subject":"論理ベクトル"},{"subitem_subject":"誤差逆伝播ニューラルネット"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"可分な一般抽象ヒルベルト空間でK-L直交系の理論","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"可分な一般抽象ヒルベルト空間でK-L直交系の理論"},{"subitem_title":"A Theory of the Karhunen-Loeve Orthogonal System in Any Separable Hilbert Space"}]},"item_type_id":"5","owner":"3","path":["233"],"pubdate":{"attribute_name":"公開日","attribute_value":"2009-05-21"},"publish_date":"2009-05-21","publish_status":"0","recid":"3055","relation_version_is_last":true,"title":["可分な一般抽象ヒルベルト空間でK-L直交系の理論"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-05-16T16:52:50.578131+00:00"}