The　recent　advances　of　compressive　sensing　(CS)　have　witnessed　a　great　potential　of　efficient　compressive　data　gathering　(CDG)　in　wireless　sensor　network　systems　(WSNSs).　However,　most　existing　work　on　CDG　mainly　focuses　on　multihop　relaying　strategies　to　improve　the　performance　of　data　gathering.　In　this　paper,　we　propose　a　mobile　CDG　scheme　including　a　random　walk-based　algorithm　and　a　kernel-based　method　for　sparsifying　sensory　data　from　irregular　deployments.　The　proposed　scheme　allows　a　mobile　collector　to　harvest　data　by　sequentially　visiting　a　number　of　nodes　along　a　random　path.　More　importantly,　toward　building　the　gap　between　CS　and　machine　learning　theories,　we　explore　a　theoretical　foundation　for　understanding　the　feasibility　of　the　proposed　scheme.　We　prove　that　the　CS　matrices,　constructed　from　the　proposed　random　walk　algorithm　combined　with　a　kernel-based　sparsity　basis,　satisfy　the　restricted　isometry　property.　Particularly,　we　also　show　that　m　=　O(k　log(n/k))　measurements　collected　by　a　mobile　collector　are　sufficient　to　recover　a　k-sparse　signal　and　t　=　O(k　log(n/k))　steps　are　required　to　collect　these　measurements　in　a　network　with　n　nodes.　Finally,　we　also　present　extensive　numerical　results　to　validate　the　effectiveness　of　the　proposed　scheme　by　evaluating　the　performance　in　terms　of　energy　consumption　and　the　impact　of　packet　losses.　The　numerical　results　demonstrate　that　the　proposed　scheme　is　able　to　not　only　significantly　reduce　communication　cost　but　also　combat　unreliable　wireless　links　under　various　packet　losses　compared　to　the　state-of-　the-art　schemes,　which　provides　an　efficient　alternative　to　data　relaying　approaches　for　CDG　in　WSNS.