یادگیری متریک نیمه نظارتی در فضای لایه‌ای با بهره‌گیری دقیق‌تر از دانش پیشین
محورهای موضوعی : مهندسی برق و کامپیوترزهره کریمی 1 , سعید شیری قیداری 2 , روح‌اله رمضانی 3
1 - دانشگاه صنعتی امیرکبیر
2 - دانشگاه صنعتی امیرکبیر
3 - دانشگاه دامغان
کلید واژه: یادگیری متریک نیمه‌نظارتیفضای لایه‌ایلاپلاسینفرض همواربودن,
چکیده مقاله :
یادگیری متریک نیمه‌نظارتی مبتنی بر منیفلد در سال‌های اخیر بسیار مورد توجه واقع شده است. این رویکردها، منظم‌سازی مبتنی بر فرض همواربودن داده‌ها روی منیفلد را اعمال می‌کنند، هرچند در معرض دو چالش قرار دارند: 1) شباهت بین دسته‌های مختلف، تقاطع منیفلدها با یکدیگر را ایجاد می‌کند که با فرض همواربودن برچسب در این نواحی در تناقض است. 2) دسته‌بند NN1 که برای تعیین برچسب داده‌ها در مسایل یادگیری متریک اعمال می‌شود با وجود تعداد کم داده‌های برچسب‌دار دقت مناسب را ندارد. در این مقاله روشی برای یادگیری متریک نیمه‌نظارتی با فرض قرارگیری داده‌ها در فضای لایه‌ای ارائه شده که در آن از دانش پیشین موجود که همان فرض همواربودن داده‌ها روی هر منیفلد است به صورت دقیق‌تر بهره‌برداری شده است. در مرحله یادگیری متریک، فرض همواربودن در نواحی تقاطع اعمال نشده و در مرحله دسته‌بندی، داده‌های برچسب‌دار در نقاط داخلی منیفلدها بر اساس فرض همواربودن توسعه داده شده است. تفکیک نقاط تقاطع منیفلدها از سایر نقاط بر مبنای رفتار متمایز لاپلاسین تابع هموار روی هر منیفلد در نقاط داخلی نسبت به سایر نقاط صورت می‌گیرد. آزمایش‌ها نشان‌دهنده دقت خوب روش پیشنهادی نسبت به روش‌های مشابه است.
Semi-supervised metric learning has attracted increasing interest in recent years. They enforce smoothness label assumption on the manifold. However, they suffer from two challenges: (1) since data in each class lies on one manifold and the similarity between classes leads the intersection between manifolds, the smoothness assumption on the manifold is violated in intersecting regions. (2) 1NN classifier, which is applied for predicting the label of classes in metric learning methods, is suffered from the rare of labeled data and has not suitable accuracy. In this paper, a novel method for learning semi-supervised metric in the stratified space has been proposed that exploit the prior knowledge, which is the smoothness assumption on each manifold, more accurate than existing methods. In the metric learning stage, it doesn’t apply smoothness assumption on the intersecting regions and in the classification stage, labeled data in the interior regions of manifolds are extended based on the smoothness assumption. The different behavior of the Laplacian of piecewise smooth function on stratified space is exploited for the distinction of the intersecting regions from interior regions of manifolds. The results of experiments verify the improvement of the classification accuracy of the proposed method in the comparison with other methods.
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